thermal separation processes

Principles of Thermal Separation Processes Thermal Separation Process Modes 7 Mass Balance, Energy Balance, Exergy Balance 8 Mass, Energy and Heat Balances The Nernst Distribution Law 19

Klaus Sattler, Hans Jacob Feindt

Thermal

Separation Processes

0 VCH Vcrlagsgescllschaft mbH, D-60451 Wcinheim (Federal Rcpuhlic ot Germany) IWS

Distribution:

VCH, P 0 Box 10 1161 D-69451 Weinheim Federal Kcpublic of Germany

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ISBN 3-527-28622-5

Klaus Sattler, Hans Jacob Feindt

Thermal

Principles and Design

Weinheim - New York

Base1 - Cambridge - Tokyo

Prof Dipl.-Ing Klaus Sattler

Fachhochschule fur Technik

This book was carefullyproduced Nevertheless, authors and publisher donotwarrant the information contai- ned therein to be free of errors Readers are advised to keep in mind that statements, data, illustrations, proce- dural details or other items may inadvertently be inaccurate

Published jointly by

VCH Verlagsgesellschaft Weinheim (Federal Republic of Germany)

VCH Publishers New York NY (USA)

Editorial Directors: Philomena Ryan-Bugler, Louise Elsam, Karin Sora

Production Manager: Claudia Gross1

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A catalogue record for this book is available from the British Library

Die Deutsche Bibliothek - CIP-Einheitsaufnahme

Sattler, Klaus:

Thermal separation processes : principles and design /

Klaus Sattlcr ; Hans Jacob Feindt - 1 ed -

Wcinhcim ; Ncw York ; Bascl ; Cambridge ; Tokyo : VCH, 1995

ISBN 3-527-28622-5 (Weinheim )

N E : Feindt, Hans Jacob:

0 VCH Verlagsgesellschaft mbH, D-69451 Wcinhcim (Federal Rcpublie of Germany), 1995

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Foreword

tions into their components and the drying

in the chemical, petroleum, food, and phar-

maceutical industries As environmental

protection has become an increasingly im-

portant consideration to industry, separa-

tion processes have become more important

in direct proportion

This book provides a clear fundamental

tant separation processes As indicated by

the title the book deals with separation pro-

cesses in which heat is an input to the com-

plete process of separating the constituents

of a mixture The flow of heat in the pro-

cess is clear in distillation, crystallization

tion, extraction and adsorption, where the

heat flow is required to regenerate the sol-

vent or adsorbent

Each of these six subjects is given thorough coverage in its own chapter These chapters follow a comprehensive develop- ment of the physical chemistry and engineer- ing which provide the principles upon which the separation processes are based The in- dividual process treatments cover computa- tional algorithms, equipment design criteria and energy conservation The overall treat- ment permits the evaluation of competing

optimal process

This book is intended as a college or

university level text for students in chemical engineering and related fields It is also com- plete enough and detailed enough in its development of each topic to be useful as a reference for practicing engineers both new

to and experienced in the area of separations CCNY, New York

Preface

This book, transformed from the original

two German editions “Thermische Trenn-

They have been successfully used as text-

books for university and college students

and as reference texts in seminars and train-

ing programs for practising engineers in

Germany, Austria and Switzerland

The book presents a clear and very prac-

tice-oriented overview of thermal separa-

tion technologies An extensive introduc-

tion elucidates the physical, physico-chemi-

cal, and chemical engineering fundamentals

and principles of the different unit opera-

tions used to separate homogenous gaseous

and liquid mixtures The introduction is fol-

tory figures and tables referring to process

and basic design, flow-sheets, basic en-

gineering and examples for the application

of the unit operations distillation, absorp-

tion, adsorption, drying, liquid-liquid and

solid-liquid extraction, evaporation and

crystallization of solutions, melt crystalliza-

tion and desublimation A comprehensive

reference list allows follow up of special

separation problems

The book enables the reader to choose

and evaluate thermal separation processes

and to model and design the necessary sep-

aration plant equipment

Chemical and mechanical engineers, chemists, physisists, bio-technologists in research and development, plant design, production, environmental protection and administration and students in engineering and natural sciences will find this treat- ment of exceptional value and practical use

Due to the quantity of the topics covered exercises could not be included in this book An additional collection of illustra- tions with reference to basic engineering and design of the necessary equipment of thermal separation units is available in

fahren Aufgaben und Liisungen, Ausle- gungsbeispiele) and will be translated into the English language

We are very much obliged to Prof

H Weinstein, City University of New York for his advice and his Foreword to this book Many thanks are also given to Philomena Ryan-Bugler, Louise Elsam, Karin Sora and the production team of VCH Verlagsgesellschaft for the accurate lectorship and book production Special thanks are also given to Paul Fursey,

for his assistance in copy-editing

Principles of Thermal Separation Processes

Thermal Separation Process Modes 7

Mass Balance, Energy Balance, Exergy Balance 8

Mass, Energy and Heat Balances

The Nernst Distribution Law 19

Representation of Liquid-Liquid Phase Equilibrium 23 Vapor-Liquid Equilibrium 28

One Component Systems 28

Two and Multicomponent Systems 30

Henry’s Law, Gas Solubility 44

Boiling Equilibrium of a Solid Solution, Decrease of

Vapor Pressure and Increase of Boiling Point 51

Gas-Solid Phase Equilibrium 52

Gas-Solid Phase Equilibrium, Sublimation 52

Gas-Solid Phase Equilibrium with Adsorption/Desorption and Convective Solid Drying (Adsorption Equilibrium) 54

