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Coulson & Richardson’s

CHEMICAL ENGINEERING

VOLUME 6

Chemical Engineering, Volume 1, Sixth edition

Fluid Flow, Heat Transfer and Mass Transfer

J. M. Coulson and J. F. Richardson

with J. R. Backhurst and J. H. Harker

Chemical Engineering, Volume 2, Fifth edition

Particle Technology and Separation Processes

J. F. Richardson and J. H. Harker

with J. R. Backhurst

Chemical Engineering, Volume 3, Third edition

Chemical & Biochemical Reactors & Process Control

Edited by J. F. Richardson and D. G. Peacock

Chemical Engineering, Second edition

Solutions to the Problems in Volume 1

J. R. Backhurst and J. H. Harker with J. F. Richardson

Chemical Engineering, Solutions to the Problems

in Volumes 2 and 3

J. R. Backhurst and J. H. Harker with J. F. Richardson

Chemical Engineering, Volume 6, Fourth edition

Chemical Engineering Design

R. K. Sinnott

Coulson & Richardson’s

CHEMICAL ENGINEERING

VOLUME 6

FOURTH EDITION

Chemical Engineering Design

R. K. SINNOTT

AMSTERDAM ž BOSTON ž HEIDELBERG ž LONDON ž NEW YORK ž OXFORD

PARIS ž SAN DIEGO ž SAN FRANCISCO ž SINGAPORE ž SYDNEY ž TOKYO

Linacre House, Jordan Hill, Oxford OX2 8DP

30 Corporate Drive, MA 01803

First published 1983

Second edition 1993

Reprinted with corrections 1994

Reprinted with revisions 1996

Third edition 1999

Reprinted 2001, 2003

Fourth edition 2005

Copyright 1993, 1996, 1999, 2005 R. K. Sinnott. All rights reserved

The right of R. K. Sinnott to be identified as the author of this work

has been asserted in accordance with the Copyright, Designs and

Patents Act 1988

No part of this publication may be reproduced in any material form (including

photocopying or storing in any medium by electronic means and whether

or not transiently or incidentally to some other use of this publication) without

the written permission of the copyright holder except in accordance with the

provisions of the Copyright, Designs and Patents Act 1988 or under the terms of

a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road,

London, England W1T 4LP. Applications for the copyright holder’s written

permission to reproduce any part of this publication should be addressed

to the publisher

Permissions may be sought directly from Elsevier’s Science & Technology Rights

Department in Oxford, UK: phone: (C44) (0)1865 843830; fax: (C44) (0)1865 853333;

e-mail: permissions@elsevier.co.uk. You may also complete your request on-line via

the Elsevier homepage (http://www.elsevier.com), by selecting ‘Customer Support’

and then ‘Obtaining Permissions’

British Library Cataloguing in Publication Data

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

Library of Congress Cataloguing in Publication Data

A catalogue record for this book is available from the Library of Congress

ISBN 0 7506 6538 6

For information on all Elsevier Butterworth-Heinemann

publications visit our website at http://books.elsevier.com

Typeset by Laserwords Private Limited, Chennai, India

Contents

PREFACE TO FOURTH EDITION

xvii

PREFACE TO THIRD EDITION

xx

PREFACE TO SECOND EDITION

xxi

PREFACE TO FIRST EDITION

xxiii

SERIES EDITOR’S PREFACE

xxiv

ACKNOWLEDGEMENT

xxv

1

Introduction to Design

1

1.1

Introduction

1

1.2

Nature of design

1

1.2.1

The design objective (the need)

3

1.2.2

Data collection

3

1.2.3

Generation of possible design solutions

3

1.2.4

Selection

4

1.3

The anatomy of a chemical manufacturing process

5

1.3.1

Continuous and batch processes

7

1.4

The organisation of a chemical engineering project

7

1.5

Project documentation

10

1.6

Codes and standards

12

1.7

Factors of safety (design factors)

13

1.8

Systems of units

14

1.9

Degrees of freedom and design variables. The mathematical representation

of the design problem

15

1.9.1

Information flow and design variables

15

1.9.2

Selection of design variables

19

1.9.3

Information flow and the structure of design problems

20

1.10 Optimisation

24

1.10.1

General procedure

25

1.10.2

Simple models

25

1.10.3 Multiple variable problems

27

1.10.4

Linear programming

29

1.10.5

Dynamic programming

29

1.10.6

Optimisation of batch and semicontinuous processes

29

1.11 References

30

1.12 Nomenclature

31

1.13 Problems

32

2 Fundamentals of Material Balances

34

2.1

Introduction

34

2.2

The equivalence of mass and energy

34

2.3

Conservation of mass

34

2.4

Units used to express compositions

35

2.5

Stoichiometry

36

v

2.7

Choice of basis for calculations

40

2.8

Number of independent components

40

2.9

Constraints on flows and compositions

41

2.10 General algebraic method

42

2.11 Tie components

44

2.12 Excess reagent

46

2.13 Conversion and yield

47

2.14 Recycle processes

50

2.15 Purge

52

2.16 By-pass

53

2.17 Unsteady-state calculations

54

2.18 General procedure for material-balance problems

56

2.19 References (Further Reading)

57

2.20 Nomenclature

57

2.21 Problems

57

3 Fundamentals of Energy Balances (and Energy Utilisation)

60

3.1

Introduction

60

3.2

Conservation of energy

60

3.3

Forms of energy (per unit mass of material)

61

3.3.1

Potential energy

61

3.3.2

Kinetic energy

61

3.3.3

Internal energy

61

3.3.4

Work

61

3.3.5

Heat

62

3.3.6

Electrical energy

62

3.4

The energy balance

62

3.5

Calculation of specific enthalpy

67

3.6 Mean heat capacities

68

3.7

The effect of pressure on heat capacity

70

3.8

Enthalpy of mixtures

71

3.8.1

Integral heats of solution

72

3.9

Enthalpy-concentration diagrams

73

3.10 Heats of reaction

75

3.10.1

Effect of pressure on heats of reaction

77

3.11 Standard heats of formation

79

3.12 Heats of combustion

80

3.13 Compression and expansion of gases

81

3.13.1 Mollier diagrams

82

3.13.2

Polytropic compression and expansion

84

3.13.3 Multistage compressors

90

3.13.4

Electrical drives

93

3.14 Energy balance calculations

93

3.15 Unsteady state energy balances

99

3.16 Energy recovery

101

3.16.1

Heat exchange

101

3.16.2

Heat-exchanger networks

101

3.16.3 Waste-heat boilers

102

3.16.4

High-temperature reactors

103

3.16.5

Low-grade fuels

105

3.16.6

High-pressure process streams

107

3.16.7

Heat pumps

110

3.17 Process integration and pinch technology

111

3.17.1

Pinch technology

111

3.17.2

The problem table method

115

3.17.3

The heat exchanger network

117

3.17.4 Minimum number of exchangers

121

3.17.5

Threshold problems

123

3.17.7

Process integration: integration of other process operations

124

3.18 References

127

3.19 Nomenclature

128

3.20 Problems

130

4 Flow-sheeting

133

4.1

Introduction

133

4.2

Flow-sheet presentation

133

4.2.1

Block diagrams

134

4.2.2

Pictorial representation

134

4.2.3

Presentation of stream flow-rates

134

4.2.4

Information to be included

135

4.2.5

Layout

139

4.2.6

Precision of data

139

4.2.7

Basis of the calculation

140

4.2.8

Batch processes

140

4.2.9

Services (utilities)

140

4.2.10

Equipment identification

140

4.2.11

Computer aided drafting

140

4.3 Manual flow-sheet calculations

141

4.3.1

Basis for the flow-sheet calculations

142

4.3.2

Flow-sheet calculations on individual units

143

4.4

Computer-aided flow-sheeting

168

4.5

Full steady-state simulation programs

168

4.5.1

Information flow diagrams

171

4.6 Manual calculations with recycle streams

172

4.6.1

The split-fraction concept

172

4.6.2

Illustration of the method

176

4.6.3

Guide rules for estimating split-fraction coefficients

185

4.7

References

187

4.8

Nomenclature

188

4.9

Problems

188

5 Piping and Instrumentation

194

5.1

Introduction

194

5.2

The P and I diagram

194

5.2.1

Symbols and layout

195

5.2.2

Basic symbols

195

5.3

Valve selection

197

5.4

Pumps

199

5.4.1

Pump selection

199

5.4.2

Pressure drop in pipelines

201

5.4.3

Power requirements for pumping liquids

206

5.4.4

Characteristic curves for centrifugal pumps

208

5.4.5

System curve (operating line)

210

5.4.6

Net positive suction head (NPSH)

212

5.4.7

Pump and other shaft seals

213

5.5 Mechanical design of piping systems

216

5.5.1

Wall thickness: pipe schedule

216

5.5.2

Pipe supports

217

5.5.3

Pipe fittings

217

5.5.4

Pipe stressing

217

5.5.5

Layout and design

218

5.6

Pipe size selection

218

5.7

Control and instrumentation

227

5.7.1

Instruments

227

5.7.2

Instrumentation and control objectives

227

5.7.3

Automatic-control schemes

228

5.8.1

Level control

229

5.8.2

Pressure control

229

5.8.3

Flow control

229

5.8.4

Heat exchangers

230

5.8.5

Cascade control

231

5.8.6

Ratio control

231

5.8.7

Distillation column control

231

5.8.8

Reactor control

233

5.9

Alarms and safety trips, and interlocks

235

5.10 Computers and microprocessors in process control

236

5.11 References

238

5.12 Nomenclature

239

5.13 Problems

240

6 Costing and Project Evaluation

243

6.1

Introduction

243

6.2

Accuracy and purpose of capital cost estimates

243

6.3

Fixed and working capital

244

6.4

Cost escalation (inflation)

245

6.5

Rapid capital cost estimating methods

247

6.5.1

Historical costs

247

6.5.2

Step counting methods

249

6.6

The factorial method of cost estimation

250

6.6.1

Lang factors

251

6.6.2

Detailed factorial estimates

251

6.7

Estimation of purchased equipment costs

253

6.8

Summary of the factorial method

260

6.9

Operating costs

260

6.9.1

Estimation of operating costs

261

6.10 Economic evaluation of projects

270

6.10.1

Cash flow and cash-flow diagrams

270

6.10.2

Tax and depreciation

272

6.10.3

Discounted cash flow (time value of money)

272

6.10.4

Rate of return calculations

273

6.10.5

Discounted cash-flow rate of return (DCFRR)

273

6.10.6

Pay-back time

274

6.10.7

Allowing for inflation

274

6.10.8

Sensitivity analysis

274

6.10.9

Summary

275

6.11 Computer methods for costing and project evaluation

278

6.12 References

279

6.13 Nomenclature

279

6.14 Problems

280

7 Materials of Construction

284

7.1

Introduction

284

7.2 Material properties

284

7.3 Mechanical properties

285

7.3.1

Tensile strength

285

7.3.2

Stiffness

285

7.3.3

Toughness

286

7.3.4

Hardness

286

7.3.5

Fatigue

286

7.3.6

Creep

287

7.3.7

Effect of temperature on the mechanical properties

287

7.4

Corrosion resistance

287

7.4.1

Uniform corrosion

288

7.4.2

Galvanic corrosion

289

7.4.4

Intergranular corrosion

290

7.4.5

Effect of stress

290

7.4.6

Erosion-corrosion

291

7.4.7

High-temperature oxidation

291

7.4.8

Hydrogen embrittlement

292

7.5

Selection for corrosion resistance

292

7.6 Material costs

293

7.7

Contamination

294

7.7.1

Surface finish

295

7.8

Commonly used materials of construction

295

7.8.1

Iron and steel

295

7.8.2

Stainless steel

296

7.8.3

Nickel

298

7.8.4

Monel

299

7.8.5

Inconel

299

7.8.6

The Hastelloys

299

7.8.7

Copper and copper alloys

299

7.8.8

Aluminium and its alloys

299

7.8.9

Lead

300

7.8.10

Titanium

300

7.8.11

Tantalum

300

7.8.12

Zirconium

300

7.8.13

Silver

301

7.8.14

Gold

301

7.8.15

Platinum

301

7.9

Plastics as materials of construction for chemical plant

301

7.9.1

Poly-vinyl chloride (PVC)

302

7.9.2

Polyolefines

302

7.9.3

Polytetrafluroethylene (PTFE)

302

7.9.4

Polyvinylidene fluoride (PVDF)

302

7.9.5

Glass-fibre reinforced plastics (GRP)

302

7.9.6

Rubber

303

7.10 Ceramic materials (silicate materials)

303

7.10.1

Glass

304

7.10.2

Stoneware

304

7.10.3

Acid-resistant bricks and tiles

304

7.10.4

Refractory materials (refractories)

304

7.11 Carbon

305

7.12 Protective coatings

305

7.13 Design for corrosion resistance

305

7.14 References

305

7.15 Nomenclature

307

7.16 Problems

307

8 Design Information and Data

309

8.1

Introduction

309

8.2

Sources of information on manufacturing processes

309

8.3

General sources of physical properties

311

8.4

Accuracy required of engineering data

312

8.5

Prediction of physical properties

313

8.6

Density

314

8.6.1

Liquids

314

8.6.2

Gas and vapour density (specific volume)

315

8.7

Viscosity

316

8.7.1

Liquids

316

8.7.2

Gases

320

8.8

Thermal conductivity

320

8.8.1

Solids

320

8.8.2

Liquids

321

8.8.4

Mixtures

322

8.9

Specific heat capacity

322

8.9.1

Solids and liquids

322

8.9.2

Gases

325

8.10 Enthalpy of vaporisation (latent heat)

328

8.10.1 Mixtures

329

8.11 Vapour pressure

330

8.12 Diffusion coefficients (diffusivities)

331

8.12.1

Gases

331

8.12.2

Liquids

333

8.13 Surface tension

335

8.13.1 Mixtures

335

8.14 Critical constants

336

8.15 Enthalpy of reaction and enthalpy of formation

339

8.16 Phase equilibrium data

339

8.16.1

Experimental data

339

8.16.2

Phase equilibria

339

8.16.3

Equations of state

341

8.16.4

Correlations for liquid phase activity coefficients

342

8.16.5

Prediction of vapour-liquid equilibria

346

8.16.6 K -values for hydrocarbons

348

8.16.7

Sour-water systems (Sour)

348

8.16.8

Vapour-liquid equilibria at high pressures

348

8.16.9

Liquid-liquid equilibria

348

8.16.10 Choice of phase equilibria for design calculations

350

8.16.11 Gas solubilities

351

8.16.12 Use of equations of state to estimate specific enthalpy and density

353

8.17 References

353

8.18 Nomenclature

357

8.19 Problems

358

9 Safety and Loss Prevention

360

9.1

Introduction

360

9.2

Intrinsic and extrinsic safety

361

9.3

The hazards

361

9.3.1

Toxicity

361

9.3.2

Flammability

363

9.3.3

Explosions

365

9.3.4

Sources of ignition

366

9.3.5

Ionising radiation

368

9.3.6

Pressure

368

9.3.7

Temperature deviations

369

9.3.8

Noise

370

9.4

Dow fire and explosion index

371

9.4.1

Calculation of the Dow F & EI

371

9.4.2

Potential loss

375

9.4.3

Basic preventative and protective measures

377

9.4.4

Mond fire, explosion, and toxicity index

378

9.4.5

Summary

379

9.5

Hazard and operability studies

381

9.5.1

Basic principles

382

9.5.2

Explanation of guide words

383

9.5.3

Procedure

384

9.6

Hazard analysis

389

9.7

Acceptable risk and safety priorities

390

9.8

Safety check lists

392

9.9 Major hazards

394

9.9.1

Computer software for quantitative risk analysis

395

9.11 Problems

398

10 Equipment Selection, Specification and Design

400

10.1

Introduction

400

10.2 Separation processes

401

10.3 Solid-solid separations

401

10.3.1

Screening (sieving)

401

10.3.2

Liquid-solid cyclones

404

10.3.3

Hydroseparators and sizers (classifiers)

405

10.3.4

Hydraulic jigs

405

10.3.5

Tables

405

10.3.6

Classifying centrifuges

406

10.3.7

Dense-medium separators (sink and float processes)

406

10.3.8

Flotation separators (froth-flotation)

407

10.3.9

Magnetic separators

407

10.3.10 Electrostatic separators

408

10.4 Liquid-solid (solid-liquid) separators

408

10.4.1

Thickeners and clarifiers

408

10.4.2

Filtration

409

10.4.3

Centrifuges

415

10.4.4

Hydrocyclones (liquid-cyclones)

422

10.4.5

Pressing (expression)

426

10.4.6

Solids drying

426

10.5 Separation of dissolved solids

434

10.5.1

Evaporators

434

10.5.2

Crystallisation

437

10.6 Liquid-liquid separation

440

10.6.1

Decanters (settlers)

440

10.6.2

Plate separators

445

10.6.3

Coalescers

445

10.6.4

Centrifugal separators

446

10.7 Separation of dissolved liquids

446

10.7.1

Solvent extraction and leaching

447

10.8 Gas-solids separations (gas cleaning)

448

10.8.1

Gravity settlers (settling chambers)

448

10.8.2

Impingement separators

448

10.8.3

Centrifugal separators (cyclones)

450

10.8.4

Filters

458

10.8.5 Wet scrubbers (washing)

459

10.8.6

Electrostatic precipitators

459

10.9 Gas liquid separators

460

10.9.1

Settling velocity

461

10.9.2

Vertical separators

461

10.9.3

Horizontal separators

463

10.10 Crushing and grinding (comminution) equipment

465

10.11 Mixing equipment

468

10.11.1 Gas mixing

468

10.11.2 Liquid mixing

468

10.11.3 Solids and pastes

476

10.12 Transport and storage of materials

476

10.12.1 Gases

477

10.12.2 Liquids

479

10.12.3 Solids

481

10.13 Reactors

482

10.13.1 Principal types of reactor

483

10.13.2 Design procedure

486

10.14 References

486

10.15 Nomenclature

490

10.16 Problems

491

11.1

Introduction

493

11.2 Continuous distillation: process description

494

11.2.1

Reflux considerations

495

11.2.2

Feed-point location

496

11.2.3

Selection of column pressure

496

11.3 Continuous distillation: basic principles

497

11.3.1

Stage equations

497

11.3.2

Dew points and bubble points

498

11.3.3

Equilibrium flash calculations

499

11.4 Design variables in distillation

501

11.5 Design methods for binary systems

503

11.5.1

Basic equations

503

11.5.2

McCabe-Thiele method

505

11.5.3

Low product concentrations

507

11.5.4

The Smoker equations

512

11.6 Multicomponent distillation: general considerations

515

11.6.1

Key components

516

11.6.2

Number and sequencing of columns

517

11.7 Multicomponent distillation: short-cut methods for stage and reflux requirements

517

11.7.1

Pseudo-binary systems

518

11.7.2

Smith-Brinkley method

522

11.7.3

Empirical correlations

523

11.7.4

Distribution of non-key components (graphical method)

526

11.8 Multicomponent systems: rigorous solution procedures (computer methods)

542

11.8.1

Lewis-Matheson method

543

11.8.2

Thiele-Geddes method

544

11.8.3

Relaxation methods

545

11.8.4

Linear algebra methods

545

11.9 Other distillation systems

546

11.9.1

Batch distillation

546

11.9.2

Steam distillation

546

11.9.3

Reactive distillation

547

11.10 Plate efficiency

547

11.10.1 Prediction of plate efficiency

548

11.10.2 O’Connell’s correlation

550

11.10.3 Van Winkle’s correlation

552

11.10.4 AIChE method

553

11.10.5 Entrainment

556

11.11 Approximate column sizing

557

11.12 Plate contactors

557

11.12.1 Selection of plate type

560

11.12.2 Plate construction

561

11.13 Plate hydraulic design

565

11.13.1 Plate-design procedure

567

11.13.2 Plate areas

567

11.13.3 Diameter

567

11.13.4 Liquid-flow arrangement

569

11.13.5 Entrainment

570

11.13.6 Weep point

571

11.13.7 Weir liquid crest

572

11.13.8 Weir dimensions

572

11.13.9 Perforated area

572

11.13.10 Hole size

573

11.13.11 Hole pitch

574

11.13.12 Hydraulic gradient

574

11.13.13 Liquid throw

575

11.13.14 Plate pressure drop

575

11.13.15 Downcomer design [back-up]

577

11.14 Packed columns

587

11.14.1 Types of packing

589

11.14.3 Prediction of the height of a transfer unit (HTU)

597

11.14.4 Column diameter (capacity)

602

11.14.5 Column internals

609

11.14.6 Wetting rates

616

11.15 Column auxiliaries

616

11.16 Solvent extraction (liquid liquid extraction)

617

11.16.1 Extraction equipment

617

11.16.2 Extractor design

618

11.16.3 Extraction columns

623

11.16.4 Supercritical fluid extraction

624

11.17 References

624

11.18 Nomenclature

627

11.19 Problems

630

12 Heat-transfer Equipment

634

12.1

Introduction

634

12.2 Basic design procedure and theory

635

12.2.1

Heat exchanger analysis: the effectiveness NTU method

636

12.3 Overall heat-transfer coefficient

636

12.4 Fouling factors (dirt factors)

638

12.5 Shell and tube exchangers: construction details

640

12.5.1

Heat-exchanger standards and codes

644

12.5.2

Tubes

645

12.5.3

Shells

647

12.5.4

Tube-sheet layout (tube count)