Liquid-Solid Phase Equilibrium 60

Solubility of Solids in Liquid Solvents 60

Melting Pressure Curve 62

Decrease in the Freezing Point

Equilibrium 65

Separation Factor and Relative Volatility 67

Minimum Separation Work 67

1

8

63

Mass Transfer Fundamentals 68

Mass Transfer by Molecular Diffusion 69

Steady-State Diffusion 69

Unsteady-State Diffusion 70

Diffusion Coefficient 70

Mass Transfer by Convection 72

Overall Mass Transfer 74

Two Film Theory, Mass Transfer Coefficient and Turbulence Theory Steady-State Cocurrent Operation 77

Steady-State Countercurrent Operation 79

Theory of Separation Stages 79

Method to Determine the Number of Theoretical Separation Stages for a Countercurrent Column 82

Calculation for Counterflow Columns 86

Mass Balances 89

Phase Equilibrium Relationship 89

Enthalpy Balances 89

Stoichiometric Conditions for the Sum of the Concentration

at Each Equilibrium Stage 90

Two-Directional Mass Transfer Between Phases 91

One-Directional Mass Transfer 92

Steady-State Crossflow Operation 94

General Procedure to Design Equipment for the Thermal Separation

of Mixtures 94

75

Distillation and Partial Condensation 101

Concepts of Simple Distillation, Rectification and

Partial Condensation 101

Discontinuously and Continuously Operated Simple Distillation,

Flash Distillation 103

Discontinuously Operated Simple Distillation 103

Continuously Operated Simple Distillation 107

Heat Requirement of Simple Distillation Units

Flash Distillation 111

Carrier Distillation 113

Vacuum and Molecular Distillation 116

Countercurrent Distillation (Rectification) 119

Process Variations of Rectification 119

Continuously Operated Rectification in Rectification Columns

with Enriching and Stripping Zones

Stripping (Exhausting) Column 120

109

119

Combinations of Different Variations 123

Rectification with an Entrainer 123

Heteroazeotropic Rectification 129

Two Pressure Operation 130

Diffusion Distillation 131

Continuous Adiabatic Rectification 134

Flow Rates 135

Energy Saving Steps 138

Determination of the Number of Separation Stages and Column

Height for Heat and Mass Transfer

Minimum Reflux Ratio, Optimal Economic Reflux Ratio 157

Feed Stage 157

Discontinuous Adiabatic Rectification 158

Amount of Overhead Product 160

Heat Requirement 161

Still Diameter, Free Vapor Space, Column Diameter

McCabe-Thiele Method to Determine the Number of Theoretical Separation Stages 163

Semicontinuous Adiabatic Rectification 163

Internals in Rectification Columns 165

Column Trays 167

Random Packing, Packing with Regular Geometry 196

Choice, Optimization and Control of Rectification Units 216

Rectification Units Accessories 218

Parallel Flow Distillation 222

Principle of Absorption and Desorption, Processes and Process

Examples 239

Requirements of the Wash Liquid or Solvent, Solvent Consumption 243

Determination of the Column Cross-Sectional Area 248

Determination of the Number of Stages and Column Height for Mass and Heat Transfer 250

Processes and Examples 282

Adsorbents, Selection of Adsorbent 291

Adsorbents 291

Requirements for the Adsorbent, Adsorbent Selection

Technical Adsorbents, Characteristic Data of Adsorbents 293

Adsorption Kinetics 293

Variation of Adsorption, Design of Adsorbers 301

Multistage Adsorption with Cross Flow of Gas and

Concepts, Processes and Examples 317

Characteristics of the Moist Product, Movement of Moisture

Mass and Heat Transfer in Convection Drying 331

Drying Kinetics, Course of Drying, Drying Time

Convection Drying 340

Drying Gas and Heat Requirements in Convection Drying 340

Steps in Energy Saving 343

Variations of Convection Drying 346

Overview of Dryers, Dryer Selection and Design 357

Individual Presentation of Selected Dryer Types with Design Aids 363 Chamber Dryer 363

Tunnel Dryer 364

Belt Dryer 364

Multiple Plate Dryer 364

Rotary Dryer 364

Fluidized Bed Dryer 366

Air-Flow Dryer, Pneumatic (Flash) Dryer 374

Spray Dryer 377

Drum Dryer 381

Thin Film Evaporation Dryer

(Vertical and Horizontal Dryer) 381

Fields of Application and Process Examples

Liquid-Liquid Extraction Variations 400

Single Stage Extraction 400

Differential Stagewise Extraction 403

Multistage Cross-Current Extraction 403

Multistage Countercurrent Extraction 407

Countercurrent Extraction with Extract Reflux 421

Countercurrent Distribution 424

Mixer-Settler, Mixer-Settler Cascade 425

Countercurrent Columns with and without Energy Supply 426

Selection and Design of Extraction Apparatus 456

395

Solvent Evaporation, Crystallization 475

Basic Concept and Processing Modes of Crystallization

Solution Evaporation with Mechanical and Thermal Vapor

Types of Evaporators to Concentrate Solutions 500

Balancing of Crystallizers 500

Crystallization Kinetics, Crystal Seed Formation, Crystal Growth 508

Frequently Used Nomenclature

Vapor; vapor flow rate

Enrichment ratio, stage efficiency factor

Force

Loading factor for column trays

Feed; feed flow rate

Free internal energy

Gas; gas flow rate

Free enthalpy, Gibbs free energy

Enthalpy

Height equivalent to one theoretical stage

Height of a transfer unit

Phase equilibrium constant, distribution coefficient

Liquid; liquid flow rate

Characteristic length

Molar mass

Number of stages

Number of transfer units

Heat; heat flow rate

Reflux; reflux flow rate

N m/s v m = 1/pa

kg, kmol; kg/h, kmol/h

kJ

kg, kmol; kg/h, kmol/h

m

kg/kmol

kg, kmol; kg/h, kmol/h

kJ/(kmol + K)