647

12.5.5

Shell types (passes)

649

12.5.6

Shell and tube designation

649

12.5.7

Baffles

650

12.5.8

Support plates and tie rods

652

12.5.9

Tube sheets (plates)

652

12.5.10 Shell and header nozzles (branches)

653

12.5.11 Flow-induced tube vibrations

653

12.6 Mean temperature difference (temperature driving force)

655

12.7 Shell and tube exchangers: general design considerations

660

12.7.1

Fluid allocation: shell or tubes

660

12.7.2

Shell and tube fluid velocities

660

12.7.3

Stream temperatures

661

12.7.4

Pressure drop

661

12.7.5

Fluid physical properties

661

12.8 Tube-side heat-transfer coefficient and pressure drop (single phase)

662

12.8.1

Heat transfer

662

12.8.2

Tube-side pressure drop

666

12.9 Shell-side heat-transfer and pressure drop (single phase)

669

12.9.1

Flow pattern

669

12.9.2

Design methods

670

12.9.3

Kern’s method

671

12.9.4

Bell’s method

693

12.9.5

Shell and bundle geometry

702

12.9.6

Effect of fouling on pressure drop

705

12.9.7

Pressure-drop limitations

705

12.10 Condensers

709

12.10.1 Heat-transfer fundamentals

710

12.10.2 Condensation outside horizontal tubes

710

12.10.3 Condensation inside and outside vertical tubes

711

12.10.4 Condensation inside horizontal tubes

716

12.10.5 Condensation of steam

717

12.10.6 Mean temperature difference

717

12.10.7 Desuperheating and sub-cooling

717

12.10.9 Pressure drop in condensers

723

12.11 Reboilers and vaporisers

728

12.11.1 Boiling heat-transfer fundamentals

731

12.11.2 Pool boiling

732

12.11.3 Convective boiling

735

12.11.4 Design of forced-circulation reboilers

740

12.11.5 Design of thermosyphon reboilers

741

12.11.6 Design of kettle reboilers

750

12.12 Plate heat exchangers

756

12.12.1 Gasketed plate heat exchangers

756

12.12.2 Welded plate

764

12.12.3 Plate-fin

764

12.12.4 Spiral heat exchangers

765

12.13 Direct-contact heat exchangers

766

12.14 Finned tubes

767

12.15 Double-pipe heat exchangers

768

12.16 Air-cooled exchangers

769

12.17 Fired heaters (furnaces and boilers)

769

12.17.1 Basic construction

770

12.17.2 Design

771

12.17.3 Heat transfer

772

12.17.4 Pressure drop

774

12.17.5 Process-side heat transfer and pressure drop

774

12.17.6 Stack design

774

12.17.7 Thermal efficiency

775

12.18 Heat transfer to vessels

775

12.18.1

Jacketed vessels

775

12.18.2

Internal coils

777

12.18.3 Agitated vessels

778

12.19 References

782

12.20 Nomenclature

786

12.21 Problems

790

13 Mechanical Design of Process Equipment

794

13.1

Introduction

794

13.1.1

Classification of pressure vessels

795

13.2 Pressure vessel codes and standards

795

13.3 Fundamental principles and equations

796

13.3.1

Principal stresses

796

13.3.2

Theories of failure

797

13.3.3

Elastic stability

798

13.3.4

Membrane stresses in shells of revolution

798

13.3.5

Flat plates

805

13.3.6

Dilation of vessels

809

13.3.7

Secondary stresses

809

13.4 General design considerations: pressure vessels

810

13.4.1

Design pressure

810

13.4.2

Design temperature

810

13.4.3

Materials

811

13.4.4

Design stress (nominal design strength)

811

13.4.5 Welded joint efficiency, and construction categories

812

13.4.6

Corrosion allowance

813

13.4.7

Design loads

814

13.4.8

Minimum practical wall thickness

814

13.5 The design of thin-walled vessels under internal pressure

815

13.5.1

Cylinders and spherical shells

815

13.5.2

Heads and closures

815

13.5.3

Design of flat ends

817

13.5.4

Design of domed ends

818

13.5.5

Conical sections and end closures

819

13.7 Design of vessels subject to external pressure

825

13.7.1

Cylindrical shells

825

13.7.2

Design of stiffness rings

828

13.7.3

Vessel heads

829

13.8 Design of vessels subject to combined loading

831

13.8.1 Weight loads

835

13.8.2 Wind loads (tall vessels)

837

13.8.3

Earthquake loading

839

13.8.4

Eccentric loads (tall vessels)

840

13.8.5

Torque

841

13.9 Vessel supports

844

13.9.1

Saddle supports

844

13.9.2

Skirt supports

848

13.9.3

Bracket supports

856

13.10 Bolted flanged joints

858

13.10.1 Types of flange, and selection

858

13.10.2 Gaskets

859

13.10.3 Flange faces

861

13.10.4 Flange design

862

13.10.5 Standard flanges

865

13.11 Heat-exchanger tube-plates

867

13.12 Welded joint design

869

13.13 Fatigue assessment of vessels

872

13.14 Pressure tests

872

13.15 High-pressure vessels

873

13.15.1 Fundamental equations

873

13.15.2 Compound vessels

877

13.15.3 Autofrettage

878

13.16 Liquid storage tanks

879

13.17 Mechanical design of centrifuges

879

13.17.1 Centrifugal pressure

879

13.17.2 Bowl and spindle motion: critical speed

881

13.18 References

883

13.19 Nomenclature

885

13.20 Problems

889

14 General Site Considerations

892

14.1

Introduction

892

14.2 Plant location and site selection

892

14.3 Site layout

894

14.4 Plant layout

896

14.4.1

Techniques used in site and plant layout

897

14.5 Utilities

900

14.6 Environmental considerations

902

14.6.1 Waste management

902

14.6.2

Noise

905

14.6.3

Visual impact

905

14.6.4

Legislation

905

14.6.5

Environmental auditing

906

14.7 References

906

APPENDIX A: GRAPHICAL SYMBOLS FOR PIPING SYSTEMS AND PLANT

908

APPENDIX B: CORROSION CHART

917

APPENDIX C: PHYSICAL PROPERTY DATA BANK

937

APPENDIX D: CONVERSION FACTORS FOR SOME COMMON SI UNITS

958

APPENDIX F: DESIGN PROJECTS

965

APPENDIX G: EQUIPMENT SPECIFICATION (DATA) SHEETS

990

APPENDIX H: TYPICAL SHELL AND TUBE HEAT EXCHANGER TUBE-SHEET LAYOUTS

1002

AUTHOR INDEX

1007

SUBJECT INDEX

1017

CHAPTER 1

Introduction to Design

1.1. INTRODUCTION

This chapter is an introduction to the nature and methodology of the design process, and

its application to the design of chemical manufacturing processes.

1.2. NATURE OF DESIGN

This section is a general, somewhat philosophical, discussion of the design process; how a

designer works. The subject of this book is chemical engineering design, but the method-

ology of design described in this section applies equally to other branches of engineering

design.

Design is a creative activity, and as such can be one of the most rewarding and satisfying

activities undertaken by an engineer. It is the synthesis, the putting together, of ideas to

achieve a desired purpose. The design does not exist at the commencement of the project.

The designer starts with a specific objective in mind, a need, and by developing and

evaluating possible designs, arrives at what he considers the best way of achieving that

objective; be it a better chair, a new bridge, or for the chemical engineer, a new chemical

product or a stage in the design of a production process.

When considering possible ways of achieving the objective the designer will be

constrained by many factors, which will narrow down the number of possible designs;

but, there will rarely be just one possible solution to the problem, just one design. Several

alternative ways of meeting the objective will normally be possible, even several best

designs, depending on the nature of the constraints.

These constraints on the possible solutions to a problem in design arise in many ways.

Some constraints will be fixed, invariable, such as those that arise from physical laws,

government regulations, and standards. Others will be less rigid, and will be capable of

relaxation by the designer as part of his general strategy in seeking the best design. The

constraints that are outside the designer’s influence can be termed the external constraints.

These set the outer boundary of possible designs; as shown in Figure 1.1. Within this

boundary there will be a number of plausible designs bounded by the other constraints,

the internal constraints, over which the designer has some control; such as, choice of

process, choice of process conditions, materials, equipment.

Economic considerations are obviously a major constraint on any engineering design:

plants must make a profit.

Time will also be a constraint. The time available for completion of a design will

usually limit the number of alternative designs that can be considered.

1

Plausible

designs

G

o

v

e

rnm

e

n

t c

o

n

tro

ls

Economic constraintsSa

fe

ty

re

gu

lat

ion

s

Resources

Physical lawsStandards and codesP

e

rs

o

n

n

e

l

MaterialsProcess

conditions

Ch

oic

e o

f

pro

ces

s

MethodsT

im

e

“External” constraints

“Internal” constraints

Possible designs

Figure 1.1. Design constraints

Objective

(design

specification)

Collection of data,

physical

properties design

methods

Generation of

possible designs

Selection and

evaluation

(optimisation)

Final

design

Figure 1.2. The design process

The stages in the development of a design, from the initial identification of the objective

to the final design, are shown diagrammatically in Figure 1.2. Each stage is discussed in

the following sections.

Figure 1.2 shows design as an iterative procedure; as the design develops the designer

will be aware of more possibilities and more constraints, and will be constantly seeking

new data and ideas, and evaluating possible design solutions.

Chaddock (1975) defined design as, the conversion of an ill-defined requirement into a

satisfied customer.

The designer is creating a design for an article, or a manufacturing process, to fulfil a

particular need. In the design of a chemical process, the need is the public need for the

product, the commercial opportunity, as foreseen by the sales and marketing organisation.

Within this overall objective the designer will recognise sub-objectives; the requirements

of the various units that make up the overall process.

Before starting work the designer should obtain as complete, and as unambiguous, a

statement of the requirements as possible. If the requirement (need) arises from outside the

design group, from a client or from another department, then he will have to elucidate the

real requirements through discussion. It is important to distinguish between the real needs

and the wants. The wants are those parts of the initial specification that may be thought

desirable, but which can be relaxed if required as the design develops. For example, a

particular product specification may be considered desirable by the sales department, but

may be difficult and costly to obtain, and some relaxation of the specification may be

possible, producing a saleable but cheaper product. Whenever he is in a position to do so,

the designer should always question the design requirements (the project and equipment

specifications) and keep them under review as the design progresses.

Where he writes specifications for others, such as for the mechanical design or purchase

of a piece of equipment, he should be aware of the restrictions (constraints) he is placing

on other designers. A tight, well-thought-out, comprehensive, specification of the require-

ments defines the external constraints within which the other designers must work.

1.2.2. Data collection

To proceed with a design, the designer must first assemble all the relevant facts and

data required. For process design this will include information on possible processes,

equipment performance, and physical property data. This stage can be one of the most

time consuming, and frustrating, aspects of design. Sources of process information and

physical properties are reviewed in Chapter 8.

Many design organisations will prepare a basic data manual, containing all the process

“know-how” on which the design is to be based. Most organisations will have design

manuals covering preferred methods and data for the more frequently used, routine, design

procedures.

The national standards are also sources of design methods and data; they are also design

constraints.

The constraints, particularly the external constraints, should be identified early in the

design process.

1.2.3. Generation of possible design solutions

The creative part of the design process is the generation of possible solutions to the

problem (ways of meeting the objective) for analysis, evaluation and selection. In this

activity the designer will largely rely on previous experience, his own and that of others.

be easily traced. The first motor cars were clearly horse-drawn carriages without the

horse; and the development of the design of the modern car can be traced step by step

from these early prototypes. In the chemical industry, modern distillation processes have

developed from the ancient stills used for rectification of spirits; and the packed columns

used for gas absorption have developed from primitive, brushwood-packed towers. So,

it is not often that a process designer is faced with the task of producing a design for a

completely novel process or piece of equipment.

The experienced engineer will wisely prefer the tried and tested methods, rather than

possibly more exciting but untried novel designs. The work required to develop new

processes, and the cost, is usually underestimated. Progress is made more surely in small

steps. However, whenever innovation is wanted, previous experience, through prejudice,

can inhibit the generation and acceptance of new ideas; the “not invented here” syndrome.

The amount of work, and the way it is tackled, will depend on the degree of novelty

in a design project.

Chemical engineering projects can be divided into three types, depending on the novelty

involved:

1. Modifications, and additions, to existing plant; usually carried out by the plant design

group.

2. New production capacity to meet growing sales demand, and the sale of established

processes by contractors. Repetition of existing designs, with only minor design

changes.

3. New processes, developed from laboratory research, through pilot plant, to a

commercial process. Even here, most of the unit operations and process equipment

will use established designs.

The first step in devising a new process design will be to sketch out a rough block

diagram showing the main stages in the process; and to list the primary function (objective)

and the major constraints for each stage. Experience should then indicate what types of

unit operations and equipment should be considered.

Jones (1970) discusses the methodology of design, and reviews some of the special

techniques, such as brainstorming sessions and synectics, that have been developed to

help generate ideas for solving intractable problems. A good general reference on the art

of problem solving is the classical work by Polya (1957); see also Chittenden (1987).

Some techniques for problem solving in the Chemical Industry are covered in a short text

by Casey and Frazer (1984).

The generation of ideas for possible solutions to a design problem cannot be separated

from the selection stage of the design process; some ideas will be rejected as impractical

as soon as they are conceived.

1.2.4. Selection

The designer starts with the set of all possible solutions bounded by the external

constraints, and by a process of progressive evaluation and selection, narrows down the

range of candidates to find the “best” design for the purpose.

Possible designs (credible)

within the external constraints.

Plausible designs (feasible)

within the internal constraints.

Probable designs

likely candidates.

Best design (optimum)

judged the best solution to the problem.

The selection process will become more detailed and more refined as the design progresses

from the area of possible to the area of probable solutions. In the early stages a coarse

screening based on common sense, engineering judgement, and rough costings will usually

suffice. For example, it would not take many minutes to narrow down the choice of raw

materials for the manufacture of ammonia from the possible candidates of, say, wood,

peat, coal, natural gas, and oil, to a choice of between gas and oil, but a more detailed

study would be needed to choose between oil and gas. To select the best design from the

probable designs, detailed design work and costing will usually be necessary. However,

where the performance of candidate designs is likely to be close the cost of this further

refinement, in time and money, may not be worthwhile, particularly as there will usually

be some uncertainty in the accuracy of the estimates.

The mathematical techniques that have been developed to assist in the optimisation of

designs, and plant performance, are discussed briefly in Section 1.10.

Rudd and Watson (1968) and Wells (1973) describe formal techniques for the prelim-

inary screening of alternative designs.

1.3. THE ANATOMY OF A CHEMICAL MANUFACTURING

PROCESS

The basic components of a typical chemical process are shown in Figure 1.3, in which

each block represents a stage in the overall process for producing a product from the raw

materials. Figure 1.3 represents a generalised process; not all the stages will be needed for

any particular process, and the complexity of each stage will depend on the nature of the

process. Chemical engineering design is concerned with the selection and arrangement

of the stages, and the selection, specification and design of the equipment required to

perform the stage functions.

Raw

material

storage

Feed

preparation

Reaction

Product

separation

Product

purification

Product

storage

Sales

Recycle of unreacted

material

By-products

Wastes

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

Stage 6

Figure 1.3. Anatomy of a chemical process

Stage 1. Raw material storage

Unless the raw materials (also called essential materials, or feed stocks) are supplied

as intermediate products (intermediates) from a neighbouring plant, some provision will

interruptions in supply. Even when the materials come from an adjacent plant some

provision is usually made to hold a few hours, or even days, supply to decouple the

processes. The storage required will depend on the nature of the raw materials, the method

of delivery, and what assurance can be placed on the continuity of supply. If materials are

delivered by ship (tanker or bulk carrier) several weeks stocks may be necessary; whereas

if they are received by road or rail, in smaller lots, less storage will be needed.

Stage 2. Feed preparation

Some purification, and preparation, of the raw materials will usually be necessary before

they are sufficiently pure, or in the right form, to be fed to the reaction stage. For example,

acetylene generated by the carbide process contains arsenical and sulphur compounds, and

other impurities, which must be removed by scrubbing with concentrated sulphuric acid

(or other processes) before it is sufficiently pure for reaction with hydrochloric acid to

produce dichloroethane. Liquid feeds will need to be vaporised before being fed to gas-

phase reactors, and solids may need crushing, grinding and screening.

Stage 3. Reactor

The reaction stage is the heart of a chemical manufacturing process. In the reactor the

raw materials are brought together under conditions that promote the production of the

desired product; invariably, by-products and unwanted compounds (impurities) will also

be formed.

Stage 4. Product separation

In this first stage after the reactor the products and by-products are separated from any

unreacted material. If in sufficient quantity, the unreacted material will be recycled to

the reactor. They may be returned directly to the reactor, or to the feed purification and

preparation stage. The by-products may also be separated from the products at this stage.

Stage 5. Purification

Before sale, the main product will usually need purification to meet the product specifi-

cation. If produced in economic quantities, the by-products may also be purified for sale.

Stage 6. Product storage

Some inventory of finished product must be held to match production with sales. Provision

for product packaging and transport will also be needed, depending on the nature of the

product. Liquids will normally be dispatched in drums and in bulk tankers (road, rail and

sea), solids in sacks, cartons or bales.

The stock held will depend on the nature of the product and the market.

Ancillary processes

In addition to the main process stages shown in Figure 1.3, provision will have to be

made for the supply of the services (utilities) needed; such as, process water, cooling

offices and other accommodation, and laboratories; see Chapter 14.

1.3.1. Continuous and batch processes

Continuous processes are designed to operate 24 hours a day, 7 days a week, throughout

the year. Some down time will be allowed for maintenance and, for some processes,

catalyst regeneration. The plant attainment; that is, the percentage of the available hours

in a year that the plant operates, will usually be 90 to 95%.

Attainment % D hours operated

8760

ð 100

Batch processes are designed to operate intermittently. Some, or all, the process units

being frequently shut down and started up.

Continuous processes will usually be more economical for large scale production. Batch

processes are used where some flexibility is wanted in production rate or product speci-

fication.

Choice of continuous versus batch production

The choice between batch or continuous operation will not be clear cut, but the following

rules can be used as a guide.

Continuous

1. Production rate greater than 5 ð 106 kg/h

2. Single product

3. No severe fouling

4. Good catalyst life

5. Proven processes design

6. Established market

Batch

1. Production rate less than 5 ð 106 kg/h

2. A range of products or product specifications

3. Severe fouling

4. Short catalyst life

5. New product

6. Uncertain design

1.4. THE ORGANISATION OF A CHEMICAL ENGINEERING

PROJECT

The design work required in the engineering of a chemical manufacturing process can be

divided into two broad phases.

Phase 1. Process design, which covers the steps from the initial selection of the process

to be used, through to the issuing of the process flow-sheets; and includes the selection,

Initial evaluation.

Process selection.

Preliminary flow diagrams.

Detailed process design.

Flow-sheets.

Chemical engineering equipment

design and specifications.

Reactors, Unit operations, Heat exchangers,

Miscellaneous equipment.

Materials selection.

Process manuals

Material and energy balances.

Preliminary equipment selection

and design.

Process flow-sheeting.

Preliminary cost estimation.

Authorisation of funds.

Piping and instrument design

Instrument selection

and specification

Pumps and compressors.

Selection and specification

Vessel design

Heat exchanger design

Utilities and other services.

Design and specification

Electrical,

Motors, switch gear,

substations, etc.

Piping design

Structural design

Plant layout

General civil work.

Foundations, drains,

roads, etc.

Buildings.

Offices, laboratories,

control rooms, etc.

Project cost estimation.

Capital authorisation

Purchasing/procurement

Raw material specification.

(contracts)

Construction

Start-up

Operating manuals

Operation

Sales

Figure 1.4. The structure of a chemical engineering project

this phase is the responsibility of the Process Design Group, and the work will be mainly

done by chemical engineers. The process design group may also be responsible for the

preparation of the piping and instrumentation diagrams.

Phase 2. The detailed mechanical design of equipment; the structural, civil and electrical

design; and the specification and design of the ancillary services. These activities will be

the responsibility of specialist design groups, having expertise in the whole range of

engineering disciplines.

Other specialist groups will be responsible for cost estimation, and the purchase and

procurement of equipment and materials.

The sequence of steps in the design, construction and start-up of a typical chemical

process plant is shown diagrammatically in Figure 1.4 and the organisation of a typical

project group in Figure 1.5. Each step in the design process will not be as neatly separated

from the others as is indicated in Figure 1.4; nor will the sequence of events be as clearly

defined. There will be a constant interchange of information between the various design

sections as the design develops, but it is clear that some steps in a design must be largely

completed before others can be started.

A project manager, often a chemical engineer by training, is usually responsible for the

co-ordination of the project, as shown in Figure 1.5.

Specialist design sections

Vessels Layout Piping Heat exchangers

valves fired heaters

Control Civil work

and instruments structures Electrical

buildings

Compressors

and turbines Utilities

pumps

Process section

Process evaluation

Flow-sheeting

Equipment specifications

Construction section

Construction

Start-up

Project

manager

Procurement

section

Estimating

Inspection

Scheduling

Figure 1.5. Project organisation

As was stated in Section 1.2.1, the project design should start with a clear specification

defining the product, capacity, raw materials, process and site location. If the project is

based on an established process and product, a full specification can be drawn up at

the start of the project. For a new product, the specification will be developed from an

economic evaluation of possible processes, based on laboratory research, pilot plant tests

and product market research.

Barrow (1964) and Baasel (1974).

Some of the larger chemical manufacturing companies have their own project design

organisations and carry out the whole project design and engineering, and possibly

construction, within their own organisation. More usually the design and construction, and

possibly assistance with start-up, is entrusted to one of the international contracting firms.

The operating company will often provide the “know-how” for the process, and will

work closely with the contractor throughout all stages of the project.

1.5. PROJECT DOCUMENTATION

As shown in Figure 1.5 and described in Section 1.4, the design and engineering of

a chemical process requires the co-operation of many specialist groups. Effective co-

operation depends on effective communications, and all design organisations have formal

procedures for handling project information and documentation. The project documen-

tation will include:

1. General correspondence within the design group and with:

government departments

equipment vendors

site personnel

the client

2. Calculation sheets

design calculations

costing

computer print-out

3. Drawings

flow-sheets

piping and instrumentation diagrams

layout diagrams

plot/site plans

equipment details

piping diagrams

architectural drawings

design sketches

4. Specification sheets

for equipment, such as:

heat exchangers

pumps

5. Purchase orders

quotations

invoices

All documents should be assigned a code number for easy cross referencing, filing and

retrieval.

Calculation sheets

The design engineer should develop the habit of setting out calculations so that they can

be easily understood and checked by others. It is good practice to include on calculation

sufficient detail for the methods, as well as the arithmetic, to be checked. Design calcula-

tions are normally set out on standard sheets. The heading at the top of each sheet should

include: the project title and identification number and, most importantly, the signature

(or initials) of the person who checked the calculation.

Drawings

All project drawings are normally drawn on specially printed sheets, with the company

name; project title and number; drawing title and identification number; draughtsman’s

name and person checking the drawing; clearly set out in a box in the bottom right-hand

corner. Provision should also be made for noting on the drawing all modifications to the

initial issue.

Drawings should conform to accepted drawing conventions, preferably those laid down

by the national standards. The symbols used for flow-sheets and piping and instrument

diagrams are discussed in Chapter 4. Drawings and sketches are normally made on

detail paper (semi-transparent) in pencil, so modifications can be easily made, and prints

taken.

In most design offices Computer Aided Design (CAD) methods are now used to produce

the drawings required for all the aspects of a project: flow-sheets, piping and instrumen-

tation, mechanical and civil work.

Specification sheets

Standard specification sheets are normally used to transmit the information required for

the detailed design, or purchase, of equipment items; such as, heat exchangers, pumps,

columns.

As well as ensuring that the information is clearly and unambiguously presented,

standard specification sheets serve as check lists to ensure that all the information required

is included.

Examples of equipment specification sheets are given in Appendix G.

Process manuals

Process manuals are often prepared by the process design group to describe the process and

the basis of the design. Together with the flow-sheets, they provide a complete technical

description of the process.

Operating manuals

Operating manuals give the detailed, step by step, instructions for operation of the process

and equipment. They would normally be prepared by the operating company personnel,

but may also be issued by a contractor as part of the contract package for a less experienced

client. The operating manuals would be used for operator instruction and training, and

for the preparation of the formal plant operating instructions.

The need for standardisation arose early in the evolution of the modern engineering

industry; Whitworth introduced the first standard screw thread to give a measure of

interchangeability between different manufacturers in 1841. Modern engineering standards

cover a much wider function than the interchange of parts. In engineering practice

they cover:

1. Materials, properties and compositions.

2. Testing procedures for performance, compositions, quality.

3. Preferred sizes; for example, tubes, plates, sections.

4. Design methods, inspection, fabrication.

5. Codes of practice, for plant operation and safety.

The terms STANDARD and CODE are used interchangeably, though CODE should

really be reserved for a code of practice covering say, a recommended design or operating

procedure; and STANDARD for preferred sizes, compositions, etc.

All of the developed countries, and many of the developing countries, have national

standards organisations, responsible for the issue and maintenance of standards for the

manufacturing industries, and for the protection of consumers. In the United Kingdom

preparation and promulgation of national standards are the responsibility of the British

Standards Institution (BSI). The Institution has a secretariat and a number of technical

personnel, but the preparation of the standards is largely the responsibility of committees

of persons from the appropriate industry, the professional engineering institutions and

other interested organisations.

In the United States the government organisation responsible for coordinating infor-

mation on standards is the National Bureau of Standards; standards are issued by Federal,

State and various commercial organisations. The principal ones of interest to chemical

engineers are those issued by the American National Standards Institute (ANSI), the

American Petroleum Institute (API), the American Society for Testing Materials (ASTM),

and the American Society of Mechanical Engineers (ASME) (pressure vessels). Burklin

(1979) gives a comprehensive list of the American codes and standards.

The International Organization for Standardization (ISO) coordinates the publication of

international standards.

All the published British standards are listed, and their scope and application described,

in the British Standards Institute Catalogue; which the designer should consult. The

catalogue is available online, go to the BSI group home page, www.bsi-global.com.

As well as the various national standards and codes, the larger design organisations

will have their own (in-house) standards. Much of the detail in engineering design work

is routine and repetitious, and it saves time and money, and ensures a conformity between

projects, if standard designs are used whenever practicable.

Equipment manufacturers also work to standards to produce standardised designs and

size ranges for commonly used items; such as electric motors, pumps, pipes and pipe

fittings. They will conform to national standards, where they exist, or to those issued by

trade associations. It is clearly more economic to produce a limited range of standard

sizes than to have to treat each order as a special job.

of a piece of equipment into the rest of the plant. For example, if a standard range of

centrifugal pumps is specified the pump dimensions will be known, and this facilitates the

design of the foundations plates, pipe connections and the selection of the drive motors:

standard electric motors would be used.

For an operating company, the standardisation of equipment designs and sizes increases

interchangeability and reduces the stock of spares that have to be held in maintenance

stores.

Though there are clearly considerable advantages to be gained from the use of standards

in design, there are also some disadvantages. Standards impose constraints on the designer.

The nearest standard size will normally be selected on completing a design calculation

(rounding-up) but this will not necessarily be the optimum size; though as the standard

size will be cheaper than a special size, it will usually be the best choice from the point of

view of initial capital cost. Standard design methods must, of their nature, be historical,

and do not necessarily incorporate the latest techniques.

The use of standards in design is illustrated in the discussion of the pressure vessel

design standards (codes) in Chapter 13.

1.7. FACTORS OF SAFETY (DESIGN FACTORS)

Design is an inexact art; errors and uncertainties will arise from uncertainties in the design

data available and in the approximations necessary in design calculations. To ensure that

the design specification is met, factors are included to give a margin of safety in the

design; safety in the sense that the equipment will not fail to perform satisfactorily, and

that it will operate safely: will not cause a hazard. “Design factor” is a better term to use,

as it does not confuse safety and performance factors.

In mechanical and structural design, the magnitude of the design factors used to allow

for uncertainties in material properties, design methods, fabrication and operating loads

are well established. For example, a factor of around 4 on the tensile strength, or about

2.5 on the 0.1 per cent proof stress, is normally used in general structural design. The

selection of design factors in mechanical engineering design is illustrated in the discussion

of pressure vessel design in Chapter 13.

Design factors are also applied in process design to give some tolerance in the design.

For example, the process stream average flows calculated from material balances are

usually increased by a factor, typically 10 per cent, to give some flexibility in process

operation. This factor will set the maximum flows for equipment, instrumentation, and

piping design. Where design factors are introduced to give some contingency in a process

design, they should be agreed within the project organisation, and clearly stated in the

project documents (drawings, calculation sheets and manuals). If this is not done, there

is a danger that each of the specialist design groups will add its own “factor of safety”;

resulting in gross, and unnecessary, over-design.

When selecting the design factor to use a balance has to be made between the desire

to make sure the design is adequate and the need to design to tight margins to remain

competitive. The greater the uncertainty in the design methods and data, the bigger the

design factor that must be used.

To be consistent with the other volumes in this series, SI units have been used in this

book. However, in practice the design methods, data and standards which the designer will

use are often only available in the traditional scientific and engineering units. Chemical

engineering has always used a diversity of units; embracing the scientific CGS and MKS

systems, and both the American and British engineering systems. Those engineers in the

older industries will also have had to deal with some bizarre traditional units; such as

degrees Twaddle (density) and barrels for quantity. Desirable as it may be for industry

world-wide to adopt one consistent set of units, such as SI, this is unlikely to come about

for many years, and the designer must contend with whatever system, or combination of

systems, his organisation uses. For those in the contracting industry this will also mean

working with whatever system of units the client requires.

It is usually the best practice to work through design calculations in the units in which

the result is to be presented; but, if working in SI units is preferred, data can be converted

to SI units, the calculation made, and the result converted to whatever units are required.

Conversion factors to the SI system from most of the scientific and engineering units used

in chemical engineering design are given in Appendix D.

Some license has been taken in the use of the SI system in this volume. Temperatures are

given in degrees Celsius (ŽC); degrees Kelvin are only used when absolute temperature

is required in the calculation. Pressures are often given in bar (or atmospheres) rather

than in the Pascals (N/m2), as this gives a better feel for the magnitude of the pressures.

In technical calculations the bar can be taken as equivalent to an atmosphere, whatever

definition is used for atmosphere. The abbreviations bara and barg are often used to denote

bar absolute and bar gauge; analogous to psia and psig when the pressure is expressed

in pound force per square inch. When bar is used on its own, without qualification, it is

normally taken as absolute.

For stress, N/mm2 have been used, as these units are now generally accepted by

engineers, and the use of a small unit of area helps to indicate that stress is the intensity of

force at a point (as is also pressure). For quantity, kmol are generally used in preference

to mol, and for flow, kmol/h instead of mol/s, as this gives more sensibly sized figures,

which are also closer to the more familiar lb/h.

For volume and volumetric flow, m3 and m3/h are used in preference to m3/s, which

gives ridiculously small values in engineering calculations. Litres per second are used for

small flow-rates, as this is the preferred unit for pump specifications.

Where, for convenience, other than SI units have been used on figures or diagrams, the

scales are also given in SI units, or the appropriate conversion factors are given in the

text. The answers to some examples are given in British engineering units as well as SI,

to help illustrate the significance of the values.

Some approximate conversion factors to SI units are given in Table 1.1. These are

worth committing to memory, to give some feel for the units for those more familiar with

the traditional engineering units. The exact conversion factors are also shown in the table.

A more comprehensive table of conversion factors is given in Appendix D.

Engineers need to be aware of the difference between US gallons and imperial gallons

(UK) when using American literature and equipment catalogues. Equipment quoted in an

Quantity

British

SI unit

Eng. unit

approx.

exact

Energy

1 Btu

1 kJ

1.05506

Specific enthalpy

1 Btu/lb

2 kJ/kg

2.326

Specific heat capacity

1 Btu/lb°F

4 kJ/kg°C

4.1868

(CHU/lb°C)

Heat transfer coeff.

1 Btu/ft2h°F

6 W/m2 °C

5.678

(CHU/ft2h°C)

Viscosity

1 centipoise

1 mNs/m2

1.000

1 lbf/ft h

0.4 mNs/m2

0.4134

Surface tension

1 dyne/cm

1 mN/m

1.000

Pressure

1 lbf/in2

7 kN/m2

6.894

1 atm

1 bar

1.01325

105 N/m2

Density

1 lb/ft3

16 kg/m3

16.0190

1 g/cm3

1 kg/m3

Volume

1 imp gal.

4.5 ð 103 m3

4.5461 ð 103

Flow-rate

1 imp gal/m

16 m3/h

16.366

Note:

1 US gallon D 0.84 imperial gallons (UK)

1 barrel (oil) D 50 US gall ³ 0.19 m3 (exact 0.1893)

1 kWh D 3.6 MJ

American catalogue in US gallons or gpm (gallons per minute) will have only 80 per cent

of the rated capacity when measured in imperial gallons.

The electrical supply frequency in these two countries is also different: 60 Hz in the US

and 50 Hz in the UK. So a pump specified as 50 gpm (US gallons), running at 1750 rpm

(revolutions per second) in the US would only deliver 35 imp gpm if operated in the UK;

where the motor speed would be reduced to 1460 rpm: so beware.

1.9. DEGREES OF FREEDOM AND DESIGN VARIABLES.

THE MATHEMATICAL REPRESENTATION OF

THE DESIGN PROBLEM

In Section 1.2 it was shown that the designer in seeking a solution to a design problem

works within the constraints inherent in the particular problem.

In this section the structure of design problems is examined by representing the general

design problem in a mathematical form.

1.9.1. Information flow and design variables

A process unit in a chemical process plant performs some operation on the inlet material

streams to produce the desired outlet streams. In the design of such a unit the design

calculations model the operation of the unit. A process unit and the design equations

Input

streams

Input

information

Output

streams

Output

information

Unit

Calculation

method

Figure 1.6. The “design unit”

representing the unit are shown diagrammatically in Figure 1.6. In the “design unit” the

flow of material is replaced by a flow of information into the unit and a flow of derived

information from the unit.

The information flows are the values of the variables which are involved in the design;

such as, stream compositions, temperatures, pressure, stream flow-rates, and stream

enthalpies. Composition, temperature and pressure are intensive variables: independent of

the quantity of material (flow-rate). The constraints on the design will place restrictions on

the possible values that these variables can take. The values of some of the variables will

be fixed directly by process specifications. The values of other variables will be determined

by “design relationships” arising from constraints. Some of the design relationships will

be in the form of explicit mathematical equations (design equations); such as those

arising from material and energy balances, thermodynamic relationships, and equipment

performance parameters. Other relationships will be less precise; such as those arising

from the use of standards and preferred sizes, and safety considerations.

The difference between the number of variables involved in a design and the number

of design relationships has been called the number of “degrees of freedom”; similar to the

use of the term in the phase rule. The number of variables in the system is analogous to the

number of variables in a set of simultaneous equations, and the number of relationships

analogous to the number of equations. The difference between the number of variables

and equations is called the variance of the set of equations.

If Nv is the number of possible variables in a design problem and Nr the number of

design relationships, then the “degrees of freedom” Nd is given by:

Nd D Nv Nr

1.1

Nd represents the freedom that the designer has to manipulate the variables to find the

best design.

If Nv D Nr,Nd D 0 and there is only one, unique, solution to the problem. The problem

is not a true design problem, no optimisation is possible.

If Nv < Nr,Nd < 0, and the problem is over defined; only a trivial solution is possible.

If Nv > Nr,Nd > 0, and there is an infinite number of possible solutions. However,

for a practical problem there will be only a limited number of feasible solutions. The

value of Nd is the number of variables which the designer must assign values to solve

the problem.

How the number of process variables, design relationships, and design variables defines

a system can be best illustrated by considering the simplest system; a single-phase, process

stream.

Consider a single-phase stream, containing C components.

Variable

Number

Stream flow-rate

1

Composition (component concentrations)

C

Temperature

1

Pressure

1

Stream enthalpy

1

Total, Nv D CC 4

Relationships between variables

Number

Composition1

1

Enthalpy2

1

Total, Nr D 2

Degrees of freedom Nd D Nv Nr D CC 4 2 D CC 2

(1) The sum of the mass or mol, fractions, must equal one.

(2) The enthalpy is a function of stream composition, temperature and pressure.

Specifying (CC 2) variables completely defines the stream.

Flash distillation

The idea of degrees of freedom in the design process can be further illustrated by consid-

ering a simple process unit, a flash distillation. (For a description of flash distillation see

Volume 2, Chapter 11).

F2, P2, T2, (xi)2

F3, P3, T3, (xi)3

F1, P1, T1, (xi)1

q

Figure 1.7. Flash distillation

The unit is shown in Figure 1.7, where:

F D stream flow rate,

P D pressure,

T D temperature,

xi D concentration, component i,

q D heat input.

Suffixes, 1 D inlet, 2 D outlet vapour, 3 D outlet liquid.

Variable

Number

Streams (free variables)1

3CC 21

Still

pressure

1

temperature

1

heat input

1

Nr D 3CC 9

Relationship

Number

Material balances (each component)

C

Heat balance, overall

1

v l e relationships2

C

Equilibrium still restriction3

4

2CC 5

Degrees of freedom Nd D 3CC 9 2CC 5 D CC 4

(1) The degrees of freedom for each stream. The total variables in each stream could have been used, and

the stream relationships included in the count of relationships.

This shows how the degrees of freedom for a complex unit can be built up from the degrees of freedom of

its components. For more complex examples see Kwauk (1956).

(2) Given the temperature and pressure, the concentration of any component in the vapour phase can be

obtained from the concentration in the liquid phase, from the vapour liquid equilibrium data for the system.

(3) The concept (definition) of an equilibrium separation implies that the outlet streams and the still are at

the same temperature and pressure. This gives four equations:

P2 D P3 D P

T2 D T3 D T

Though the total degrees of freedom is seen to be (CC 4) some of the variables will

normally be fixed by general process considerations, and will not be free for the designer

to select as “design variables”. The flash distillation unit will normally be one unit in a

process system and the feed composition and feed conditions will be fixed by the upstream

processes; the feed will arise as an outlet stream from some other unit. Defining the feed

fixes (CC 2) variables, so the designer is left with:

CC 4 CC 2 D 2

as design variables.

Summary

The purpose of this discussion was to show that in a design there will be a certain

number of variables that the designer must specify to define the problem, and which he

can manipulate to seek the best design. In manual calculations the designer will rarely

feel for the problem, and can change the calculation procedure, and select the design

variables, as he works through the design. He will know by experience if the problem is

correctly specified. A computer, however, has no intuition, and for computer-aided design

calculations it is essential to ensure that the necessary number of variables is specified to

define the problem correctly. For complex processes the number of variables and relating

equations will be very large, and the calculation of the degrees of freedom very involved.

Kwauk (1956) has shown how the degrees of freedom can be calculated for separation

processes by building up the complex unit from simpler units. Smith (1963) uses Kwauk’s

method, and illustrates how the idea of “degrees of freedom” can be used in the design

of separation processes.

1.9.2. Selection of design variables

In setting out to solve a design problem the designer has to decide which variables are to

be chosen as “design variables”; the ones he will manipulate to produce the best design.

The choice of design variables is important; careful selection can simplify the design

calculations. This can be illustrated by considering the choice of design variables for a

simple binary flash distillation.

For a flash distillation the total degrees of freedom was shown to be (CC 4), so for

two components Nd D 6. If the feed stream flow, composition, temperature and pressure

are fixed by upstream conditions, then the number of design variables will be:

N0d D 6 CC 2 D 6 4 D 2

So the designer is free to select two variables from the remaining variables in order to

proceed with the calculation of the outlet stream compositions and flows.

If he selects the still pressure (which for a binary system will determine the vapour

liquid equilibrium relationship) and one outlet stream flow-rate, then the outlet compo-

sitions can be calculated by simultaneous solution of the mass balance and equilibrium

relationships (equations). A graphical method for the simultaneous solution is given in

Volume 2, Chapter 11.

However, if he selects an outlet stream composition (say the liquid stream) instead of

a flow-rate, then the simultaneous solution of the mass balance and v l e relationships

would not be necessary. The stream compositions could be calculated by the following

step-by-step (sequential) procedure:

1. Specifying P determines the v l e relationship (equilibrium) curve from experi-

mental data.

2. Knowing the outlet liquid composition, the outlet vapour composition can be calcu-

lated from the v l e relationship.

3. Knowing the feed and outlet compositions, and the feed flow-rate, the outlet stream

flows can be calculated from a material balance.

4. An enthalpy balance then gives the heat input required.

The need for simultaneous solution of the design equations implies that there is a

recycle of information. Choice of an outlet stream composition as a design variable in

x3

F2

F3

T

P

F2 (or F3)

Feed

Select

(a)

(b)

F3 (or F2)

x2

x3

T

x2 (or x3)

Direction of calculation

F1

x1

P1

T1

P

x2 (or x3)

Feed

Select

Direction of calculation

F1

x1

P1

T1

Figure 1.8.

Information flow, binary flash distillation calculation (a) Information recycle (b) Information flow

reversal

effect reverses the flow of information through the problem and removes the recycle; this

is shown diagrammatically in Figure 1.8.

1.9.3. Information flow and the structure of design problems

It was shown in Section 1.9.2. by studying a relatively simple problem, that the way

in which the designer selects his design variables can determine whether the design

calculations will prove to be easy or difficult. Selection of one particular set of variables

can lead to a straightforward, step-by-step, procedure, whereas selection of another set

can force the need for simultaneous solution of some of the relationships; which often

requires an iterative procedure (cut-and-try method). How the choice of design variables,

inputs to the calculation procedure, affects the ease of solution for the general design

problem can be illustrated by studying the flow of information, using simple information

flow diagrams. The method used will be that given by Lee et al. (1966) who used a form

of directed graph; a biparte graph, see Berge (1962).