k J/K

XVI Frequently Used Nomenclature

kJ

heavy phase (moles i/moles inert, kg i/kg carrier

Ratio or loading of key component in vapor or

light phase (moles i/moles inert, kg i/kg carrier

Ah, A& Latent heat

rn, m Mass; mass flow rate

kJ/kg, kJ/kmol kJ/kg, kJ/kmol kJ/kg, kJ/kmol

m/h kg; kg/h kmol; kmol/h bar, Pa bar, Pa

Frequently Used Nomenclature XVII

Po, i

Mean residence time

Specific internal energy

Velocity

Molar fraction, heavy phase

Molar fraction, light phase

Variable distance length or height

Tray spacing

Separation factor

Heat transfer coefficient

Mass transfer coefficient

Activity coefficient

Film thickness, layer thickness

Porosity, void fraction of a bed of solids,

kJ/(kg K),

m

- W/(m2 K) m/h

XVIII Frequently Used Nomenclature

-

Basic Concepts

1.1 Principles of

Thermal Separation Processes

are produced by the chemical and physical

conversion of raw materials or intermediate

products The production unit is a com-

pletely integrated technical operating unit

on the site It is connected with other units

on the site by transportation and personnel

routes, and pipelines for raw materials, aux-

iliary substances, products, utilities, and en-

ergy It usually consists of the actual pro-

duction unit and several off-site facilities, as

shown in Fig 1-1

The main unit contains the unitprocesses

and operations, such as separation, combi-

nation, division, formulation, heat trans-

fer, conveying, storage, packing Figure 1-2

shows a general set-up which is independent

from the type of process The combination

of unit processes and operations with re-

spect to product properties depends on the

product produced

During the chemical conversion of raw

materials, homogeneous and heterogeneous

mixtures (Figs 1-2 and 1-3) are generated

Both reactants and products may be found

in these mixtures, according to the yield

and conversion of the chemical reaction

By means of thermal separation processes

these mixtures must be treated to obtain the

desired products to a demanded purity and

to enable the raw materials to be recycled

Processes to separate physically homo-

geneous (one phase) and heterogeneous

(two or multiphase) mixtures are listed in

Table 1-1 The driving force of the separa-

tion process usually forms the criteria for the separation Homogeneous mixtures with a molecularly dispersed distribution of individual components may only be sepa-

cess

Thermal separation processes are mass transfer operations, driven by molecular forces Mass, and often heat, is exchanged between at least two phases of different composition The phases are the mixture phase(s) and a selective auxiliary phase The auxiliary phase is generated by either add- ing heat and/or by means of an auxiliary substance The required driving forces, con- centration, and temperature gradients, are formed due to the auxiliary phase

In Fig 1-4 thermal separation processes are listed and are denoted by the phases contributing to mass transfer in Table 1-2 Thermal separations of mixtures are car- ried out in the following individual steps :

by supplying energy to the system, or by adding an auxiliary component

heat, is exchanged between phases This

is achieved by the addition or removal of energy

- Step 3 : After completion of the inter-

change process, the phases are separated Together with the separation of the

ture occurs

All thermal separation processes follow

thermal separation processes are now for- mulated and will be discussed in detail

Thermal Separation Processes: Principles and Design

Klaus Sattler, Hans Jacob Feindt copyright 0 VCH Verlagsgesellschaft mhH, 1995

Process consisting of physical and chemical unit operations to

produce desired products

Off-sites, auxiliary equipment

- process control of the main plant

control room sometimes with a process control computer, control devices for drives, production lab, instrument air sta- tion

- supply of energy to main plant, generation and distribution

of electrical power, heating system for heating media such as hot water, steam, dyphil, salt melts