The general design problem can be represented in mathematical symbolism as a series

of equations:

fivj D 0

where j D 1, 2, 3,..., Nv,

i D 1, 2, 3,..., Nr

Consider the following set of such equations:

f1v1, v2 D 0

f2v1, v2, v3, v5 D 0

f4v2, v4, v5, v6 D 0

f5v5, v6, v7 D 0

There are seven variables, Nv D 7, and five equations (relationships) Nr D 5, so the

number of degrees of freedom is:

Nd D Nv Nr D 7 5 D 2

The task is to select two variables from the total of seven in such a way as to give the

simplest, most efficient, method of solution to the seven equations. There are twenty-one

ways of selecting two items from seven.

In Lee’s method the equations and variables are represented by nodes on the biparte

graph (circles), connected by edges (lines), as shown in Figure 1.9.

f1

v1

v1

f node

v node

Figure 1.9. Nodes and edges on a biparte graph

Figure 1.9 shows that equation f1 contains (is connected to) variables v1 and v2. The

complete graph for the set of equations is shown in Figure 1.10.

f1

f2

f3

f4

v1

v2

v3

v4

v5

v6

v7

f5

Figure 1.10. Biparte graph for the complete set of equations

The number of edges connected to a node defines the local degree of the node p.

For example, the local degree of the f1 node is 2, pf1 D 2, and at the v5 node it is 3,

pv5 D 3. Assigning directions to the edges of Figure 1.10 (by putting arrows on the

lines) identifies one possible order of solution for the equations. If a variable vj is defined

as an output variable from an equation fi, then the direction of information flow is from

the node fi to the node vj and all other edges will be oriented into fi. What this means,

mathematically, is that assigning vj as an output from fi rearranges that equation so that:

fiv1, v2,... , vn D vj

vj is calculated from equation fi.

assigned as output variables from an f node. They are inputs to the system and their edges

must be oriented into the system of equations.

If, for instance, variables v3 and v4 are selected as design variables, then Figure 1.11

shows one possible order of solution of the set of equations. Different types of arrows

are used to distinguish between input and output variables, and the variables selected as

design variables are enclosed in a double circle.

f1

f2

f3

f4

f5

v1

v2

v5

v6

v7

v3

v4

Design variables (inputs)

Inputs

Outputs

Figure 1.11. An order of solution

Tracing the order of the solution of the equations as shown in Figure 1.11 shows how

the information flows through the system of equations:

1. Fixing v3 and v4 enables f3 to be solved, giving v1 as the output. v1 is an input to

f1 and f2.

2. With v1 as an input, f1 can be solved giving v2; v2 is an input to f2 and f4.

3. Knowing v3, v1 and v2, f2 can be solved to give v5; v5 is an input to f4 and f5.

4. Knowing v4, v2 and v5, f4 can be solved to give v6; v6 is an input to f5.

5. Knowing v6 and v5, f5 can be solved to give v7; which completes the solution.

This order of calculation can be shown more clearly by redrawing Figure 1.11 as shown

in Figure 1.12.

f3

f1

f2

f4

f5

v1

v2

v5

v6

v7

v3

v4

v2

v5

v3

v4

Figure 1.12. Figure 1.11 redrawn to show order of solution

taneous solution of any of the equations. The fortuitous selection of v3 and v4 as design

variables has given an efficient order of solution of the equations.

If for a set of equations an order of solution exists such that there is no need for the

simultaneous solution of any of the equations, the system is said to be “acyclic”, no

recycle of information.

If another pair of variables had been selected, for instance v5 and v7, an acyclic order

of solution for the set of equations would not necessarily have been obtained.

For many design calculations it will not be possible to select the design variables so as

to eliminate the recycle of information and obviate the need for iterative solution of the

design relationships.

For example, the set of equations given below will be cyclic for all choices of the two

possible design variables.

f1x1,x2 D 0

f2x1,x3,x4 D 0

f3x2,x3,x4,x5,x6 D 0

f4x4,x5,x6 D 0

Nd D 6 4 D 2

The biparte graph for this example, with x3 and x5 selected as the design variables

(inputs), is shown in Figure 1.13.

f1

f2

f3

f4

x6

x4

x2

x1

x3

x5

Figure 1.13.

One strategy for the solution of this cyclic set of equations would be to guess (assign

a value to) x6. The equations could then be solved sequentially, as shown in Figure 1.14,

to produce a calculated value for x6, which could be compared with the assumed value

and the procedure repeated until a satisfactory convergence of the assumed and calculated

value had been obtained. Assigning a value to x6 is equivalent to “tearing” the recycle

loop at x6 (Figure 1.15). Iterative methods for the solution of equations are discussed by

Henley and Rosen (1969).

When a design problem cannot be reduced to an acyclic form by judicious selection of

the design variables, the design variables should be chosen so as to reduce the recycle of

f1

f2

f3

f4

x6

x6

x4

x2

x1

3

5

Assumed

value

Calculated

value

Figure 1.14.

f4

f2

f1

f3

x6

x5

x3

x5

x6

x4

x4

x1

x3

x2

Figure 1.15.

information to a minimum. Lee and Rudd (1966) and Rudd and Watson (1968) give an

algorithm that can be used to help in the selection of the best design variables in manual

calculations.

The recycle of information, often associated with the actual recycle of process material,

will usually occur in any design problem involving large sets of equations; such as in the

computer simulation of chemical processes. Efficient methods for the solution of sets of

equations are required in computer-aided design procedures to reduce the computer time

needed. Several workers have published algorithms for the efficient ordering of recycle

loops for iterative solution procedures, and some references to this work are given in the

chapter on flow-sheeting, Chapter 4.

1.10. OPTIMISATION

Design is optimisation: the designer seeks the best, the optimum, solution to a problem.

Much of the selection and choice in the design process will depend on the intuitive

judgement of the designer; who must decide when more formal optimisation techniques

can be used to advantage.

The task of formally optimising the design of a complex processing plant involving

several hundred variables, with complex interactions, is formidable, if not impossible.

The task can be reduced by dividing the process into more manageable units, identifying

the key variables and concentrating work where the effort involved will give the greatest

necessarily give the optimum design for the whole process. The optimisation of one unit

may be at the expense of another. For example, it will usually be satisfactory to optimise

the reflux ratio for a fractionating column independently of the rest of the plant; but if the

column is part of a separation stage following a reactor, in which the product is separated

from the unreacted materials, then the design of the column will interact with, and may

well determine, the optimisation of the reactor design.

In this book the discussion of optimisation methods will, of necessity, be limited to a

brief review of the main techniques used in process and equipment design. The extensive

literature on the subject should be consulted for full details of the methods available, and

their application and limitations; see Beightler and Wilde (1967), Beveridge and Schechter

(1970), Stoecker (1989), Rudd and Watson (1968), Edgar and Himmelblau (2001). The

books by Rudd and Watson (1968) and Edgar and Himmelblau (2001) are particularly

recommended to students.

1.10.1. General procedure

When setting out to optimise any system, the first step is clearly to identify the objective:

the criterion to be used to judge the system performance. In engineering design the

objective will invariably be an economic one. For a chemical process, the overall objective

for the operating company will be to maximise profits. This will give rise to sub-objectives,

which the designer will work to achieve. The main sub-objective will usually be to

minimise operating costs. Other sub-objectives may be to reduce investment, maximise

yield, reduce labour requirements, reduce maintenance, operate safely.

When choosing his objectives the designer must keep in mind the overall objective.

Minimising cost per unit of production will not necessarily maximise profits per unit time;

market factors, such as quality and delivery, may determine the best overall strategy.

The second step is to determine the objective function: the system of equations, and

other relationships, which relate the objective with the variables to be manipulated to

optimise the function. If the objective is economic, it will be necessary to express the

objective function in economic terms (costs).

Difficulties will arise in expressing functions that depend on value judgements; for

example, the social benefits and the social costs that arise from pollution.

The third step is to find the values of the variables that give the optimum value of the

objective function (maximum or minimum). The best techniques to be used for this step

will depend on the complexity of the system and on the particular mathematical model

used to represent the system.

A mathematical model represents the design as a set of equations (relationships) and, as

was shown in Section 1.9.1, it will only be possible to optimise the design if the number

of variables exceeds the number of relationships; there is some degree of freedom in the

system.

1.10.2. Simple models

If the objective function can be expressed as a function of one variable (single degree of

freedom) the function can be differentiated, or plotted, to find the maximum or minimum.

trated in Example 1.1, and in the derivation of the formula for optimum pipe diameter in

Chapter 5. The determination of the economic reflux ratio for a distillation column, which

is discussed in Volume 2, Chapter 11, is an example of the use of a graphical procedure

to find the optimum value.

Example 1.1

The optimum proportions for a cylindrical container. A classical example of the optimi-

sation of a simple function.

The surface area, A, of a closed cylinder is:

A D ð Dð L C 2

4

D2

where D D vessel diameter

L D vessel length (or height)

This will be the objective function which is to be minimised; simplified:

fD ð L D Dð L C D

2

2

equation A

For a given volume, V, the diameter and length are related by:

V D

4

D2 ð L

and

L D 4V

D2

equation B

and the objective function becomes

fD D 4V

D

C D

2

2

Setting the differential of this function zero will give the optimum value for D

4V

D2

C D D 0

D D 3

√

4V

From equation B, the corresponding length will be:

L D 3

√

4V

So for a cylindrical container the minimum surface area to enclose a given volume is

obtained when the length is made equal to the diameter.

In practice, when cost is taken as the objective function, the optimum will be nearer

L D 2D; the proportions of the ubiquitous tin can, and oil drum. This is because the cost

material (the surface area); see Wells (1973).

If the vessel is a pressure vessel the optimum length to diameter ratio will be even

greater, as the thickness of plate required is a direct function of the diameter; see

Chapter 13. Urbaniec (1986) gives procedures for the optimisation of tanks and vessel,

and other process equipment.

1.10.3. Multiple variable problems

The general optimisation problem can be represented mathematically as:

f D fv1, v2, v3,. .., vn

1.2

where f is the objective function and v1, v2, v3,... , vn are the variables.

In a design situation there will be constraints on the possible values of the objective

function, arising from constraints on the variables; such as, minimum flow-rates, maximum

allowable concentrations, and preferred sizes and standards.

Some may be equality constraints, expressed by equations of the form:

m D mv1, v2, v3,. .., vn D 0

1.3

Others as inequality constraints:

p D pv1, v2, v3,.. . , vn Pp

1.4

The problem is to find values for the variables v1 to vn that optimise the objective function:

that give the maximum or minimum value, within the constraints.

Analytical methods

If the objective function can be expressed as a mathematical function the classical methods

of calculus can be used to find the maximum or minimum. Setting the partial derivatives

to zero will produce a set of simultaneous equations that can be solved to find the optimum

values. For the general, unconstrained, objective function, the derivatives will give the

critical points; which may be maximum or minimum, or ridges or valleys. As with single

variable functions, the nature of the first derivative can be found by taking the second

derivative. For most practical design problems the range of values that the variables

can take will be subject to constraints (equations 1.3 and 1.4), and the optimum of the

constrained objective function will not necessarily occur where the partial derivatives

of the objective function are zero. This situation is illustrated in Figure 1.16 for a two-

dimensional problem. For this problem, the optimum will lie on the boundary defined by

the constraint y D a.

The method of Lagrange’s undetermined multipliers is a useful analytical technique for

dealing with problems that have equality constraints (fixed design values). Examples of

the use of this technique for simple design problems are given by Stoecker (1989), Peters

and Timmerhaus (1991) and Boas (1963a).

Feasible region

Minimum of

function

y = a

f(v)v

Figure 1.16. Effect of constraints on optimum of a function

Search methods

The nature of the relationships and constraints in most design problems is such that

the use of analytical methods is not feasible. In these circumstances search methods,

that require only that the objective function can be computed from arbitrary values of

the independent variables, are used. For single variable problems, where the objective

function is unimodal, the simplest approach is to calculate the value of the objective

function at uniformly spaced values of the variable until a maximum (or minimum) value

is obtained. Though this method is not the most efficient, it will not require excessive

computing time for simple problems. Several more efficient search techniques have been

developed, such as the method of the golden section; see Boas (1963b) and Edgar and

Himmelblau (2001).

Efficient search methods will be needed for multi-dimensional problems, as the number

of calculations required and the computer time necessary will be greatly increased,

compared with single variable problems; see Himmelblau (1963), Stoecker (1971),

Beveridge and Schechter (1970), and Baasel (1974).

Two variable problems can be plotted as shown in Figure 1.17. The values of the

objective function are shown as contour lines, as on a map, which are slices through the

three-dimensional model of the function. Seeking the optimum of such a function can be

Yield contours

75%

Temperature

Pressure80%

85%

90%

Figure 1.17. Yield as a function of reactor temperature and pressure

this type of problem is the gradient method (method of steepest ascent, or descent), see

Edgar and Himmelblau (2001).

1.10.4. Linear programming

Linear programming is an optimisation technique that can be used when the objective

function and constraints can be expressed as a linear function of the variables; see Driebeek

(1969), Williams (1967) and Dano (1965).

The technique is useful where the problem is to decide the optimum utilisation of

resources. Many oil companies use linear programming to determine the optimum schedule

of products to be produced from the crude oils available. Algorithms have been developed

for the efficient solution of linear programming problems and the SIMPLEX algorithm,

Dantzig (1963), is the most commonly used.

Examples of the application of linear programming in chemical process plant design

and operation are given by Allen (1971), Rudd and Watson (1968), Stoecker (1991), and

Urbaniec (1986).

1.10.5. Dynamic programming

Dynamic programming is a technique developed for the optimisation of large systems;

see Nemhauser (1966), Bellman (1957) and Aris (1963).

The basic approach used is to divide the system into convenient sub-systems and

optimise each sub-system separately, while taking into account the interactions between

the sub-systems. The decisions made at each stage contribute to the overall systems

objective function, and to optimise the overall objective function an appropriate combi-

nation of the individual stages has to be found. In a typical process plant system the

possible number of combinations of the stage decisions will be very large. The dynamic

programming approach uses Bellman’s “Principle of Optimality”,† which enables the

optimum policy to be found systematically and efficiently by calculating only a fraction

of the possible combinations of stage decisions. The method converts the problem from

the need to deal with “N” optimisation decisions simultaneously to a sequential set of “N”

problems. The application of dynamic programming to design problems is well illustrated

in Rudd and Watson’s book; see also Wells (1973) and Edgar and Himmelblau (2001).

1.10.6. Optimisation of batch and semicontinuous processes

In batch operation there will be periods when product is being produced, followed by non-

productive periods when the product is discharged and the equipment prepared for the

next batch. The rate of production will be determined by the total batch time, productive

† Bellman’s (1957) principle of optimality: “An optimal policy has the property that, whatever the initial state

and the initial decision are, the remaining decisions must constitute an optimal policy with regard to the state

resulting from the first decision.”

Batches per year D 8760 ð plant attainment

batch cycle time

1.5

where the “plant attainment” is the fraction of the total hours in a year (8760) that the

plant is in operation.

Annual production D quantity produced per batch ð batches per year.

Cost per unit of production D annual cost of production

annual production rate

1.6

With many batch processes, the production rate will decrease during the production

period; for example, batch reactors and plate and frame filter presses, and there will

be an optimum batch size, or optimum cycle time, that will give the minimum cost per

unit of production.

For some processes, though they would not be classified as batch processes, the period

of continuous production will be limited by gradual changes in process conditions; such

as, the deactivation of catalysts or the fouling of heat-exchange surfaces. Production will

be lost during the periods when the plant is shut down for catalyst renewal or equipment

clean-up, and, as with batch process, there will be an optimum cycle time to give the

minimum production cost.

The optimum time between shut-downs can be found by determining the relationship

between cycle time and cost per unit of production (the objective function) and using one

of the optimisation techniques outlined in this section to find the minimum.

With discontinuous processes, the period between shut-downs will usually be a function

of equipment size. Increasing the size of critical equipment will extend the production

period, but at the expense of increased capital cost. The designer must strike a balance

between the savings gained by reducing the non-productive period and the increased

investment required.

1.11. REFERENCES

ALLEN, D. H. (1971) Brit. Chem. Eng. 16, 685. Linear programming models.

ARIS, R. (1963) Discrete Dynamic Programming (Blaisdell).

BAASEL, W. D. (1965) Chem. Eng., NY 72 (Oct. 25th) 147. Exploring response surfaces to establish optimum

conditions.

BAASEL, W. D. (1974) Preliminary Chemical Engineering Plant Design (Elsevier).

BEIGHTLER, C. S. and WILDE, D. J. (1967) Foundations of Optimisation (Prentice-Hall).

BELLMAN, R. (1957) Dynamic Programming (Princeton University, New York).

BERGE, C. (1962) Theory of Graphs and its Applications (Wiley).

BEVERIDGE, G. S. G. and SCHECHTER, R. S. (1970) Optimisation: Theory and Practice (McGraw-Hill).

BOAS, A. H. (1963a) Chem. Eng., NY 70 (Jan. 7th) 95. How to use Lagrange multipliers.

BOAS, A. H. (1963b) Chem. Eng., NY 70 (Feb. 4th) 105. How search methods locate optimum in univariate

problems.

BURKLIN, C. R. (1979) The Process Plant Designers Pocket Handbook of Codes and Standards (Gulf).

CASEY, R. J. and FRAZER, M. J. (1984) Problem Solving in the Chemical Industry (Pitman).

CHADDOCK, D. H. (1975) Paper read to S. Wales Branch, Institution of Mechanical Engineers (Feb. 27th).

Thought structure, or what makes a designer tick.

solving approach.

DANO, S. (1965) Linear Programming in Industry (Springer-Verlag).

DANTZIG, G. B. (1963) Linear Programming and Extensions (Princeton University Press).

DRIEBEEK, N. J. (1969) Applied Linear Programming (Addison-Wesley).

EDGAR, T. E. and HIMMELBLAU, D. M., 2nd edn (2001) Optimization of Chemical Processes (McGraw-Hill).

HENLEY, E. J. and ROSEN, E. M. (1969) Material and Energy Balance Computations (Wiley).

HIMMELBLAU, D. M. (1963) Ind. Eng. Chem. Process Design and Development 2, 296. Process optimisation by

search techniques.

JONES, C. J. (1970) Design Methods: Seeds of Human Futures (Wiley).

KWAUK, M. (1956) AIChE Jl 2, 240. A system for counting variables in separation processes.

LEE, W. CHRISTENSEN J. H. and RUDD, D. F. (1966): AIChE Jl 12, 1104. Design variable selection to simplify

process calculations.

LEE, W. and RUDD, D. F. (1966) AIChE Jl 12, 1185. On the ordering of recycle calculations.

NEMHAUSER, G. L. (1966) Introduction to Dynamic Programming (Wiley).

PETERS, M. S. and TIMMERHAUS, K. D. (1991) Plant Design and Economics for Chemical Engineers, 4th edn

(McGraw-Hill).

POLYA, G. (1957) How to Solve It, 2nd edn (Doubleday).

RASE H. F and BARROW, M. H. (1964) Project Engineering (Wiley).

RUDD, D. F. and WATSON, C. C. (1968) Strategy of Process Design (Wiley).

SMITH, B. D. (1963) Design of Equilibrium Stage Processes (McGraw-Hill).

STOECKER, W. F. (1989) Design of Thermal Systems 3rd edn (McGraw-Hill).

URBANIEC, K. (1986) Optimal Design of Process Equipment (Ellis Horwood).

WELLS, G. L. (1973) Process Engineering with Economic Objective (Leonard Hill).

WILDE, D. J. (1964) Optimum Seeking Methods (Prentice-Hall).

WILLIAMS, N. (1967) Linear and Non-linear Programming in Industry (Pitman).

1.12. NOMENCLATURE

Dimensions

in MLTq

C

Number of components

D

Diameter

L

F

Stream flow rate

MT1

f

General function

fi

General function (design relationship)

f1, f2 ... General functions (design relationships)

L

Length

L

Nd

Degrees of freedom in a design problem

N0d

Degrees of freedom (variables free to be selected as design variables)

Nr

Number of design relationships

Nv

Number of variables

P

Pressure

ML1T2

Pp

Inequality constraints

q

Heat input, flash distillation

ML2T3

T

Temperature

q

vj

Variables

v1, v2 ... Variables

x1,x2 ... Variables

Equality constraint function

Inequality constraint function

Suffixes

1

Inlet, flash distillation

2

Vapour outlet, flash distillation

3

Liquid outlet, flash distillation

1.1. Given that 1 in D 25.4 mm; 1 lbm D 0.4536 kg; 1 ŽF D 0.556 ŽC; 1 cal D 4.1868 J;

g D 9.807 m s2, calculate conversion factors to SI units for the following

terms:

i. feet

ii. pounds mass

iii. pounds force

iv. horse power (1 HP D 550 foot pounds per second)

v. psi (pounds per square inch)

vi. lb ft1 s1 (viscosity)

vii. poise (gm cm1 s1)

viii. Btu (British Thermal Unit)

ix. CHU (Centigrade Heat Unit) also known as PCU (Pound Centigrade Unit)

x. Btu ft2 h1 ŽF1 (heat transfer coefficient).

1.2. Determine the degrees of freedom available in the design of a simple heat

exchanger. Take the exchanger as a double-pipe exchanger transferring heat

between two single-phase streams.

1.3. A separator divides a process stream into three phases: a liquid organic stream, a

liquid aqueous stream, and a gas stream. The feed stream contains three compo-

nents, all of which are present to some extent in the separated steams. The compo-

sition and flowrate of the feed stream are known. All the streams will be at the same

temperature and pressure. The phase equilibria for the three phases is available.

How many design variables need to be specified in order to calculate the output

stream compositions and flow rates?

1.4. A rectangular tank with a square base is constructed from 5 mm steel plates. If

the capacity required is eight cubic metres determine the optimum dimensions if

the tank has:

i. a closed top

ii. an open top.

1.5. Estimate the optimum thickness of insulation for the roof of a house, given the

following information. The insulation will be installed flat on the attic floor.

Overall heat transfer coefficient for the insulation as a function of thickness, U

values (see Chapter 12):

thickness, mm

0

25

50

100

150

200

250

U, Wm2 ŽC1

20

0.9

0.7

0.3

0.25

0.20

0.15

Average temperature difference between inside and outside of house 10 ŽC; heating

period 200 days in a year.

Cost of insulation, including installation, £70/m3. Capital charges (see Chapter 6)

15 per cent per year. Cost of fuel, allowing for the efficiency of the heating

system, 6p/MJ.

Note: the rate at which heat is being lost is given by U ðT, W/m2, where U

is the overall coefficient and T the temperature difference; see Chapter 12.

given the following information. The insulation will be installed flat on the attic

floor.

Overall heat transfer coefficient for the insulation as a function of thickness, U

values (see Chapter 12):

thickness, mm

0

25

50

100

150

200

250

U, Wm2 ŽC1

20

0.9

0.7

0.3

0.25

0.20

0.15

Average temperature difference between inside and outside of house 12 ŽC; heating

period 250 days in a year. Cost of insulation, including installation, $120/m3.

Capital charges (see chapter 6) 20 per cent per year. Cost of fuel, allowing for the

efficiency of the heating system, 9c/MJ.

Note: the rate at which heat is being lost is given by UðT, W/m2, where U

is the overall coefficient and T the temperature difference; see Chapter 12.

1.7. What is the optimum practical shape for a dwelling, to minimise the heat losses

through the building fabric?

Why is this optimum shape seldom used?

What people do use the optimum shape for their winter dwellings? Is heat retention

their only consideration in their selection of this shape?

1.8. You are part of the design team working on a project for the manufacture of

cyclohexane.

The chief engineer calls you into his office and asks you to prepare an outline

design for an inert gas purging and blanketing system for the reactors and other

equipment, on shutdown. This request arises from a report into an explosion and

fire at another site manufacturing a similar product.

Following the steps given in Figure 1.2, find what you consider the best solution

to this design problem.

CHAPTER 2

Fundamentals of Material Balances

2.1. INTRODUCTION

Material balances are the basis of process design. A material balance taken over the

complete process will determine the quantities of raw materials required and products

produced. Balances over individual process units set the process stream flows and

compositions.

A good understanding of material balance calculations is essential in process design.

In this chapter the fundamentals of the subject are covered, using simple examples to

illustrate each topic. Practice is needed to develop expertise in handling what can often

become very involved calculations. More examples and a more detailed discussion of the

subject can be found in the numerous specialist books written on material and energy

balance computations. Several suitable texts are listed under the heading of “Further

Reading” at the end of this chapter.

The application of material balances to more complex problems is discussed in “Flow-

sheeting”, Chapter 4.

Material balances are also useful tools for the study of plant operation and trouble

shooting. They can be used to check performance against design; to extend the often

limited data available from the plant instrumentation; to check instrument calibrations;

and to locate sources of material loss.

2.2. THE EQUIVALENCE OF MASS AND ENERGY

Einstein showed that mass and energy are equivalent. Energy can be converted into mass,

and mass into energy. They are related by Einstein’s equation:

E D mc2

2.1

where E D energy, J,

m D mass, kg,

c D the speed of light in vacuo, 3 ð 108 m/s.

The loss of mass associated with the production of energy is significant only in nuclear

reactions. Energy and matter are always considered to be separately conserved in chemical

reactions.

2.3. CONSERVATION OF MASS

The general conservation equation for any process system can be written as:

Material out D Material in C Generation Consumption Accumulation

34

mass is neither generated nor consumed; but if a chemical reaction takes place a particular

chemical species may be formed or consumed in the process. If there is no chemical

reaction the steady-state balance reduces to

Material out D Material in

A balance equation can be written for each separately identifiable species present, elements,

compounds or radicals; and for the total material.

Example 2.1

2000 kg of a 5 per cent slurry of calcium hydroxide in water is to be prepared by diluting

a 20 per cent slurry. Calculate the quantities required. The percentages are by weight.

Solution

Let the unknown quantities of the 20% slurry and water be X and Y respectively.

Material balance on Ca(OH)2

In

Out

X

20

100

D 2000 ð 5

100

a

Balance on water

X

100 20

100

C Y D 2000 100 5

100

b

From equation a X D 500 kg.

Substituting into equation b gives Y D 1500 kg

Check material balance on total quantity:

XC Y D 2000

500 C 1500 D 2000, correct

2.4. UNITS USED TO EXPRESS COMPOSITIONS

When specifying a composition as a percentage it is important to state clearly the basis:

weight, molar or volume.

The abbreviations w/w and v/v are used to designate weight basis and volume basis.

Example 2.2

Technical grade hydrochloric acid has a strength of 28 per cent w/w, express this as a

mol fraction.

Basis of calculation 100 kg of 28 per cent w/w acid.

Molecular mass: water 18, HCl 36.5

Mass HCl D 100 ð 0.28 D 28 kg

Mass water D 100 ð 0.72 D 72 kg

kmol HCl D 28

36.5

D 0.77

kmol water D 72

18

D 4.00

Total mols

D 4.77

mol fraction HCl D 0.77

4.77

D 0.16

mol fraction water D 4.00

4.77

D 0.84

Check total

1.00

Within the accuracy needed for technical calculations, volume fractions can be taken

as equivalent to mol fractions for gases, up to moderate pressures (say 25 bar).

Trace quantities are often expressed as parts per million (ppm). The basis, weight or

volume, needs to be stated.

ppm D quantity of component

total quantity

ð 106

Note. 1 ppm D 104 per cent.

Minute quantities are sometimes quoted in ppb, parts per billion. Care is needed here,

as the billion is usually an American billion (109), not the UK billion (1012).

2.5. STOICHIOMETRY

Stoichiometry (from the Greek stoikeion

element) is the practical application of the

law of multiple proportions. The stoichiometric equation for a chemical reaction states

unambiguously the number of molecules of the reactants and products that take part; from

which the quantities can be calculated. The equation must balance.

With simple reactions it is usually possible to balance the stoichiometric equation by

inspection, or by trial and error calculations. If difficulty is experienced in balancing

complex equations, the problem can always be solved by writing a balance for each

element present. The procedure is illustrated in Example 2.3.

Example 2.3

Write out and balance the overall equation for the manufacture of vinyl chloride from

ethylene, chlorine and oxygen.

CHEMICAL ENGINEERING

VOLUME 6

Chemical Engineering, Volume 1, Sixth edition

Fluid Flow, Heat Transfer and Mass Transfer

J. M. Coulson and J. F. Richardson

with J. R. Backhurst and J. H. Harker

Chemical Engineering, Volume 2, Fifth edition

Particle Technology and Separation Processes

J. F. Richardson and J. H. Harker

with J. R. Backhurst

Chemical Engineering, Volume 3, Third edition

Chemical & Biochemical Reactors & Process Control

Edited by J. F. Richardson and D. G. Peacock

Chemical Engineering, Second edition

Solutions to the Problems in Volume 1

J. R. Backhurst and J. H. Harker with J. F. Richardson

Chemical Engineering, Solutions to the Problems

in Volumes 2 and 3

J. R. Backhurst and J. H. Harker with J. F. Richardson

Chemical Engineering, Volume 6, Fourth edition

Chemical Engineering Design

R. K. Sinnott

Coulson & Richardson’s

CHEMICAL ENGINEERING

VOLUME 6

FOURTH EDITION

Chemical Engineering Design

R. K. SINNOTT

AMSTERDAM ž BOSTON ž HEIDELBERG ž LONDON ž NEW YORK ž OXFORD

PARIS ž SAN DIEGO ž SAN FRANCISCO ž SINGAPORE ž SYDNEY ž TOKYO

Linacre House, Jordan Hill, Oxford OX2 8DP

30 Corporate Drive, MA 01803

First published 1983

Second edition 1993

Reprinted with corrections 1994

Reprinted with revisions 1996

Third edition 1999

Reprinted 2001, 2003

Fourth edition 2005

Copyright 1993, 1996, 1999, 2005 R. K. Sinnott. All rights reserved

The right of R. K. Sinnott to be identified as the author of this work

has been asserted in accordance with the Copyright, Designs and

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permission to reproduce any part of this publication should be addressed

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Typeset by Laserwords Private Limited, Chennai, India

Contents

PREFACE TO FOURTH EDITION

xvii

PREFACE TO THIRD EDITION

xx

PREFACE TO SECOND EDITION

xxi

PREFACE TO FIRST EDITION

xxiii

SERIES EDITOR’S PREFACE

xxiv

ACKNOWLEDGEMENT

xxv

1

Introduction to Design

1

1.1

Introduction

1

1.2

Nature of design

1

1.2.1

The design objective (the need)

3

1.2.2

Data collection

3

1.2.3

Generation of possible design solutions

3

1.2.4

Selection

4

1.3

The anatomy of a chemical manufacturing process

5

1.3.1

Continuous and batch processes

7

1.4

The organisation of a chemical engineering project

7

1.5

Project documentation

10

1.6

Codes and standards

12

1.7

Factors of safety (design factors)

13

1.8

Systems of units

14

1.9

Degrees of freedom and design variables. The mathematical representation

of the design problem

15

1.9.1

Information flow and design variables

15

1.9.2

Selection of design variables

19

1.9.3

Information flow and the structure of design problems

20

1.10 Optimisation

24

1.10.1

General procedure

25

1.10.2

Simple models

25

1.10.3 Multiple variable problems

27

1.10.4

Linear programming

29

1.10.5

Dynamic programming

29

1.10.6

Optimisation of batch and semicontinuous processes

29

1.11 References

30

1.12 Nomenclature

31

1.13 Problems

32

2 Fundamentals of Material Balances

34

2.1

Introduction

34

2.2

The equivalence of mass and energy

34

2.3

Conservation of mass

34

2.4

Units used to express compositions

35

2.5

Stoichiometry

36

v

2.7

Choice of basis for calculations

40

2.8

Number of independent components

40

2.9

Constraints on flows and compositions

41

2.10 General algebraic method

42

2.11 Tie components

44

2.12 Excess reagent

46

2.13 Conversion and yield

47

2.14 Recycle processes

50

2.15 Purge

52

2.16 By-pass

53

2.17 Unsteady-state calculations

54

2.18 General procedure for material-balance problems

56

2.19 References (Further Reading)

57

2.20 Nomenclature

57

2.21 Problems

57

3 Fundamentals of Energy Balances (and Energy Utilisation)

60

3.1

Introduction

60

3.2

Conservation of energy

60

3.3

Forms of energy (per unit mass of material)

61

3.3.1

Potential energy

61

3.3.2

Kinetic energy

61

3.3.3

Internal energy

61

3.3.4

Work

61

3.3.5

Heat

62

3.3.6

Electrical energy

62

3.4

The energy balance

62

3.5

Calculation of specific enthalpy

67

3.6 Mean heat capacities

68

3.7

The effect of pressure on heat capacity

70

3.8

Enthalpy of mixtures

71

3.8.1

Integral heats of solution

72

3.9

Enthalpy-concentration diagrams

73

3.10 Heats of reaction

75

3.10.1

Effect of pressure on heats of reaction

77

3.11 Standard heats of formation

79

3.12 Heats of combustion

80

3.13 Compression and expansion of gases

81

3.13.1 Mollier diagrams

82

3.13.2

Polytropic compression and expansion

84

3.13.3 Multistage compressors

90

3.13.4

Electrical drives

93

3.14 Energy balance calculations

93

3.15 Unsteady state energy balances

99

3.16 Energy recovery

101

3.16.1

Heat exchange

101

3.16.2

Heat-exchanger networks

101

3.16.3 Waste-heat boilers

102

3.16.4

High-temperature reactors

103

3.16.5

Low-grade fuels

105

3.16.6

High-pressure process streams

107

3.16.7

Heat pumps

110

3.17 Process integration and pinch technology

111

3.17.1

Pinch technology

111

3.17.2

The problem table method

115

3.17.3

The heat exchanger network

117

3.17.4 Minimum number of exchangers

121

3.17.5

Threshold problems

123

3.17.7

Process integration: integration of other process operations

124

3.18 References

127

3.19 Nomenclature

128

3.20 Problems

130

4 Flow-sheeting

133

4.1

Introduction

133

4.2

Flow-sheet presentation

133

4.2.1

Block diagrams

134

4.2.2

Pictorial representation

134

4.2.3

Presentation of stream flow-rates

134

4.2.4

Information to be included

135

4.2.5

Layout

139

4.2.6

Precision of data

139

4.2.7

Basis of the calculation

140

4.2.8

Batch processes

140

4.2.9

Services (utilities)

140

4.2.10

Equipment identification

140

4.2.11

Computer aided drafting

140

4.3 Manual flow-sheet calculations

141

4.3.1

Basis for the flow-sheet calculations

142

4.3.2

Flow-sheet calculations on individual units

143

4.4

Computer-aided flow-sheeting

168

4.5

Full steady-state simulation programs

168

4.5.1

Information flow diagrams

171

4.6 Manual calculations with recycle streams

172

4.6.1

The split-fraction concept

172

4.6.2

Illustration of the method

176

4.6.3

Guide rules for estimating split-fraction coefficients

185

4.7

References

187

4.8

Nomenclature

188

4.9

Problems

188

5 Piping and Instrumentation

194

5.1

Introduction

194

5.2

The P and I diagram

194

5.2.1

Symbols and layout

195

5.2.2

Basic symbols

195

5.3

Valve selection

197

5.4

Pumps

199

5.4.1

Pump selection

199

5.4.2

Pressure drop in pipelines

201

5.4.3

Power requirements for pumping liquids

206

5.4.4

Characteristic curves for centrifugal pumps

208

5.4.5

System curve (operating line)

210

5.4.6

Net positive suction head (NPSH)

212

5.4.7

Pump and other shaft seals

213

5.5 Mechanical design of piping systems

216

5.5.1

Wall thickness: pipe schedule

216

5.5.2

Pipe supports

217

5.5.3

Pipe fittings

217

5.5.4

Pipe stressing

217

5.5.5

Layout and design

218

5.6

Pipe size selection

218

5.7

Control and instrumentation

227

5.7.1

Instruments

227

5.7.2

Instrumentation and control objectives

227

5.7.3

Automatic-control schemes

228

5.8.1

Level control

229

5.8.2

Pressure control

229

5.8.3

Flow control

229

5.8.4

Heat exchangers

230

5.8.5

Cascade control

231

5.8.6

Ratio control

231

5.8.7

Distillation column control

231

5.8.8

Reactor control

233

5.9

Alarms and safety trips, and interlocks

235

5.10 Computers and microprocessors in process control

236

5.11 References

238

5.12 Nomenclature

239

5.13 Problems

240

6 Costing and Project Evaluation

243

6.1

Introduction

243

6.2

Accuracy and purpose of capital cost estimates

243

6.3

Fixed and working capital

244

6.4

Cost escalation (inflation)

245

6.5

Rapid capital cost estimating methods

247

6.5.1

Historical costs

247

6.5.2

Step counting methods

249

6.6

The factorial method of cost estimation

250

6.6.1

Lang factors

251

6.6.2

Detailed factorial estimates

251

6.7

Estimation of purchased equipment costs

253

6.8

Summary of the factorial method

260

6.9

Operating costs

260

6.9.1

Estimation of operating costs

261

6.10 Economic evaluation of projects

270

6.10.1

Cash flow and cash-flow diagrams

270

6.10.2

Tax and depreciation

272

6.10.3

Discounted cash flow (time value of money)

272

6.10.4

Rate of return calculations

273

6.10.5

Discounted cash-flow rate of return (DCFRR)

273

6.10.6

Pay-back time

274

6.10.7

Allowing for inflation

274

6.10.8

Sensitivity analysis

274

6.10.9

Summary

275

6.11 Computer methods for costing and project evaluation

278

6.12 References

279

6.13 Nomenclature

279

6.14 Problems

280

7 Materials of Construction

284

7.1

Introduction

284

7.2 Material properties

284

7.3 Mechanical properties

285

7.3.1

Tensile strength

285

7.3.2

Stiffness

285

7.3.3

Toughness

286

7.3.4

Hardness

286

7.3.5

Fatigue

286

7.3.6

Creep

287

7.3.7

Effect of temperature on the mechanical properties

287

7.4

Corrosion resistance

287

7.4.1

Uniform corrosion

288

7.4.2

Galvanic corrosion

289

7.4.4

Intergranular corrosion

290

7.4.5

Effect of stress

290

7.4.6

Erosion-corrosion

291

7.4.7

High-temperature oxidation

291

7.4.8

Hydrogen embrittlement

292

7.5

Selection for corrosion resistance

292

7.6 Material costs

293

7.7

Contamination

294

7.7.1

Surface finish

295

7.8

Commonly used materials of construction

295

7.8.1

Iron and steel

295

7.8.2

Stainless steel

296

7.8.3

Nickel

298

7.8.4

Monel

299

7.8.5

Inconel

299

7.8.6

The Hastelloys

299

7.8.7

Copper and copper alloys

299

7.8.8

Aluminium and its alloys

299

7.8.9

Lead

300

7.8.10

Titanium

300

7.8.11

Tantalum

300

7.8.12

Zirconium

300

7.8.13

Silver

301

7.8.14

Gold

301

7.8.15

Platinum

301

7.9

Plastics as materials of construction for chemical plant

301

7.9.1

Poly-vinyl chloride (PVC)

302

7.9.2

Polyolefines

302

7.9.3

Polytetrafluroethylene (PTFE)

302

7.9.4

Polyvinylidene fluoride (PVDF)

302

7.9.5

Glass-fibre reinforced plastics (GRP)

302

7.9.6

Rubber

303

7.10 Ceramic materials (silicate materials)

303

7.10.1

Glass

304

7.10.2

Stoneware

304

7.10.3

Acid-resistant bricks and tiles

304

7.10.4

Refractory materials (refractories)

304

7.11 Carbon

305

7.12 Protective coatings

305

7.13 Design for corrosion resistance

305

7.14 References

305

7.15 Nomenclature

307

7.16 Problems

307

8 Design Information and Data

309

8.1

Introduction

309

8.2

Sources of information on manufacturing processes

309

8.3

General sources of physical properties

311

8.4

Accuracy required of engineering data

312

8.5

Prediction of physical properties

313

8.6

Density

314

8.6.1

Liquids

314

8.6.2

Gas and vapour density (specific volume)

315

8.7

Viscosity

316

8.7.1

Liquids

316

8.7.2

Gases

320

8.8

Thermal conductivity

320

8.8.1

Solids

320

8.8.2

Liquids

321

8.8.4

Mixtures

322

8.9

Specific heat capacity

322

8.9.1

Solids and liquids

322

8.9.2

Gases

325

8.10 Enthalpy of vaporisation (latent heat)

328

8.10.1 Mixtures

329

8.11 Vapour pressure

330

8.12 Diffusion coefficients (diffusivities)

331

8.12.1

Gases

331

8.12.2

Liquids

333

8.13 Surface tension

335

8.13.1 Mixtures

335

8.14 Critical constants

336

8.15 Enthalpy of reaction and enthalpy of formation

339

8.16 Phase equilibrium data

339

8.16.1

Experimental data

339

8.16.2

Phase equilibria

339

8.16.3

Equations of state

341

8.16.4

Correlations for liquid phase activity coefficients

342

8.16.5

Prediction of vapour-liquid equilibria

346

8.16.6 K -values for hydrocarbons

348

8.16.7

Sour-water systems (Sour)

348

8.16.8

Vapour-liquid equilibria at high pressures

348

8.16.9

Liquid-liquid equilibria

348

8.16.10 Choice of phase equilibria for design calculations

350

8.16.11 Gas solubilities

351

8.16.12 Use of equations of state to estimate specific enthalpy and density

353

8.17 References

353

8.18 Nomenclature

357

8.19 Problems

358

9 Safety and Loss Prevention

360

9.1

Introduction

360

9.2

Intrinsic and extrinsic safety

361

9.3

The hazards

361

9.3.1

Toxicity

361

9.3.2

Flammability

363

9.3.3

Explosions

365

9.3.4

Sources of ignition

366

9.3.5

Ionising radiation

368

9.3.6

Pressure

368

9.3.7

Temperature deviations

369

9.3.8

Noise

370

9.4

Dow fire and explosion index

371

9.4.1

Calculation of the Dow F & EI

371

9.4.2

Potential loss

375

9.4.3

Basic preventative and protective measures

377

9.4.4

Mond fire, explosion, and toxicity index

378

9.4.5

Summary

379

9.5

Hazard and operability studies

381

9.5.1

Basic principles

382

9.5.2

Explanation of guide words

383

9.5.3

Procedure

384

9.6

Hazard analysis

389

9.7

Acceptable risk and safety priorities

390

9.8

Safety check lists

392

9.9 Major hazards

394

9.9.1

Computer software for quantitative risk analysis

395

9.11 Problems

398

10 Equipment Selection, Specification and Design

400

10.1

Introduction

400

10.2 Separation processes

401

10.3 Solid-solid separations

401

10.3.1

Screening (sieving)