- provision of auxiliary materials (adjuvants) such as heat

transfer media, coolants, catalysts, solvents, inerts

- storage of raw and auxiliary materials, and products, spare

parts, tools and materials for repair work and maintenance

~~

~~~ ~_~

- transport to the process unit of the raw material and auxiliary

materials, transport of the products (roads, rail connections, harbor)

- disposal

treatment of waste gas and wastewater, reprocessing of solid residue and waste disposal

- facilities for the operating personnel

Fig 1-1 General production process set-up

Excess energy

*

Main products

~ Path of raw material or product

Fig 1-2 Basic flow chart for the

main part of a production plant

1.1 Principles of Thermal Separation Processes

Phases in Cocurrent Flow

Phases in Countercurrent Flow

Phases taking place in mass and heat trans- Phases taking place in mass and heat trans- fer are guided in cocurrent flow through the fer are guided in countercurrent flow separation apparatus The maximum effi- through the separation apparatus In this

same as that for a single theoretical separa- with the aid of internals, thereby achieving

I Counterflow liquid-liquid extraction ~ Cristallization from a solution

Drying Fractionating,

Principle of classification

r - - - l

,_ - - _, Simple phase transfomiation

t) fractionating Auxiliary product: required for separation tf not required tor separation

Fig 1-4 Summary of thermal separation processes

4 1 Basic Concepts

Table 1-1 Summary of separation processes

Classes of Driving force Nature of Separation processes

separation of separation mixture

Pressure Electrical field Concentration gradient

Electrical field

Magnetic field

Concentration gradient Temperature gradient

Heterogeneous

Heterogeneous Homogeneous

Sedimentation (s - 1) Filtration (s - 1)

Pressing (s - I)

Centrifugation (s - 1) Hydrocyclone separation (s - 1)

Classification Sieving (s - s)

Air classification (s - g) Hydraulic classification (s - 1) Ultrafiltration (s - 1)

Reverse osmosis (hyperfiltration) (s - 1) Dialysis (s - 1)

Electrodialysis (s - 1) Electrophoresis ( s - 1) Permeation (1 - 1, g - g)

Gas diffusion (g - g) Electro osmosis (s - 1) Electrical dust removal (s - g) Magnetic separation (s - s)

Distillation (1 - 1)

partial condensation (g - g) Absorption (g - g), (A) Adsorption (g - g, s - I), (A)

Chromatography (g - g, 1 - 1)

Extraction (s - s, 1 - I), (A)

Sublimation (g - g) Crystallization ( s - 1, 1 - 1) Drying (s - 1)

Thermal diffusion (g - g, 1 - 1)

~

Abbreviations: s solid, 1 liquid, g gas to characterize the state of the components of the mixture to

be separated, (A) thermal separation process with auxilliary component

maximum possible interfacial area (phase

boundary) for mass transfer is obtained

and, hence, the highest possible mass trans-

fer coefficient values Figure 1-5 shows a

“separation column” with stages connected

mixture is exchanged from the heavy phase

to the light phase Both phases may contain all components of the mixture

A closer inspection of stage n shows that

is in contact with the light phase with a

1.1 Principles of Thermal Separation Processes 5

Table 1-2 Characteristics of thermal separation processes by the phases in which mass and heat

transfer occurs

~~

Liquid-liquid extraction Crystallization from a melt

Thermal diffusion Thermal diffusion

-

Concen- tration

of solutions

-

~

Gas drying

Crystal- lization from a solution

~~

Absorption Desorption by stripping Adsorption Drying

Solid-liquid extraction (leaching) Adsortpion

Abbreviations: g gas phase, 1 liquid phase, s solid phase

not phase equilibrium concentrations, the

librium, and mass and heat transfer take

riched in the light phase up to a final con-

centration y,, while the heavy phase is re-

duced in component i from x,, to x , - ~

With stage n as a theoretical separation

stage, the leaving phases are in equilibrium

sible Therefore, y, and x , - ~ are phase

equilibrium concentrations

The heavy phase, with concentration

x,, - arrives at stage n - 1 and comes into

contact with the light phase, with concen-

tration y n P 2 An exchange, similar to that

in stage n, takes place

The discussed example shows that for countercurrent phase flow, single stages are connected in series in one separation appa- ratus The light phase leaving a stage is guided to the following stage whereas the heavy phase is guided to the previous stage

ration apparatus where mass or heat trans- fer take place in which entering phases are not in phase equilibrium, while the leaving phases have reached phase equilibrium (see

Chapter 1.4)

In a practical separation stage, equilib- rium is often not achieved The efficiency

6 1 Basic Concepts

L-l -r

only locally valid or constant across the cross section of the column

Phases in Cross Flow

(Cross Flow Principle) Phases taking part in mass and heat trans- fer flow across through the separation ap- paratus at an angle of 90" to each other The separation efficiency depends on the equilibrium location and the ratio of the phase fluxes, but is often low in an individ- ual separation stage To separate a mixture

Fig 1-5 Countercurrent flow of two phases in a

and obtain pure products, several separa-

separation apparatus

n - 1, n Stages connected in series tion stages are connected in series This is

LP Upflowing light phase done most effectively with countercurrent

HP Downflowing heavy phase phase flow Phase cross flow and parallel

stages are sometimes used However, cocur-

Molar fraction of the key component in

the heavy phase

Molar fraction of the key component in

the light phase

compared with a theoretical stage is ex-

pressed as the stage efficiency factor, E (ex-

efficiency) (Fig 1-5):

~i~~ Requirement

The time needed to separate a mixture in a discontinuous operation is the effective resi- dence time For continuous operation, it is

in the separation apparatus:

of the key component in the

rium concentration at x, -

y, - y n p 1 actual enrichment of the key

component in the light phase

This often has to be distinguished as a local

transfer ratio, as opposed to an overall

ration apparatus (determined by the volume of the apparatus and the degree

of filling) effective volumetric flow of the mixture Short-, medium- and long-term separation processes can be distinguished depending

on the time requirement:

1.2 Thermal Separation Process Modes 7

- Short-term processes (t, < 30 sec)

Examples: Spray drying, gas adsorption,

precipitation crystallization

- Medium-term processes (30 sec< t, < 2h)

Examples: Absorption, rectification, drum

drying, pneumatic-conveyor drying, sub-

limation, extraction, crystallization, liq-

uid adsorption

tumbling drying, vacuum freeze drying,

persing, pulsing, stirring and pump cir- culation devices

- Work, to operate peripheral machines

such as compressors and vacuum pumps

1.2 Thermal Separation Process Modes

Apparatus for the thermal separation of

tinuously (intermittently, batch production,

(steady-state) In the following section, the operating modes are briefly illustrated The

For the thermal separation of a mixture in

an apparatus, energy has to be supplied in

the form of:

flowing masses and to supply latent heat

advantages and disadvantages are listed in Table 1-3

Table 1-3 Comparison of continuous and discontinuous operation to achieve the same separation problem

Mathematical description of the separation process,

modeling

Investment cost of separation unit

Operating cost of separation unit

Operation of separation unit

Automatic control of separation process

Environmental pollution, possibility of accident

Operation reliability, flexibility in the case of breakdown

of separation unit parts, safety buffer

Flexibility to adjust to other mixtures to be separated

Simpler Less Less Easier Possible with less expense Less Less

Higher Better

8 1 Basic Concepts

eration the mixture being separated is con-

tinuously fed to the separation device It is

continuously separated into two or more

fractions, which are continuously with-

drawn from the separation device

An ideal binary mixture can be separated

into almost pure components in a separa-

tion column operated continuously with

in series are needed

Discontinuous Operation: With discontin-

uous operation the mixture being separated

is charged to the separation device During

a time period, the “batch period”, the mix-

ture is separated mainly into two fractions

of defined different compositions One

fraction is continuously withdrawn from

the separation device, while the other re-

mains in the device and is withdrawn at the

end of the batch time

separation of a mixture; the obtained frac-

tions are treated in subsequent stages (this is

the case for multistage discontinuous sepa-

ration)

Alternating Operation : If in a separation

apparatus after a loading process (separa-

tion of a mixture) an unloading process (the

tion) is required, at least two sets of equip-

ment are operated alternately Therefore,

steady separation of the mixture is guaran-

teed

In the case of the adsorption of a sub-

sorber (see Chapter 4), for example, a solid

f s u m of amount) f sum of amount )

adsorbent adsorbes adsorbate (key compo- nent in the gas phase) Adsorption contin- ues to an upper loading limit After the maximum load has been reached in the first adsorber, operation is switched to the sec- ond adsorber The loaded adsorber is then regenerated by dampening, drying and cooling After the regeneration cycle is fin-

again

1.3 Mass Balance, Energy Balance, Exergy Balance

In general, the first step in the design of a separation plant is the balancing of individ- ual apparatuses and parts of the plant Bal- ances are done with respect to energy and mass fluxes, in connection with a schematic representation of the process (flow dia- gram)

1.3.1 Mass, Energy and Heat Balances

The balancing of chemical engineering sys- tems follows the sequence listed in Fig 1-6

Of the variables listed for process design,

heat, enthalpy, and exergy) are of most in- terest These variables may also be used for

and synthesis

Based on the laws of conservation of mass, energy and momentum, balance equations are set up [1.1] - [1.5] For a gen- eral open system

f s u m of amount) f increase of \

entering generated in leaving mass stored

-k 1 in the system (transport) (transformation) (transport) (accumulation)

[ the system + [ the system = 1 the system

1.3 Mass Balance, Energy Balance, Exergy Balance 9

interest in a quantitative form

Determination of the balance size of measured or valuable system properties

(total mass, component mass, atomic mass;

state variables such as enthalpy, entropy; momentum; cost)

Process description 4l Formulation of balance eauation to obtain a list of all balance variables of 1

Fig 1-6 Balancing of processes (schematic simplification of the concepts) [1.1]

tegral or differential balance equation is

generated :

0 Differential, to investigate a process in a

differential volume element or at an in-

terfacial surface element

0 Integral to determine the streams enter- ing and leaving the system

Differential balance equations lead to ve- locity, concentration, and temperature pro-

faces, after solving the corresponding diffe- rential equation system with suitable bound-

10 1 Basic Concepts

ary conditions Integral balance equations

give a basis for evaluation of the total sys-

tem with respect to energy and mass

Results of integral balance equations are

often presented in a table or in a flowchart

(product and energy scheme, mass and heat

flowchart, etc.)

Mass Balance

Material balances (mass or quantity bal-

ances) can be general or total material bal-

ances over the complete system and must be

distinguished from material balances for in-

ing the terms in Fig 1-7, for an open system

the general integral balance equation is

c mi,a + mQ = c + m, (1-3)

and withdrawal of material without start up

and shut down procedures) the accumula-

rfzp ms, IjzQ,k, ms,k intensity of sources (Q)

balance area generally with respect to compo-