401

10.3.2

Liquid-solid cyclones

404

10.3.3

Hydroseparators and sizers (classifiers)

405

10.3.4

Hydraulic jigs

405

10.3.5

Tables

405

10.3.6

Classifying centrifuges

406

10.3.7

Dense-medium separators (sink and float processes)

406

10.3.8

Flotation separators (froth-flotation)

407

10.3.9

Magnetic separators

407

10.3.10 Electrostatic separators

408

10.4 Liquid-solid (solid-liquid) separators

408

10.4.1

Thickeners and clarifiers

408

10.4.2

Filtration

409

10.4.3

Centrifuges

415

10.4.4

Hydrocyclones (liquid-cyclones)

422

10.4.5

Pressing (expression)

426

10.4.6

Solids drying

426

10.5 Separation of dissolved solids

434

10.5.1

Evaporators

434

10.5.2

Crystallisation

437

10.6 Liquid-liquid separation

440

10.6.1

Decanters (settlers)

440

10.6.2

Plate separators

445

10.6.3

Coalescers

445

10.6.4

Centrifugal separators

446

10.7 Separation of dissolved liquids

446

10.7.1

Solvent extraction and leaching

447

10.8 Gas-solids separations (gas cleaning)

448

10.8.1

Gravity settlers (settling chambers)

448

10.8.2

Impingement separators

448

10.8.3

Centrifugal separators (cyclones)

450

10.8.4

Filters

458

10.8.5 Wet scrubbers (washing)

459

10.8.6

Electrostatic precipitators

459

10.9 Gas liquid separators

460

10.9.1

Settling velocity

461

10.9.2

Vertical separators

461

10.9.3

Horizontal separators

463

10.10 Crushing and grinding (comminution) equipment

465

10.11 Mixing equipment

468

10.11.1 Gas mixing

468

10.11.2 Liquid mixing

468

10.11.3 Solids and pastes

476

10.12 Transport and storage of materials

476

10.12.1 Gases

477

10.12.2 Liquids

479

10.12.3 Solids

481

10.13 Reactors

482

10.13.1 Principal types of reactor

483

10.13.2 Design procedure

486

10.14 References

486

10.15 Nomenclature

490

10.16 Problems

491

11.1

Introduction

493

11.2 Continuous distillation: process description

494

11.2.1

Reflux considerations

495

11.2.2

Feed-point location

496

11.2.3

Selection of column pressure

496

11.3 Continuous distillation: basic principles

497

11.3.1

Stage equations

497

11.3.2

Dew points and bubble points

498

11.3.3

Equilibrium flash calculations

499

11.4 Design variables in distillation

501

11.5 Design methods for binary systems

503

11.5.1

Basic equations

503

11.5.2

McCabe-Thiele method

505

11.5.3

Low product concentrations

507

11.5.4

The Smoker equations

512

11.6 Multicomponent distillation: general considerations

515

11.6.1

Key components

516

11.6.2

Number and sequencing of columns

517

11.7 Multicomponent distillation: short-cut methods for stage and reflux requirements

517

11.7.1

Pseudo-binary systems

518

11.7.2

Smith-Brinkley method

522

11.7.3

Empirical correlations

523

11.7.4

Distribution of non-key components (graphical method)

526

11.8 Multicomponent systems: rigorous solution procedures (computer methods)

542

11.8.1

Lewis-Matheson method

543

11.8.2

Thiele-Geddes method

544

11.8.3

Relaxation methods

545

11.8.4

Linear algebra methods

545

11.9 Other distillation systems

546

11.9.1

Batch distillation

546

11.9.2

Steam distillation

546

11.9.3

Reactive distillation

547

11.10 Plate efficiency

547

11.10.1 Prediction of plate efficiency

548

11.10.2 O’Connell’s correlation

550

11.10.3 Van Winkle’s correlation

552

11.10.4 AIChE method

553

11.10.5 Entrainment

556

11.11 Approximate column sizing

557

11.12 Plate contactors

557

11.12.1 Selection of plate type

560

11.12.2 Plate construction

561

11.13 Plate hydraulic design

565

11.13.1 Plate-design procedure

567

11.13.2 Plate areas

567

11.13.3 Diameter

567

11.13.4 Liquid-flow arrangement

569

11.13.5 Entrainment

570

11.13.6 Weep point

571

11.13.7 Weir liquid crest

572

11.13.8 Weir dimensions

572

11.13.9 Perforated area

572

11.13.10 Hole size

573

11.13.11 Hole pitch

574

11.13.12 Hydraulic gradient

574

11.13.13 Liquid throw

575

11.13.14 Plate pressure drop

575

11.13.15 Downcomer design [back-up]

577

11.14 Packed columns

587

11.14.1 Types of packing

589

11.14.3 Prediction of the height of a transfer unit (HTU)

597

11.14.4 Column diameter (capacity)

602

11.14.5 Column internals

609

11.14.6 Wetting rates

616

11.15 Column auxiliaries

616

11.16 Solvent extraction (liquid liquid extraction)

617

11.16.1 Extraction equipment

617

11.16.2 Extractor design

618

11.16.3 Extraction columns

623

11.16.4 Supercritical fluid extraction

624

11.17 References

624

11.18 Nomenclature

627

11.19 Problems

630

12 Heat-transfer Equipment

634

12.1

Introduction

634

12.2 Basic design procedure and theory

635

12.2.1

Heat exchanger analysis: the effectiveness NTU method

636

12.3 Overall heat-transfer coefficient

636

12.4 Fouling factors (dirt factors)

638

12.5 Shell and tube exchangers: construction details

640

12.5.1

Heat-exchanger standards and codes

644

12.5.2

Tubes

645

12.5.3

Shells

647

12.5.4

Tube-sheet layout (tube count)

647

12.5.5

Shell types (passes)

649

12.5.6

Shell and tube designation

649

12.5.7

Baffles

650

12.5.8

Support plates and tie rods

652

12.5.9

Tube sheets (plates)

652

12.5.10 Shell and header nozzles (branches)

653

12.5.11 Flow-induced tube vibrations

653

12.6 Mean temperature difference (temperature driving force)

655

12.7 Shell and tube exchangers: general design considerations

660

12.7.1

Fluid allocation: shell or tubes

660

12.7.2

Shell and tube fluid velocities

660

12.7.3

Stream temperatures

661

12.7.4

Pressure drop

661

12.7.5

Fluid physical properties

661

12.8 Tube-side heat-transfer coefficient and pressure drop (single phase)

662

12.8.1

Heat transfer

662

12.8.2

Tube-side pressure drop

666

12.9 Shell-side heat-transfer and pressure drop (single phase)

669

12.9.1

Flow pattern

669

12.9.2

Design methods

670

12.9.3

Kern’s method

671

12.9.4

Bell’s method

693

12.9.5

Shell and bundle geometry

702

12.9.6

Effect of fouling on pressure drop

705

12.9.7

Pressure-drop limitations

705

12.10 Condensers

709

12.10.1 Heat-transfer fundamentals

710

12.10.2 Condensation outside horizontal tubes

710

12.10.3 Condensation inside and outside vertical tubes

711

12.10.4 Condensation inside horizontal tubes

716

12.10.5 Condensation of steam

717

12.10.6 Mean temperature difference

717

12.10.7 Desuperheating and sub-cooling

717

12.10.9 Pressure drop in condensers

723

12.11 Reboilers and vaporisers

728

12.11.1 Boiling heat-transfer fundamentals

731

12.11.2 Pool boiling

732

12.11.3 Convective boiling

735

12.11.4 Design of forced-circulation reboilers

740

12.11.5 Design of thermosyphon reboilers

741

12.11.6 Design of kettle reboilers

750

12.12 Plate heat exchangers

756

12.12.1 Gasketed plate heat exchangers

756

12.12.2 Welded plate

764

12.12.3 Plate-fin

764

12.12.4 Spiral heat exchangers

765

12.13 Direct-contact heat exchangers

766

12.14 Finned tubes

767

12.15 Double-pipe heat exchangers

768

12.16 Air-cooled exchangers

769

12.17 Fired heaters (furnaces and boilers)

769

12.17.1 Basic construction

770

12.17.2 Design

771

12.17.3 Heat transfer

772

12.17.4 Pressure drop

774

12.17.5 Process-side heat transfer and pressure drop

774

12.17.6 Stack design

774

12.17.7 Thermal efficiency

775

12.18 Heat transfer to vessels

775

12.18.1

Jacketed vessels

775

12.18.2

Internal coils

777

12.18.3 Agitated vessels

778

12.19 References

782

12.20 Nomenclature

786

12.21 Problems

790

13 Mechanical Design of Process Equipment

794

13.1

Introduction

794

13.1.1

Classification of pressure vessels

795

13.2 Pressure vessel codes and standards

795

13.3 Fundamental principles and equations

796

13.3.1

Principal stresses

796

13.3.2

Theories of failure

797

13.3.3

Elastic stability

798

13.3.4

Membrane stresses in shells of revolution

798

13.3.5

Flat plates

805

13.3.6

Dilation of vessels

809

13.3.7

Secondary stresses

809

13.4 General design considerations: pressure vessels

810

13.4.1

Design pressure

810

13.4.2

Design temperature

810

13.4.3

Materials

811

13.4.4

Design stress (nominal design strength)

811

13.4.5 Welded joint efficiency, and construction categories

812

13.4.6

Corrosion allowance

813

13.4.7

Design loads

814

13.4.8

Minimum practical wall thickness

814

13.5 The design of thin-walled vessels under internal pressure

815

13.5.1

Cylinders and spherical shells

815

13.5.2

Heads and closures

815

13.5.3

Design of flat ends

817

13.5.4

Design of domed ends

818

13.5.5

Conical sections and end closures

819

13.7 Design of vessels subject to external pressure

825

13.7.1

Cylindrical shells

825

13.7.2

Design of stiffness rings

828

13.7.3

Vessel heads

829

13.8 Design of vessels subject to combined loading

831

13.8.1 Weight loads

835

13.8.2 Wind loads (tall vessels)

837

13.8.3

Earthquake loading

839

13.8.4

Eccentric loads (tall vessels)

840

13.8.5

Torque

841

13.9 Vessel supports

844

13.9.1

Saddle supports

844

13.9.2

Skirt supports

848

13.9.3

Bracket supports

856

13.10 Bolted flanged joints

858

13.10.1 Types of flange, and selection

858

13.10.2 Gaskets

859

13.10.3 Flange faces

861

13.10.4 Flange design

862

13.10.5 Standard flanges

865

13.11 Heat-exchanger tube-plates

867

13.12 Welded joint design

869

13.13 Fatigue assessment of vessels

872

13.14 Pressure tests

872

13.15 High-pressure vessels

873

13.15.1 Fundamental equations

873

13.15.2 Compound vessels

877

13.15.3 Autofrettage

878

13.16 Liquid storage tanks

879

13.17 Mechanical design of centrifuges

879

13.17.1 Centrifugal pressure

879

13.17.2 Bowl and spindle motion: critical speed

881

13.18 References

883

13.19 Nomenclature

885

13.20 Problems

889

14 General Site Considerations

892

14.1

Introduction

892

14.2 Plant location and site selection

892

14.3 Site layout

894

14.4 Plant layout

896

14.4.1

Techniques used in site and plant layout

897

14.5 Utilities

900

14.6 Environmental considerations

902

14.6.1 Waste management

902

14.6.2

Noise

905

14.6.3

Visual impact

905

14.6.4

Legislation

905

14.6.5

Environmental auditing

906

14.7 References

906

APPENDIX A: GRAPHICAL SYMBOLS FOR PIPING SYSTEMS AND PLANT

908

APPENDIX B: CORROSION CHART

917

APPENDIX C: PHYSICAL PROPERTY DATA BANK

937

APPENDIX D: CONVERSION FACTORS FOR SOME COMMON SI UNITS

958

APPENDIX F: DESIGN PROJECTS

965

APPENDIX G: EQUIPMENT SPECIFICATION (DATA) SHEETS

990

APPENDIX H: TYPICAL SHELL AND TUBE HEAT EXCHANGER TUBE-SHEET LAYOUTS

1002

AUTHOR INDEX

1007

SUBJECT INDEX

1017

CHAPTER 1

Introduction to Design

1.1. INTRODUCTION

This chapter is an introduction to the nature and methodology of the design process, and

its application to the design of chemical manufacturing processes.

1.2. NATURE OF DESIGN

This section is a general, somewhat philosophical, discussion of the design process; how a

designer works. The subject of this book is chemical engineering design, but the method-

ology of design described in this section applies equally to other branches of engineering

design.

Design is a creative activity, and as such can be one of the most rewarding and satisfying

activities undertaken by an engineer. It is the synthesis, the putting together, of ideas to

achieve a desired purpose. The design does not exist at the commencement of the project.

The designer starts with a specific objective in mind, a need, and by developing and

evaluating possible designs, arrives at what he considers the best way of achieving that

objective; be it a better chair, a new bridge, or for the chemical engineer, a new chemical

product or a stage in the design of a production process.

When considering possible ways of achieving the objective the designer will be

constrained by many factors, which will narrow down the number of possible designs;

but, there will rarely be just one possible solution to the problem, just one design. Several

alternative ways of meeting the objective will normally be possible, even several best

designs, depending on the nature of the constraints.

These constraints on the possible solutions to a problem in design arise in many ways.

Some constraints will be fixed, invariable, such as those that arise from physical laws,

government regulations, and standards. Others will be less rigid, and will be capable of

relaxation by the designer as part of his general strategy in seeking the best design. The

constraints that are outside the designer’s influence can be termed the external constraints.

These set the outer boundary of possible designs; as shown in Figure 1.1. Within this

boundary there will be a number of plausible designs bounded by the other constraints,

the internal constraints, over which the designer has some control; such as, choice of

process, choice of process conditions, materials, equipment.

Economic considerations are obviously a major constraint on any engineering design:

plants must make a profit.

Time will also be a constraint. The time available for completion of a design will

usually limit the number of alternative designs that can be considered.

1

Plausible

designs

G

o

v

e

rnm

e

n

t c

o

n

tro

ls

Economic constraintsSa

fe

ty

re

gu

lat

ion

s

Resources

Physical lawsStandards and codesP

e

rs

o

n

n

e

l

MaterialsProcess

conditions

Ch

oic

e o

f

pro

ces

s

MethodsT

im

e

“External” constraints

“Internal” constraints

Possible designs

Figure 1.1. Design constraints

Objective

(design

specification)

Collection of data,

physical

properties design

methods

Generation of

possible designs

Selection and

evaluation

(optimisation)

Final

design

Figure 1.2. The design process

The stages in the development of a design, from the initial identification of the objective

to the final design, are shown diagrammatically in Figure 1.2. Each stage is discussed in

the following sections.

Figure 1.2 shows design as an iterative procedure; as the design develops the designer

will be aware of more possibilities and more constraints, and will be constantly seeking

new data and ideas, and evaluating possible design solutions.

Chaddock (1975) defined design as, the conversion of an ill-defined requirement into a

satisfied customer.

The designer is creating a design for an article, or a manufacturing process, to fulfil a

particular need. In the design of a chemical process, the need is the public need for the

product, the commercial opportunity, as foreseen by the sales and marketing organisation.

Within this overall objective the designer will recognise sub-objectives; the requirements

of the various units that make up the overall process.

Before starting work the designer should obtain as complete, and as unambiguous, a

statement of the requirements as possible. If the requirement (need) arises from outside the

design group, from a client or from another department, then he will have to elucidate the

real requirements through discussion. It is important to distinguish between the real needs

and the wants. The wants are those parts of the initial specification that may be thought

desirable, but which can be relaxed if required as the design develops. For example, a

particular product specification may be considered desirable by the sales department, but

may be difficult and costly to obtain, and some relaxation of the specification may be

possible, producing a saleable but cheaper product. Whenever he is in a position to do so,

the designer should always question the design requirements (the project and equipment

specifications) and keep them under review as the design progresses.

Where he writes specifications for others, such as for the mechanical design or purchase

of a piece of equipment, he should be aware of the restrictions (constraints) he is placing

on other designers. A tight, well-thought-out, comprehensive, specification of the require-

ments defines the external constraints within which the other designers must work.

1.2.2. Data collection

To proceed with a design, the designer must first assemble all the relevant facts and

data required. For process design this will include information on possible processes,

equipment performance, and physical property data. This stage can be one of the most

time consuming, and frustrating, aspects of design. Sources of process information and

physical properties are reviewed in Chapter 8.

Many design organisations will prepare a basic data manual, containing all the process

“know-how” on which the design is to be based. Most organisations will have design

manuals covering preferred methods and data for the more frequently used, routine, design

procedures.

The national standards are also sources of design methods and data; they are also design

constraints.

The constraints, particularly the external constraints, should be identified early in the

design process.

1.2.3. Generation of possible design solutions

The creative part of the design process is the generation of possible solutions to the

problem (ways of meeting the objective) for analysis, evaluation and selection. In this

activity the designer will largely rely on previous experience, his own and that of others.

be easily traced. The first motor cars were clearly horse-drawn carriages without the

horse; and the development of the design of the modern car can be traced step by step

from these early prototypes. In the chemical industry, modern distillation processes have

developed from the ancient stills used for rectification of spirits; and the packed columns

used for gas absorption have developed from primitive, brushwood-packed towers. So,

it is not often that a process designer is faced with the task of producing a design for a

completely novel process or piece of equipment.

The experienced engineer will wisely prefer the tried and tested methods, rather than

possibly more exciting but untried novel designs. The work required to develop new

processes, and the cost, is usually underestimated. Progress is made more surely in small

steps. However, whenever innovation is wanted, previous experience, through prejudice,

can inhibit the generation and acceptance of new ideas; the “not invented here” syndrome.

The amount of work, and the way it is tackled, will depend on the degree of novelty

in a design project.

Chemical engineering projects can be divided into three types, depending on the novelty

involved:

1. Modifications, and additions, to existing plant; usually carried out by the plant design

group.

2. New production capacity to meet growing sales demand, and the sale of established

processes by contractors. Repetition of existing designs, with only minor design

changes.

3. New processes, developed from laboratory research, through pilot plant, to a

commercial process. Even here, most of the unit operations and process equipment

will use established designs.

The first step in devising a new process design will be to sketch out a rough block

diagram showing the main stages in the process; and to list the primary function (objective)

and the major constraints for each stage. Experience should then indicate what types of

unit operations and equipment should be considered.

Jones (1970) discusses the methodology of design, and reviews some of the special

techniques, such as brainstorming sessions and synectics, that have been developed to

help generate ideas for solving intractable problems. A good general reference on the art

of problem solving is the classical work by Polya (1957); see also Chittenden (1987).

Some techniques for problem solving in the Chemical Industry are covered in a short text

by Casey and Frazer (1984).

The generation of ideas for possible solutions to a design problem cannot be separated

from the selection stage of the design process; some ideas will be rejected as impractical

as soon as they are conceived.

1.2.4. Selection

The designer starts with the set of all possible solutions bounded by the external

constraints, and by a process of progressive evaluation and selection, narrows down the

range of candidates to find the “best” design for the purpose.

Possible designs (credible)

within the external constraints.

Plausible designs (feasible)

within the internal constraints.

Probable designs

likely candidates.

Best design (optimum)

judged the best solution to the problem.

The selection process will become more detailed and more refined as the design progresses

from the area of possible to the area of probable solutions. In the early stages a coarse

screening based on common sense, engineering judgement, and rough costings will usually

suffice. For example, it would not take many minutes to narrow down the choice of raw

materials for the manufacture of ammonia from the possible candidates of, say, wood,

peat, coal, natural gas, and oil, to a choice of between gas and oil, but a more detailed

study would be needed to choose between oil and gas. To select the best design from the

probable designs, detailed design work and costing will usually be necessary. However,

where the performance of candidate designs is likely to be close the cost of this further

refinement, in time and money, may not be worthwhile, particularly as there will usually

be some uncertainty in the accuracy of the estimates.

The mathematical techniques that have been developed to assist in the optimisation of

designs, and plant performance, are discussed briefly in Section 1.10.

Rudd and Watson (1968) and Wells (1973) describe formal techniques for the prelim-

inary screening of alternative designs.

1.3. THE ANATOMY OF A CHEMICAL MANUFACTURING

PROCESS

The basic components of a typical chemical process are shown in Figure 1.3, in which

each block represents a stage in the overall process for producing a product from the raw

materials. Figure 1.3 represents a generalised process; not all the stages will be needed for

any particular process, and the complexity of each stage will depend on the nature of the

process. Chemical engineering design is concerned with the selection and arrangement

of the stages, and the selection, specification and design of the equipment required to

perform the stage functions.