1.3 Mass Balance, Energy Balance, Exergy Balance 11

metric ratio of k in the reaction j

Instead of mass and mass fractions, it is convenient to use another kind of substance flow or concentration units to set up mate- rial balance equations Useful conversion relationships are given in Table 1.4

d n k

Vj,k * I/ dt

is the equivalent reaction rate of the reac-

tion j , V is the volume of reaction mass in

Table 1-4 Conversion between concentration scales of a mixture component

I) Reference is the mass of the remaining mix-

ture excluding component i, expressed as carrier

n

') Molar ratio carrier load X i = _f

Used variables:

mi

ni

mass of mixture component i

number of moles of mixture component i

c i mi

c mi total mass of the mixture

c ni total number of moles of the mixture

i

i

12 1 Basic Concepts

For a complete mass balance over a bal-

ance area at steady-state, in which only

physical transformation of matter occurs,

an equilibrium system consisting of Eq

(1-3) and k - 1 equations (1-4) for k active

components over the balance area, must be

set up Due to the valid stoichiometric con-

equation (1-4) gives

c w k = l

Ways to formulate material balances for

differential volume elements as the balance

area, and methods to solve this differential

equation system may be found in, for exam-

ple [1.1] and [1.3]

Energy and Heat Balances

Based on the law of conservation of energy,

an energy balance analogous to the material

balance may be set up for any bounded bal-

ance area Using the terms from Fig 1-7 for

the energetic and materialistic open system,

Ea+ c Ei,a + EQ = E, + c Ei,, + Es (1-8)

where

potential and kinetic energy, bind-

ing energy, heat

energy flow through the system

Ei,, energy supplied or removed by the

mass flux mi

intensity of the heat sources or

sinks inside the balance area

E,,E,

E p E s

In process design, a heat balance is often

sufficient From the first law of thermody-

namics, for the balance area in Fig 1-7, the

I

(1-9)

I

where

entering and leaving additional heat flow supplied heat flow lost

intensity of heat sources (Q) and

sinks ( S ) in the balance area

Q

Qu

QQ, Qs

dothermic nature of phase transformations and chemical reactions under steady-state conditions If, for example, over the balance area, chemical reactions involving compo-

AhR the total reaction enthalpy for com-

ponent k (ALR > 0 for endothermic

reactions, Ah;, < 0 for exothermic reaction)

1.3 Mass Balance, Energy Balance, Exergy Balance 13

getic and exergetic process analyses are

used Since exergetidanergetic flowcharts

show local internal and external irrever-

sibilities, the locations and quantities of

heat losses may be detected, leading to ther-

modynamic optimization from the consid-

eration of process energy improvements

According to Fig 1-7 the exergy balance

equation, for a steady-state open system,

under isobaric conditions, is

exergy of input Ea and output

exergy of input Yizi,a and out-

G; = Yiz; * [(hi - h,) - T, (s; - s,)] (1-12)

AG,

entropy

temperature, enthalpy and en-

tropy, referred to surrounding

conditions or to a particular sys-

tem state reference

exergy losses due to irrever-

sibilities

1.3.3 Calculation of Balance Equations

Calculation of mass, energy and exergy bal- ances for the total separation plant are usu- ally done sequentially from apparatus to apparatus They are occasionally carried out simultaneously by an iterative method, considering the corresponding equation system for the total separation process In this case, it is necessary to develop a calcu- lation flowchart with coded interface and ramification The process structure is con- veniently presented graphically After math- ematical formulation of the process, the number and values of the independent sys- tem variables are determined Finally, the balance equations are solved sequentially

gramming system is required The main program controls and organizes by assign- ing priorities to the calculations via refer- ences to the corresponding process steps, mass fluxes, and computation parameters

It organizes the intermediate storage of cal- culated mass fluxes and state variables, and transfers these as input variables to the fol- lowing stages Initial variables for each stage are calculated in subroutines, based

on stage specific theoretical and empirical models By including the graphical methods

in the balance, economic optimization by, for example, minimizing the energy flow [1.17] or optimization with respect to com- plete safe operation of the process can be performed [1.18]

It is often convenient to present the re-

More information on energetic and ex- and, if necessary, for combined processes ergetic analysis can be found in the litera- They can be quickly understood in clearly

rectification unit is given as an example in

[1.10]

(1-13)

14 1 Basic Concepts

1.4 Phase Equilibria - Phase: A physically homogeneous region

boundary Each volume element in one

1.4.1 Basic Concepts phase has identical macroscopic proper- ties The change of state variables, i e.,

temperature, pressure, composition, etc., are continuous and time independent

phase consisting of homogeneous mat- ter, which is scattered in space, and dis- persed in the continuum of the other mainly coherent phase

ally in open systems, an exchange of heat

and mass occurs at the phase interface

When phase equilibrium is reached, no fur-

ther heat or mass transfer takes place Basic

concepts and equations are now introduced

[1.20], in order to describe phase equilibria:

of matter that is separated from its sur-

equivocally and completely described by

thermodynamic, macroscopic state vari-

ables

in which matter and/or energy may

transfer with the surroundings, through

the boundaries

tems in which only energy may be ex-

changed with the surroundings The sys-

tem is closed, containing constant mass,

but is not isolated

heat or mass transfer with the surround-

ings takes place, although exchange of

energy in other forms, e.g., shaft work,