Raw

material

storage

Feed

preparation

Reaction

Product

separation

Product

purification

Product

storage

Sales

Recycle of unreacted

material

By-products

Wastes

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

Stage 6

Figure 1.3. Anatomy of a chemical process

Stage 1. Raw material storage

Unless the raw materials (also called essential materials, or feed stocks) are supplied

as intermediate products (intermediates) from a neighbouring plant, some provision will

interruptions in supply. Even when the materials come from an adjacent plant some

provision is usually made to hold a few hours, or even days, supply to decouple the

processes. The storage required will depend on the nature of the raw materials, the method

of delivery, and what assurance can be placed on the continuity of supply. If materials are

delivered by ship (tanker or bulk carrier) several weeks stocks may be necessary; whereas

if they are received by road or rail, in smaller lots, less storage will be needed.

Stage 2. Feed preparation

Some purification, and preparation, of the raw materials will usually be necessary before

they are sufficiently pure, or in the right form, to be fed to the reaction stage. For example,

acetylene generated by the carbide process contains arsenical and sulphur compounds, and

other impurities, which must be removed by scrubbing with concentrated sulphuric acid

(or other processes) before it is sufficiently pure for reaction with hydrochloric acid to

produce dichloroethane. Liquid feeds will need to be vaporised before being fed to gas-

phase reactors, and solids may need crushing, grinding and screening.

Stage 3. Reactor

The reaction stage is the heart of a chemical manufacturing process. In the reactor the

raw materials are brought together under conditions that promote the production of the

desired product; invariably, by-products and unwanted compounds (impurities) will also

be formed.

Stage 4. Product separation

In this first stage after the reactor the products and by-products are separated from any

unreacted material. If in sufficient quantity, the unreacted material will be recycled to

the reactor. They may be returned directly to the reactor, or to the feed purification and

preparation stage. The by-products may also be separated from the products at this stage.

Stage 5. Purification

Before sale, the main product will usually need purification to meet the product specifi-

cation. If produced in economic quantities, the by-products may also be purified for sale.

Stage 6. Product storage

Some inventory of finished product must be held to match production with sales. Provision

for product packaging and transport will also be needed, depending on the nature of the

product. Liquids will normally be dispatched in drums and in bulk tankers (road, rail and

sea), solids in sacks, cartons or bales.

The stock held will depend on the nature of the product and the market.

Ancillary processes

In addition to the main process stages shown in Figure 1.3, provision will have to be

made for the supply of the services (utilities) needed; such as, process water, cooling

offices and other accommodation, and laboratories; see Chapter 14.

1.3.1. Continuous and batch processes

Continuous processes are designed to operate 24 hours a day, 7 days a week, throughout

the year. Some down time will be allowed for maintenance and, for some processes,

catalyst regeneration. The plant attainment; that is, the percentage of the available hours

in a year that the plant operates, will usually be 90 to 95%.

Attainment % D hours operated

8760

ð 100

Batch processes are designed to operate intermittently. Some, or all, the process units

being frequently shut down and started up.

Continuous processes will usually be more economical for large scale production. Batch

processes are used where some flexibility is wanted in production rate or product speci-

fication.

Choice of continuous versus batch production

The choice between batch or continuous operation will not be clear cut, but the following

rules can be used as a guide.

Continuous

1. Production rate greater than 5 ð 106 kg/h

2. Single product

3. No severe fouling

4. Good catalyst life

5. Proven processes design

6. Established market

Batch

1. Production rate less than 5 ð 106 kg/h

2. A range of products or product specifications

3. Severe fouling

4. Short catalyst life

5. New product

6. Uncertain design

1.4. THE ORGANISATION OF A CHEMICAL ENGINEERING

PROJECT

The design work required in the engineering of a chemical manufacturing process can be

divided into two broad phases.

Phase 1. Process design, which covers the steps from the initial selection of the process

to be used, through to the issuing of the process flow-sheets; and includes the selection,

Initial evaluation.

Process selection.

Preliminary flow diagrams.

Detailed process design.

Flow-sheets.

Chemical engineering equipment

design and specifications.

Reactors, Unit operations, Heat exchangers,

Miscellaneous equipment.

Materials selection.

Process manuals

Material and energy balances.

Preliminary equipment selection

and design.

Process flow-sheeting.

Preliminary cost estimation.

Authorisation of funds.

Piping and instrument design

Instrument selection

and specification

Pumps and compressors.

Selection and specification

Vessel design

Heat exchanger design

Utilities and other services.

Design and specification

Electrical,

Motors, switch gear,

substations, etc.

Piping design

Structural design

Plant layout

General civil work.

Foundations, drains,

roads, etc.

Buildings.

Offices, laboratories,

control rooms, etc.

Project cost estimation.

Capital authorisation

Purchasing/procurement

Raw material specification.

(contracts)

Construction

Start-up

Operating manuals

Operation

Sales

Figure 1.4. The structure of a chemical engineering project

this phase is the responsibility of the Process Design Group, and the work will be mainly

done by chemical engineers. The process design group may also be responsible for the

preparation of the piping and instrumentation diagrams.

Phase 2. The detailed mechanical design of equipment; the structural, civil and electrical

design; and the specification and design of the ancillary services. These activities will be

the responsibility of specialist design groups, having expertise in the whole range of

engineering disciplines.

Other specialist groups will be responsible for cost estimation, and the purchase and

procurement of equipment and materials.

The sequence of steps in the design, construction and start-up of a typical chemical

process plant is shown diagrammatically in Figure 1.4 and the organisation of a typical

project group in Figure 1.5. Each step in the design process will not be as neatly separated

from the others as is indicated in Figure 1.4; nor will the sequence of events be as clearly

defined. There will be a constant interchange of information between the various design

sections as the design develops, but it is clear that some steps in a design must be largely

completed before others can be started.

A project manager, often a chemical engineer by training, is usually responsible for the

co-ordination of the project, as shown in Figure 1.5.

Specialist design sections

Vessels Layout Piping Heat exchangers

valves fired heaters

Control Civil work

and instruments structures Electrical

buildings

Compressors

and turbines Utilities

pumps

Process section

Process evaluation

Flow-sheeting

Equipment specifications

Construction section

Construction

Start-up

Project

manager

Procurement

section

Estimating

Inspection

Scheduling

Figure 1.5. Project organisation

As was stated in Section 1.2.1, the project design should start with a clear specification

defining the product, capacity, raw materials, process and site location. If the project is

based on an established process and product, a full specification can be drawn up at

the start of the project. For a new product, the specification will be developed from an

economic evaluation of possible processes, based on laboratory research, pilot plant tests

and product market research.

Barrow (1964) and Baasel (1974).

Some of the larger chemical manufacturing companies have their own project design

organisations and carry out the whole project design and engineering, and possibly

construction, within their own organisation. More usually the design and construction, and

possibly assistance with start-up, is entrusted to one of the international contracting firms.

The operating company will often provide the “know-how” for the process, and will

work closely with the contractor throughout all stages of the project.

1.5. PROJECT DOCUMENTATION

As shown in Figure 1.5 and described in Section 1.4, the design and engineering of

a chemical process requires the co-operation of many specialist groups. Effective co-

operation depends on effective communications, and all design organisations have formal

procedures for handling project information and documentation. The project documen-

tation will include:

1. General correspondence within the design group and with:

government departments

equipment vendors

site personnel

the client

2. Calculation sheets

design calculations

costing

computer print-out

3. Drawings

flow-sheets

piping and instrumentation diagrams

layout diagrams

plot/site plans

equipment details

piping diagrams

architectural drawings

design sketches

4. Specification sheets

for equipment, such as:

heat exchangers

pumps

5. Purchase orders

quotations

invoices

All documents should be assigned a code number for easy cross referencing, filing and

retrieval.

Calculation sheets

The design engineer should develop the habit of setting out calculations so that they can

be easily understood and checked by others. It is good practice to include on calculation

sufficient detail for the methods, as well as the arithmetic, to be checked. Design calcula-

tions are normally set out on standard sheets. The heading at the top of each sheet should

include: the project title and identification number and, most importantly, the signature

(or initials) of the person who checked the calculation.

Drawings

All project drawings are normally drawn on specially printed sheets, with the company

name; project title and number; drawing title and identification number; draughtsman’s

name and person checking the drawing; clearly set out in a box in the bottom right-hand

corner. Provision should also be made for noting on the drawing all modifications to the

initial issue.

Drawings should conform to accepted drawing conventions, preferably those laid down

by the national standards. The symbols used for flow-sheets and piping and instrument

diagrams are discussed in Chapter 4. Drawings and sketches are normally made on

detail paper (semi-transparent) in pencil, so modifications can be easily made, and prints

taken.

In most design offices Computer Aided Design (CAD) methods are now used to produce

the drawings required for all the aspects of a project: flow-sheets, piping and instrumen-

tation, mechanical and civil work.

Specification sheets

Standard specification sheets are normally used to transmit the information required for

the detailed design, or purchase, of equipment items; such as, heat exchangers, pumps,

columns.

As well as ensuring that the information is clearly and unambiguously presented,

standard specification sheets serve as check lists to ensure that all the information required

is included.

Examples of equipment specification sheets are given in Appendix G.

Process manuals

Process manuals are often prepared by the process design group to describe the process and

the basis of the design. Together with the flow-sheets, they provide a complete technical

description of the process.

Operating manuals

Operating manuals give the detailed, step by step, instructions for operation of the process

and equipment. They would normally be prepared by the operating company personnel,

but may also be issued by a contractor as part of the contract package for a less experienced

client. The operating manuals would be used for operator instruction and training, and

for the preparation of the formal plant operating instructions.

The need for standardisation arose early in the evolution of the modern engineering

industry; Whitworth introduced the first standard screw thread to give a measure of

interchangeability between different manufacturers in 1841. Modern engineering standards

cover a much wider function than the interchange of parts. In engineering practice

they cover:

1. Materials, properties and compositions.

2. Testing procedures for performance, compositions, quality.

3. Preferred sizes; for example, tubes, plates, sections.

4. Design methods, inspection, fabrication.

5. Codes of practice, for plant operation and safety.

The terms STANDARD and CODE are used interchangeably, though CODE should

really be reserved for a code of practice covering say, a recommended design or operating

procedure; and STANDARD for preferred sizes, compositions, etc.

All of the developed countries, and many of the developing countries, have national

standards organisations, responsible for the issue and maintenance of standards for the

manufacturing industries, and for the protection of consumers. In the United Kingdom

preparation and promulgation of national standards are the responsibility of the British

Standards Institution (BSI). The Institution has a secretariat and a number of technical

personnel, but the preparation of the standards is largely the responsibility of committees

of persons from the appropriate industry, the professional engineering institutions and

other interested organisations.

In the United States the government organisation responsible for coordinating infor-

mation on standards is the National Bureau of Standards; standards are issued by Federal,

State and various commercial organisations. The principal ones of interest to chemical

engineers are those issued by the American National Standards Institute (ANSI), the

American Petroleum Institute (API), the American Society for Testing Materials (ASTM),

and the American Society of Mechanical Engineers (ASME) (pressure vessels). Burklin

(1979) gives a comprehensive list of the American codes and standards.

The International Organization for Standardization (ISO) coordinates the publication of

international standards.

All the published British standards are listed, and their scope and application described,

in the British Standards Institute Catalogue; which the designer should consult. The

catalogue is available online, go to the BSI group home page, www.bsi-global.com.

As well as the various national standards and codes, the larger design organisations

will have their own (in-house) standards. Much of the detail in engineering design work

is routine and repetitious, and it saves time and money, and ensures a conformity between

projects, if standard designs are used whenever practicable.

Equipment manufacturers also work to standards to produce standardised designs and

size ranges for commonly used items; such as electric motors, pumps, pipes and pipe

fittings. They will conform to national standards, where they exist, or to those issued by

trade associations. It is clearly more economic to produce a limited range of standard

sizes than to have to treat each order as a special job.

of a piece of equipment into the rest of the plant. For example, if a standard range of

centrifugal pumps is specified the pump dimensions will be known, and this facilitates the

design of the foundations plates, pipe connections and the selection of the drive motors:

standard electric motors would be used.

For an operating company, the standardisation of equipment designs and sizes increases

interchangeability and reduces the stock of spares that have to be held in maintenance

stores.

Though there are clearly considerable advantages to be gained from the use of standards

in design, there are also some disadvantages. Standards impose constraints on the designer.

The nearest standard size will normally be selected on completing a design calculation

(rounding-up) but this will not necessarily be the optimum size; though as the standard

size will be cheaper than a special size, it will usually be the best choice from the point of

view of initial capital cost. Standard design methods must, of their nature, be historical,

and do not necessarily incorporate the latest techniques.

The use of standards in design is illustrated in the discussion of the pressure vessel

design standards (codes) in Chapter 13.

1.7. FACTORS OF SAFETY (DESIGN FACTORS)

Design is an inexact art; errors and uncertainties will arise from uncertainties in the design

data available and in the approximations necessary in design calculations. To ensure that

the design specification is met, factors are included to give a margin of safety in the

design; safety in the sense that the equipment will not fail to perform satisfactorily, and

that it will operate safely: will not cause a hazard. “Design factor” is a better term to use,

as it does not confuse safety and performance factors.

In mechanical and structural design, the magnitude of the design factors used to allow

for uncertainties in material properties, design methods, fabrication and operating loads

are well established. For example, a factor of around 4 on the tensile strength, or about

2.5 on the 0.1 per cent proof stress, is normally used in general structural design. The

selection of design factors in mechanical engineering design is illustrated in the discussion

of pressure vessel design in Chapter 13.

Design factors are also applied in process design to give some tolerance in the design.

For example, the process stream average flows calculated from material balances are

usually increased by a factor, typically 10 per cent, to give some flexibility in process

operation. This factor will set the maximum flows for equipment, instrumentation, and

piping design. Where design factors are introduced to give some contingency in a process

design, they should be agreed within the project organisation, and clearly stated in the

project documents (drawings, calculation sheets and manuals). If this is not done, there

is a danger that each of the specialist design groups will add its own “factor of safety”;

resulting in gross, and unnecessary, over-design.

When selecting the design factor to use a balance has to be made between the desire

to make sure the design is adequate and the need to design to tight margins to remain

competitive. The greater the uncertainty in the design methods and data, the bigger the

design factor that must be used.

To be consistent with the other volumes in this series, SI units have been used in this

book. However, in practice the design methods, data and standards which the designer will

use are often only available in the traditional scientific and engineering units. Chemical

engineering has always used a diversity of units; embracing the scientific CGS and MKS

systems, and both the American and British engineering systems. Those engineers in the

older industries will also have had to deal with some bizarre traditional units; such as

degrees Twaddle (density) and barrels for quantity. Desirable as it may be for industry

world-wide to adopt one consistent set of units, such as SI, this is unlikely to come about

for many years, and the designer must contend with whatever system, or combination of

systems, his organisation uses. For those in the contracting industry this will also mean

working with whatever system of units the client requires.

It is usually the best practice to work through design calculations in the units in which

the result is to be presented; but, if working in SI units is preferred, data can be converted

to SI units, the calculation made, and the result converted to whatever units are required.

Conversion factors to the SI system from most of the scientific and engineering units used

in chemical engineering design are given in Appendix D.

Some license has been taken in the use of the SI system in this volume. Temperatures are

given in degrees Celsius (ŽC); degrees Kelvin are only used when absolute temperature

is required in the calculation. Pressures are often given in bar (or atmospheres) rather

than in the Pascals (N/m2), as this gives a better feel for the magnitude of the pressures.

In technical calculations the bar can be taken as equivalent to an atmosphere, whatever

definition is used for atmosphere. The abbreviations bara and barg are often used to denote

bar absolute and bar gauge; analogous to psia and psig when the pressure is expressed

in pound force per square inch. When bar is used on its own, without qualification, it is

normally taken as absolute.

For stress, N/mm2 have been used, as these units are now generally accepted by

engineers, and the use of a small unit of area helps to indicate that stress is the intensity of

force at a point (as is also pressure). For quantity, kmol are generally used in preference

to mol, and for flow, kmol/h instead of mol/s, as this gives more sensibly sized figures,

which are also closer to the more familiar lb/h.

For volume and volumetric flow, m3 and m3/h are used in preference to m3/s, which

gives ridiculously small values in engineering calculations. Litres per second are used for

small flow-rates, as this is the preferred unit for pump specifications.

Where, for convenience, other than SI units have been used on figures or diagrams, the

scales are also given in SI units, or the appropriate conversion factors are given in the

text. The answers to some examples are given in British engineering units as well as SI,

to help illustrate the significance of the values.

Some approximate conversion factors to SI units are given in Table 1.1. These are

worth committing to memory, to give some feel for the units for those more familiar with

the traditional engineering units. The exact conversion factors are also shown in the table.

A more comprehensive table of conversion factors is given in Appendix D.

Engineers need to be aware of the difference between US gallons and imperial gallons

(UK) when using American literature and equipment catalogues. Equipment quoted in an

Quantity

British

SI unit

Eng. unit

approx.

exact

Energy

1 Btu

1 kJ

1.05506

Specific enthalpy

1 Btu/lb

2 kJ/kg

2.326

Specific heat capacity

1 Btu/lb°F

4 kJ/kg°C

4.1868

(CHU/lb°C)

Heat transfer coeff.

1 Btu/ft2h°F

6 W/m2 °C

5.678

(CHU/ft2h°C)

Viscosity

1 centipoise

1 mNs/m2

1.000

1 lbf/ft h

0.4 mNs/m2

0.4134

Surface tension

1 dyne/cm

1 mN/m

1.000

Pressure

1 lbf/in2

7 kN/m2

6.894

1 atm

1 bar

1.01325

105 N/m2

Density

1 lb/ft3

16 kg/m3

16.0190

1 g/cm3

1 kg/m3

Volume

1 imp gal.

4.5 ð 103 m3

4.5461 ð 103

Flow-rate

1 imp gal/m

16 m3/h

16.366

Note:

1 US gallon D 0.84 imperial gallons (UK)

1 barrel (oil) D 50 US gall ³ 0.19 m3 (exact 0.1893)

1 kWh D 3.6 MJ

American catalogue in US gallons or gpm (gallons per minute) will have only 80 per cent

of the rated capacity when measured in imperial gallons.

The electrical supply frequency in these two countries is also different: 60 Hz in the US

and 50 Hz in the UK. So a pump specified as 50 gpm (US gallons), running at 1750 rpm

(revolutions per second) in the US would only deliver 35 imp gpm if operated in the UK;

where the motor speed would be reduced to 1460 rpm: so beware.

1.9. DEGREES OF FREEDOM AND DESIGN VARIABLES.

THE MATHEMATICAL REPRESENTATION OF

THE DESIGN PROBLEM

In Section 1.2 it was shown that the designer in seeking a solution to a design problem

works within the constraints inherent in the particular problem.

In this section the structure of design problems is examined by representing the general

design problem in a mathematical form.

1.9.1. Information flow and design variables

A process unit in a chemical process plant performs some operation on the inlet material

streams to produce the desired outlet streams. In the design of such a unit the design

calculations model the operation of the unit. A process unit and the design equations

Input

streams

Input

information

Output

streams

Output

information

Unit

Calculation

method

Figure 1.6. The “design unit”

representing the unit are shown diagrammatically in Figure 1.6. In the “design unit” the

flow of material is replaced by a flow of information into the unit and a flow of derived

information from the unit.

The information flows are the values of the variables which are involved in the design;

such as, stream compositions, temperatures, pressure, stream flow-rates, and stream

enthalpies. Composition, temperature and pressure are intensive variables: independent of

the quantity of material (flow-rate). The constraints on the design will place restrictions on

the possible values that these variables can take. The values of some of the variables will

be fixed directly by process specifications. The values of other variables will be determined

by “design relationships” arising from constraints. Some of the design relationships will

be in the form of explicit mathematical equations (design equations); such as those

arising from material and energy balances, thermodynamic relationships, and equipment

performance parameters. Other relationships will be less precise; such as those arising

from the use of standards and preferred sizes, and safety considerations.

The difference between the number of variables involved in a design and the number

of design relationships has been called the number of “degrees of freedom”; similar to the

use of the term in the phase rule. The number of variables in the system is analogous to the

number of variables in a set of simultaneous equations, and the number of relationships

analogous to the number of equations. The difference between the number of variables

and equations is called the variance of the set of equations.

If Nv is the number of possible variables in a design problem and Nr the number of

design relationships, then the “degrees of freedom” Nd is given by:

Nd D Nv Nr

1.1

Nd represents the freedom that the designer has to manipulate the variables to find the

best design.

If Nv D Nr,Nd D 0 and there is only one, unique, solution to the problem. The problem

is not a true design problem, no optimisation is possible.

If Nv < Nr,Nd < 0, and the problem is over defined; only a trivial solution is possible.

If Nv > Nr,Nd > 0, and there is an infinite number of possible solutions. However,

for a practical problem there will be only a limited number of feasible solutions. The

value of Nd is the number of variables which the designer must assign values to solve

the problem.

How the number of process variables, design relationships, and design variables defines

a system can be best illustrated by considering the simplest system; a single-phase, process

stream.

Consider a single-phase stream, containing C components.