is possible

energy or matter occurs with the sur-

roundings

systems with identical macroscopic prop-

erties in each volume element

phase systems with at least one abrupt

change in macroscopic properties at the

boundar(y/ies) between the phases

dispersed phase

namicpotential), G : The relationship be-

For a closed system (constant mass or for

a pure phase), the total differential for the free enthalpy dG is

For a reversible change of state it follows

1.4 Phase Equilibria 15

With constant mass, the free enthalpy is

ture

Comparison of the coefficients in

Eq (1-15) and (1-18) gives:

(g)p= - S and (5) = V (1-19)

T

For an open system, the free enthalpy is

not only a function of pressure and temper-

ature, but also a function of the amount of

mass n of each individual component

By integrating this equation under the as- sumption of constant pressure and temper-

a definite dependency on the composition and chemical potential of the components

of the mixed phases in the system

given by

d G = - S * d T + Vedp-t

or

(1-27)

different forms and is of fundamental sig- nificance in proving the consistency of precalculated or experimentally determined

For individual components the isothermal

and isobaric change of state is

of the individual components, we can write

the free enthalpy of a system, which con- sists of a mixture, if 1 mole of the mixture

of the mixture

Hence,

(1-28)

16 1 Basic Concepts

tial, i e., the chemical potential of the com-

is the same as for the standard state of a

pure gas component at the temperature and

pressure of the system For any component

of a liquid mixture, the standard state is the

same as the standard state of a pure liquid

component at the temperature and pressure

ing enthalpy A& is

A p i = i ? T ln(y,.xi) (1-30)

where yi - xi is the activity and yi is the ac-

tivity coefficient of the component i of the

mixture The activity coefficient here is de-

fined as

lim yi = 1

X,'l

(1-31)

Equilibrium: A system is at equilibrium if,

in fixed surrounding conditions, no change

on a macroscopic scale occurs in the sys-

tem Therefore, there is no tendency toward

an exchange of matter and energy between

the phases Exchanges of matter and energy

ogeneous system are reversible

The equilibrium between the phases (the

phase equilibrium) is sensitive to changes in

the surrounding conditions Compositions

of the phases at the desired phase equilib-

rium are independent of time, the amount

of material and the direction from which

equilibrium is reached

Equilibrium Conditions: Equilibrium be-

tween the phases of a heterogeneous system

is reached if the following conditions are

valid: no local pressure differences exist

equilibrium)

dp = 0 therefore p1 = prl = (1-32)

and no local temperature difference exists

equilibrium)

d T = 0 therefore T, = T,, = (1-33)

These two conditions meet the requirements

to describe an isolated system in a state of equilibrium The system is stable, when the system entropy reaches a maximum, hence

The equilibrium condition for a closed sys- tem may be derived from the fact that any infinitesimal change of state at equilibrium

is reversible For example, we have

or

d H = T - dSi- V* dp (1-36)

and isochoric change of state are given by,

free internal energy F, and the free enthalpy

G, must be at a minimum for a system to be

1.4 Phase Equilibria 17 chanical system where the potential energy

is a minimum at equilibrium

Combining Eq (1-21) and (1-28) gives

Knowledge of the distribution coefficient

as a function of pressure and temperature is essential for the design of thermal separa-

three steps:

d G = - S d T + V - d p + z p i d n i (1-41)

system is

cient yi Of each component in each

phase at a different temperature, pressure and composition, measured experimen-

correlation

At equilibrium, mass transfer between the

rial balance requires

dn,,, = -dni,,,

and so it follows that

- Step 2 : Determination of the differences

component under the same conditions (see Step 1)

- Step 3: Evaluation of KT or the equilib- rium relationship x ~ , ~ , = f (xi,,)

(1-43)

Therefore, phase equilibrium is reached

cal species in the system is the same in all

phases

11 using Eq, (1-291, (1-30) and (1-44) it fol-

1.4.1.1 General Differential Equation for the Equilibrium Between TWO Phases

The criterion for the equilibrium of two

phases is pi,, = pi,II or dp,,, - dpi,,, = 0 The general differential equation for the

coefficient” (%equilibrium constant’? K:,

giving

xi,II = KT * xi,, (1-46)

and the relationship

(1-47) with

(1 -49)

This relationship links the state variables of

tion xi of the component i in both phases I and 11 The enthalpy A ~ Z ~ , , , ~ , and the vol- ume AK,I,II are partial molar phase trans- fer quantities

The partial molar quantities of a binary mixture may be determined by graphical method if the appropriate quantities are

sition (Fig 1-8)

(1-50) Ahi,ii = Ah,,g the molar evaporation en-

rated vapor and liquid of the system components,

+ (1 - Xl) G,p

where q,, and 1/2,p are partial molar vol-

umes of components 1 and 2 of the mixture

ies between the limits 0 and 1

1.4.1.2 The Gibbs Phase Rule

The Gibbs phase rule describes how many

In Fig 1-8 the measured volume of the mix-

ture V is plotted against the molar fraction

curve gives the points D and E Points B

F the degrees of freedom of the system at

equilibrium (chosen from the state varia-

bles pressure, temperature, concentration

of each component in each phase); num-

ber of variables describing the state of

the system which may be varied inde-

pendently without disturbing the system

equilibrium

P number of phases of the heterogeneous

system (one gas phase, one or more liq-

according the number of crystal types)

number of components of the system

forming the phases which must be in-

dependently declared

F = 0 invariant system

F = 2 divariant system, etc

The phase rule is important for thermal

separation processes as, if certain process

parameters are choosen, it establishes

which state variables are cogently fixed at

an arbitrarily adjusted phase equilibrium

(Table 1-5)

1.4.2 Liquid-Liquid Equilibrium

1.4.2.1 The Nernst Distribution Law

For a dissolved substance S in two nonideal,

immiscible, liquid solvents such as T and L

at constant pressure and temperature the

distribution according to Eq (1-45) is

pas,, + R T ha,,, =

= pos,II + R T lnczs,II (1-56) where as is the activity of S For phase

equilibrium of two liquid phases, the stan- dard state of both phases is the same (nor- malized to pure liquid S) It follows that

as,1 = as,II or YS,I * *S,I = YSJI XS,H

(1-58)

To describe the concentration dependance

of the activity coefficients Y,,~ and Y , , ~ ~ , the computational methods shown in Table 1-8 may be used, for example the NRTL or UNIQUAC methods

For a substance S distributed in phase I (raffinate R) and phase I1 (extract E) with

a small concentration of cS,, and c ~ , ~ , the

Nernst Distribution Law is an approxima- tion given by

ratio appears in both phases It is indepen-

stant pressure, constant temperature and similar molecular forms in each phase For separation by liquid-liquid extrac- tion, the Nernst distribution law describes the equilibrium between raffinate and ex-

solvent component L are not miscible (see Chapter 6)

Table 1-6 shows additional variations of the Nernst distribution law

h )

0 phase rule the Gibb’s Examples of separation processes Selected thermal 1-5 Table

Thermal separation Phases

Components Degrees

Process Consequences for

the remaining

process

of parameters

2

Pressure, concen- Concentration of

the second compo-

(a)

5 concen- phase, the the liquid nent in one of tration liquids miscible binary

mixtures component, e.g.,

tration of both components

in the

vapor phase, and the

temperature are

variables describing the system

state,

c

Number Type Number Type

freedom explanations

component Gas absorption Gas adsorption

1 Pressure

Concentrations and temperatures are

(b)

strongly fixed,

no simple separation point diagram) possible (boiling

3

Pressure, tem- Concentration of

absorbate in the

(c)

perature, partial pressure of the isotherm)

absorbate in the

gas phase

perature, partial pressure

of

the tion isotherm)

absorbate in the

gas phase

liquid phase

is fixed (absorption

3

Pressure, tem- Fixed loading

of the component

(4 (adsorp- the absorbent adsorbed in

the key com-

(e)

extraction

Key

component perature, concen-

ponent in the raffinate remains, the

Solvent tration of

the concentration of

the extract phase is

key component

in phase the liquid fixed (distribution

equilibrium)

Table 1-5

(continued)

Thermal separation Phases

Components Degrees

Process Consequences for

the remaining variables describing parameters of process the system

state,

Number Type Number Type

freedom explanations

Convection drying

of nonhygroscopic products by hot gas

(I

Drying period) Hygroscopic product (11 Drying period)

vacuum crystallization

Vacuum sublimation

Dry product Moisture Dry gas

Dry product Moisture Dry gas

Components forming a mixed crystal

Dissolved substance Solvent

Dissolved substance Solvent

Components without mixed crystals load

Pressure Fixed saturation

loading of the

temperature product with

moisture (sorption isotherm and 2nd drying

period)

Pressure, tem- perature, partial pressure of the period)

moisture in the gas

Pressure, concen- tration

of

one

component in the liquidus lines)

liquid phase

Pressure Concentration of

the dissolved

temperature

Moisture content

of the product is

fixed (sorption isotherm, 1st

drying

Solid phase concentration and

the

temperature are fixed (solidus

and

substance fixed

by the solubility

curve

Pressure Boiling point

temperature of the

saturated solution

is strongly fixed

by the pressure (vapor-pressure

curve

of

the saturated solution)

Temperature Temperature determines

the vapor-

pressure

of

the sublimable com-

ponents, corresponding

to the

sublimation pressure curve

P ,

Abbreviations:

s

solid phase (solid),

1

liquid phase (liquid), g

gas phase (gas)

22 1 Basic Concepts

Table 1-6 Additional formulae of the Nernst distribution law Correlations and conversion relation-

ships for the distribution coefficient K

0 Mole fractions x, y are used as the concentration scales for the distributed substances S

111 Watedmethyl isobutyl ketone (4-methyl-2-pentanone)/acetone

Nomenclature used in Eqs (1-59) to

CS,R = molar concentration of S in molar concentration of the

substance S in the extract

number of moles of S in the

1.4 Phase Equilibria 23

mole fraction of the sub-

stance Sin the raffinate phase

mole fraction of the sub-

stance S in the extract phase

number of moles of extract or

number of moles of carrier

mole ratio S in the extract

A schematic distribution diagram for liq-

uid-liquid extraction is shown in Fig 1-9

The Y, X distribution diagram is essential

for the design of separation apparatus

1.4.2.2 Representation of Liquid-Liquid

Phase Equilibrium

Industrial extraction process systems with

three or four liquid components are com-

mon In addition to a vapor phase two or

X-

Fig 1-9 Schematic presentation of the liquid-

liquid phase equilibrium, the loading diagram

EC I Equilibrium curve with a constant dis- tribution coefficient

EC 11, Equilibrium curve for a concentration-

EC I11 dependent distribution coefficient

Mole ratio of S in the raffinate phase

three pairs of liquid phases are possible Now equilibrium of liquid-liquid phases for ternary systems will be discussed in more detail for cases where partial miscibility of carrier liquid and solvent cannot be ne- glected, and presentation by means of an equilibrium diagram similar to Fig 1-9 is insufficient

A practical way at constant temperature and pressure to graphically describe the data of phase equilibrium of a ternary sys- tem uses an equilateral triangle (Gibbs' tri- angle) Figure 1-10 shows an equilateral tri- angle representing a three component mix- ture Each apex of the triangle corresponds