Variable

Number

Stream flow-rate

1

Composition (component concentrations)

C

Temperature

1

Pressure

1

Stream enthalpy

1

Total, Nv D CC 4

Relationships between variables

Number

Composition1

1

Enthalpy2

1

Total, Nr D 2

Degrees of freedom Nd D Nv Nr D CC 4 2 D CC 2

(1) The sum of the mass or mol, fractions, must equal one.

(2) The enthalpy is a function of stream composition, temperature and pressure.

Specifying (CC 2) variables completely defines the stream.

Flash distillation

The idea of degrees of freedom in the design process can be further illustrated by consid-

ering a simple process unit, a flash distillation. (For a description of flash distillation see

Volume 2, Chapter 11).

F2, P2, T2, (xi)2

F3, P3, T3, (xi)3

F1, P1, T1, (xi)1

q

Figure 1.7. Flash distillation

The unit is shown in Figure 1.7, where:

F D stream flow rate,

P D pressure,

T D temperature,

xi D concentration, component i,

q D heat input.

Suffixes, 1 D inlet, 2 D outlet vapour, 3 D outlet liquid.

Variable

Number

Streams (free variables)1

3CC 21

Still

pressure

1

temperature

1

heat input

1

Nr D 3CC 9

Relationship

Number

Material balances (each component)

C

Heat balance, overall

1

v l e relationships2

C

Equilibrium still restriction3

4

2CC 5

Degrees of freedom Nd D 3CC 9 2CC 5 D CC 4

(1) The degrees of freedom for each stream. The total variables in each stream could have been used, and

the stream relationships included in the count of relationships.

This shows how the degrees of freedom for a complex unit can be built up from the degrees of freedom of

its components. For more complex examples see Kwauk (1956).

(2) Given the temperature and pressure, the concentration of any component in the vapour phase can be

obtained from the concentration in the liquid phase, from the vapour liquid equilibrium data for the system.

(3) The concept (definition) of an equilibrium separation implies that the outlet streams and the still are at

the same temperature and pressure. This gives four equations:

P2 D P3 D P

T2 D T3 D T

Though the total degrees of freedom is seen to be (CC 4) some of the variables will

normally be fixed by general process considerations, and will not be free for the designer

to select as “design variables”. The flash distillation unit will normally be one unit in a

process system and the feed composition and feed conditions will be fixed by the upstream

processes; the feed will arise as an outlet stream from some other unit. Defining the feed

fixes (CC 2) variables, so the designer is left with:

CC 4 CC 2 D 2

as design variables.

Summary

The purpose of this discussion was to show that in a design there will be a certain

number of variables that the designer must specify to define the problem, and which he

can manipulate to seek the best design. In manual calculations the designer will rarely

feel for the problem, and can change the calculation procedure, and select the design

variables, as he works through the design. He will know by experience if the problem is

correctly specified. A computer, however, has no intuition, and for computer-aided design

calculations it is essential to ensure that the necessary number of variables is specified to

define the problem correctly. For complex processes the number of variables and relating

equations will be very large, and the calculation of the degrees of freedom very involved.

Kwauk (1956) has shown how the degrees of freedom can be calculated for separation

processes by building up the complex unit from simpler units. Smith (1963) uses Kwauk’s

method, and illustrates how the idea of “degrees of freedom” can be used in the design

of separation processes.

1.9.2. Selection of design variables

In setting out to solve a design problem the designer has to decide which variables are to

be chosen as “design variables”; the ones he will manipulate to produce the best design.

The choice of design variables is important; careful selection can simplify the design

calculations. This can be illustrated by considering the choice of design variables for a

simple binary flash distillation.

For a flash distillation the total degrees of freedom was shown to be (CC 4), so for

two components Nd D 6. If the feed stream flow, composition, temperature and pressure

are fixed by upstream conditions, then the number of design variables will be:

N0d D 6 CC 2 D 6 4 D 2

So the designer is free to select two variables from the remaining variables in order to

proceed with the calculation of the outlet stream compositions and flows.

If he selects the still pressure (which for a binary system will determine the vapour

liquid equilibrium relationship) and one outlet stream flow-rate, then the outlet compo-

sitions can be calculated by simultaneous solution of the mass balance and equilibrium

relationships (equations). A graphical method for the simultaneous solution is given in

Volume 2, Chapter 11.

However, if he selects an outlet stream composition (say the liquid stream) instead of

a flow-rate, then the simultaneous solution of the mass balance and v l e relationships

would not be necessary. The stream compositions could be calculated by the following

step-by-step (sequential) procedure:

1. Specifying P determines the v l e relationship (equilibrium) curve from experi-

mental data.

2. Knowing the outlet liquid composition, the outlet vapour composition can be calcu-

lated from the v l e relationship.

3. Knowing the feed and outlet compositions, and the feed flow-rate, the outlet stream

flows can be calculated from a material balance.

4. An enthalpy balance then gives the heat input required.

The need for simultaneous solution of the design equations implies that there is a

recycle of information. Choice of an outlet stream composition as a design variable in

x3

F2

F3

T

P

F2 (or F3)

Feed

Select

(a)

(b)

F3 (or F2)

x2

x3

T

x2 (or x3)

Direction of calculation

F1

x1

P1

T1

P

x2 (or x3)

Feed

Select

Direction of calculation

F1

x1

P1

T1

Figure 1.8.

Information flow, binary flash distillation calculation (a) Information recycle (b) Information flow

reversal

effect reverses the flow of information through the problem and removes the recycle; this

is shown diagrammatically in Figure 1.8.

1.9.3. Information flow and the structure of design problems

It was shown in Section 1.9.2. by studying a relatively simple problem, that the way

in which the designer selects his design variables can determine whether the design

calculations will prove to be easy or difficult. Selection of one particular set of variables

can lead to a straightforward, step-by-step, procedure, whereas selection of another set

can force the need for simultaneous solution of some of the relationships; which often

requires an iterative procedure (cut-and-try method). How the choice of design variables,

inputs to the calculation procedure, affects the ease of solution for the general design

problem can be illustrated by studying the flow of information, using simple information

flow diagrams. The method used will be that given by Lee et al. (1966) who used a form

of directed graph; a biparte graph, see Berge (1962).

The general design problem can be represented in mathematical symbolism as a series

of equations:

fivj D 0

where j D 1, 2, 3,..., Nv,

i D 1, 2, 3,..., Nr

Consider the following set of such equations:

f1v1, v2 D 0

f2v1, v2, v3, v5 D 0

f4v2, v4, v5, v6 D 0

f5v5, v6, v7 D 0

There are seven variables, Nv D 7, and five equations (relationships) Nr D 5, so the

number of degrees of freedom is:

Nd D Nv Nr D 7 5 D 2

The task is to select two variables from the total of seven in such a way as to give the

simplest, most efficient, method of solution to the seven equations. There are twenty-one

ways of selecting two items from seven.

In Lee’s method the equations and variables are represented by nodes on the biparte

graph (circles), connected by edges (lines), as shown in Figure 1.9.

f1

v1

v1

f node

v node

Figure 1.9. Nodes and edges on a biparte graph

Figure 1.9 shows that equation f1 contains (is connected to) variables v1 and v2. The

complete graph for the set of equations is shown in Figure 1.10.

f1

f2

f3

f4

v1

v2

v3

v4

v5

v6

v7

f5

Figure 1.10. Biparte graph for the complete set of equations

The number of edges connected to a node defines the local degree of the node p.

For example, the local degree of the f1 node is 2, pf1 D 2, and at the v5 node it is 3,

pv5 D 3. Assigning directions to the edges of Figure 1.10 (by putting arrows on the

lines) identifies one possible order of solution for the equations. If a variable vj is defined

as an output variable from an equation fi, then the direction of information flow is from

the node fi to the node vj and all other edges will be oriented into fi. What this means,

mathematically, is that assigning vj as an output from fi rearranges that equation so that:

fiv1, v2,... , vn D vj

vj is calculated from equation fi.

assigned as output variables from an f node. They are inputs to the system and their edges

must be oriented into the system of equations.

If, for instance, variables v3 and v4 are selected as design variables, then Figure 1.11

shows one possible order of solution of the set of equations. Different types of arrows

are used to distinguish between input and output variables, and the variables selected as

design variables are enclosed in a double circle.

f1

f2

f3

f4

f5

v1

v2

v5

v6

v7

v3

v4

Design variables (inputs)

Inputs

Outputs

Figure 1.11. An order of solution

Tracing the order of the solution of the equations as shown in Figure 1.11 shows how

the information flows through the system of equations:

1. Fixing v3 and v4 enables f3 to be solved, giving v1 as the output. v1 is an input to

f1 and f2.

2. With v1 as an input, f1 can be solved giving v2; v2 is an input to f2 and f4.

3. Knowing v3, v1 and v2, f2 can be solved to give v5; v5 is an input to f4 and f5.

4. Knowing v4, v2 and v5, f4 can be solved to give v6; v6 is an input to f5.

5. Knowing v6 and v5, f5 can be solved to give v7; which completes the solution.

This order of calculation can be shown more clearly by redrawing Figure 1.11 as shown

in Figure 1.12.

f3

f1

f2

f4

f5

v1

v2

v5

v6

v7

v3

v4

v2

v5

v3

v4

Figure 1.12. Figure 1.11 redrawn to show order of solution

taneous solution of any of the equations. The fortuitous selection of v3 and v4 as design

variables has given an efficient order of solution of the equations.

If for a set of equations an order of solution exists such that there is no need for the

simultaneous solution of any of the equations, the system is said to be “acyclic”, no

recycle of information.

If another pair of variables had been selected, for instance v5 and v7, an acyclic order

of solution for the set of equations would not necessarily have been obtained.

For many design calculations it will not be possible to select the design variables so as

to eliminate the recycle of information and obviate the need for iterative solution of the

design relationships.

For example, the set of equations given below will be cyclic for all choices of the two

possible design variables.

f1x1,x2 D 0

f2x1,x3,x4 D 0

f3x2,x3,x4,x5,x6 D 0

f4x4,x5,x6 D 0

Nd D 6 4 D 2

The biparte graph for this example, with x3 and x5 selected as the design variables

(inputs), is shown in Figure 1.13.

f1

f2

f3

f4

x6

x4

x2

x1

x3

x5

Figure 1.13.

One strategy for the solution of this cyclic set of equations would be to guess (assign

a value to) x6. The equations could then be solved sequentially, as shown in Figure 1.14,

to produce a calculated value for x6, which could be compared with the assumed value

and the procedure repeated until a satisfactory convergence of the assumed and calculated

value had been obtained. Assigning a value to x6 is equivalent to “tearing” the recycle

loop at x6 (Figure 1.15). Iterative methods for the solution of equations are discussed by

Henley and Rosen (1969).

When a design problem cannot be reduced to an acyclic form by judicious selection of

the design variables, the design variables should be chosen so as to reduce the recycle of

f1

f2

f3

f4

x6

x6

x4

x2

x1

3

5

Assumed

value

Calculated

value

Figure 1.14.

f4

f2

f1

f3

x6

x5

x3

x5

x6

x4

x4

x1

x3

x2

Figure 1.15.

information to a minimum. Lee and Rudd (1966) and Rudd and Watson (1968) give an

algorithm that can be used to help in the selection of the best design variables in manual

calculations.

The recycle of information, often associated with the actual recycle of process material,

will usually occur in any design problem involving large sets of equations; such as in the

computer simulation of chemical processes. Efficient methods for the solution of sets of

equations are required in computer-aided design procedures to reduce the computer time

needed. Several workers have published algorithms for the efficient ordering of recycle

loops for iterative solution procedures, and some references to this work are given in the

chapter on flow-sheeting, Chapter 4.

1.10. OPTIMISATION

Design is optimisation: the designer seeks the best, the optimum, solution to a problem.

Much of the selection and choice in the design process will depend on the intuitive

judgement of the designer; who must decide when more formal optimisation techniques

can be used to advantage.

The task of formally optimising the design of a complex processing plant involving

several hundred variables, with complex interactions, is formidable, if not impossible.

The task can be reduced by dividing the process into more manageable units, identifying

the key variables and concentrating work where the effort involved will give the greatest

necessarily give the optimum design for the whole process. The optimisation of one unit

may be at the expense of another. For example, it will usually be satisfactory to optimise

the reflux ratio for a fractionating column independently of the rest of the plant; but if the

column is part of a separation stage following a reactor, in which the product is separated

from the unreacted materials, then the design of the column will interact with, and may

well determine, the optimisation of the reactor design.

In this book the discussion of optimisation methods will, of necessity, be limited to a

brief review of the main techniques used in process and equipment design. The extensive

literature on the subject should be consulted for full details of the methods available, and

their application and limitations; see Beightler and Wilde (1967), Beveridge and Schechter

(1970), Stoecker (1989), Rudd and Watson (1968), Edgar and Himmelblau (2001). The

books by Rudd and Watson (1968) and Edgar and Himmelblau (2001) are particularly

recommended to students.

1.10.1. General procedure

When setting out to optimise any system, the first step is clearly to identify the objective:

the criterion to be used to judge the system performance. In engineering design the

objective will invariably be an economic one. For a chemical process, the overall objective

for the operating company will be to maximise profits. This will give rise to sub-objectives,

which the designer will work to achieve. The main sub-objective will usually be to

minimise operating costs. Other sub-objectives may be to reduce investment, maximise

yield, reduce labour requirements, reduce maintenance, operate safely.

When choosing his objectives the designer must keep in mind the overall objective.

Minimising cost per unit of production will not necessarily maximise profits per unit time;

market factors, such as quality and delivery, may determine the best overall strategy.

The second step is to determine the objective function: the system of equations, and

other relationships, which relate the objective with the variables to be manipulated to

optimise the function. If the objective is economic, it will be necessary to express the

objective function in economic terms (costs).

Difficulties will arise in expressing functions that depend on value judgements; for

example, the social benefits and the social costs that arise from pollution.

The third step is to find the values of the variables that give the optimum value of the

objective function (maximum or minimum). The best techniques to be used for this step

will depend on the complexity of the system and on the particular mathematical model

used to represent the system.

A mathematical model represents the design as a set of equations (relationships) and, as

was shown in Section 1.9.1, it will only be possible to optimise the design if the number

of variables exceeds the number of relationships; there is some degree of freedom in the

system.

1.10.2. Simple models

If the objective function can be expressed as a function of one variable (single degree of

freedom) the function can be differentiated, or plotted, to find the maximum or minimum.

trated in Example 1.1, and in the derivation of the formula for optimum pipe diameter in

Chapter 5. The determination of the economic reflux ratio for a distillation column, which

is discussed in Volume 2, Chapter 11, is an example of the use of a graphical procedure

to find the optimum value.

Example 1.1

The optimum proportions for a cylindrical container. A classical example of the optimi-

sation of a simple function.

The surface area, A, of a closed cylinder is:

A D ð Dð L C 2

4

D2

where D D vessel diameter

L D vessel length (or height)

This will be the objective function which is to be minimised; simplified:

fD ð L D Dð L C D

2

2

equation A

For a given volume, V, the diameter and length are related by:

V D

4

D2 ð L

and

L D 4V

D2

equation B

and the objective function becomes

fD D 4V

D

C D

2

2

Setting the differential of this function zero will give the optimum value for D

4V

D2

C D D 0

D D 3

√

4V

From equation B, the corresponding length will be:

L D 3

√

4V

So for a cylindrical container the minimum surface area to enclose a given volume is

obtained when the length is made equal to the diameter.

In practice, when cost is taken as the objective function, the optimum will be nearer

L D 2D; the proportions of the ubiquitous tin can, and oil drum. This is because the cost

material (the surface area); see Wells (1973).

If the vessel is a pressure vessel the optimum length to diameter ratio will be even

greater, as the thickness of plate required is a direct function of the diameter; see

Chapter 13. Urbaniec (1986) gives procedures for the optimisation of tanks and vessel,

and other process equipment.

1.10.3. Multiple variable problems

The general optimisation problem can be represented mathematically as:

f D fv1, v2, v3,. .., vn

1.2

where f is the objective function and v1, v2, v3,... , vn are the variables.

In a design situation there will be constraints on the possible values of the objective

function, arising from constraints on the variables; such as, minimum flow-rates, maximum

allowable concentrations, and preferred sizes and standards.

Some may be equality constraints, expressed by equations of the form:

m D mv1, v2, v3,. .., vn D 0

1.3

Others as inequality constraints:

p D pv1, v2, v3,.. . , vn Pp

1.4

The problem is to find values for the variables v1 to vn that optimise the objective function:

that give the maximum or minimum value, within the constraints.

Analytical methods

If the objective function can be expressed as a mathematical function the classical methods

of calculus can be used to find the maximum or minimum. Setting the partial derivatives

to zero will produce a set of simultaneous equations that can be solved to find the optimum

values. For the general, unconstrained, objective function, the derivatives will give the

critical points; which may be maximum or minimum, or ridges or valleys. As with single

variable functions, the nature of the first derivative can be found by taking the second

derivative. For most practical design problems the range of values that the variables

can take will be subject to constraints (equations 1.3 and 1.4), and the optimum of the

constrained objective function will not necessarily occur where the partial derivatives

of the objective function are zero. This situation is illustrated in Figure 1.16 for a two-

dimensional problem. For this problem, the optimum will lie on the boundary defined by

the constraint y D a.

The method of Lagrange’s undetermined multipliers is a useful analytical technique for

dealing with problems that have equality constraints (fixed design values). Examples of

the use of this technique for simple design problems are given by Stoecker (1989), Peters

and Timmerhaus (1991) and Boas (1963a).

Feasible region

Minimum of

function

y = a

f(v)v

Figure 1.16. Effect of constraints on optimum of a function

Search methods

The nature of the relationships and constraints in most design problems is such that

the use of analytical methods is not feasible. In these circumstances search methods,

that require only that the objective function can be computed from arbitrary values of

the independent variables, are used. For single variable problems, where the objective

function is unimodal, the simplest approach is to calculate the value of the objective

function at uniformly spaced values of the variable until a maximum (or minimum) value

is obtained. Though this method is not the most efficient, it will not require excessive

computing time for simple problems. Several more efficient search techniques have been

developed, such as the method of the golden section; see Boas (1963b) and Edgar and

Himmelblau (2001).

Efficient search methods will be needed for multi-dimensional problems, as the number

of calculations required and the computer time necessary will be greatly increased,

compared with single variable problems; see Himmelblau (1963), Stoecker (1971),

Beveridge and Schechter (1970), and Baasel (1974).

Two variable problems can be plotted as shown in Figure 1.17. The values of the

objective function are shown as contour lines, as on a map, which are slices through the

three-dimensional model of the function. Seeking the optimum of such a function can be

Yield contours

75%

Temperature

Pressure80%

85%

90%

Figure 1.17. Yield as a function of reactor temperature and pressure

this type of problem is the gradient method (method of steepest ascent, or descent), see

Edgar and Himmelblau (2001).

1.10.4. Linear programming

Linear programming is an optimisation technique that can be used when the objective

function and constraints can be expressed as a linear function of the variables; see Driebeek

(1969), Williams (1967) and Dano (1965).

The technique is useful where the problem is to decide the optimum utilisation of

resources. Many oil companies use linear programming to determine the optimum schedule

of products to be produced from the crude oils available. Algorithms have been developed

for the efficient solution of linear programming problems and the SIMPLEX algorithm,

Dantzig (1963), is the most commonly used.

Examples of the application of linear programming in chemical process plant design

and operation are given by Allen (1971), Rudd and Watson (1968), Stoecker (1991), and

Urbaniec (1986).

1.10.5. Dynamic programming

Dynamic programming is a technique developed for the optimisation of large systems;

see Nemhauser (1966), Bellman (1957) and Aris (1963).

The basic approach used is to divide the system into convenient sub-systems and

optimise each sub-system separately, while taking into account the interactions between

the sub-systems. The decisions made at each stage contribute to the overall systems

objective function, and to optimise the overall objective function an appropriate combi-

nation of the individual stages has to be found. In a typical process plant system the

possible number of combinations of the stage decisions will be very large. The dynamic

programming approach uses Bellman’s “Principle of Optimality”,† which enables the

optimum policy to be found systematically and efficiently by calculating only a fraction

of the possible combinations of stage decisions. The method converts the problem from

the need to deal with “N” optimisation decisions simultaneously to a sequential set of “N”

problems. The application of dynamic programming to design problems is well illustrated

in Rudd and Watson’s book; see also Wells (1973) and Edgar and Himmelblau (2001).

1.10.6. Optimisation of batch and semicontinuous processes

In batch operation there will be periods when product is being produced, followed by non-

productive periods when the product is discharged and the equipment prepared for the

next batch. The rate of production will be determined by the total batch time, productive

† Bellman’s (1957) principle of optimality: “An optimal policy has the property that, whatever the initial state

and the initial decision are, the remaining decisions must constitute an optimal policy with regard to the state

resulting from the first decision.”

Batches per year D 8760 ð plant attainment

batch cycle time

1.5

where the “plant attainment” is the fraction of the total hours in a year (8760) that the

plant is in operation.

Annual production D quantity produced per batch ð batches per year.

Cost per unit of production D annual cost of production

annual production rate

1.6

With many batch processes, the production rate will decrease during the production

period; for example, batch reactors and plate and frame filter presses, and there will

be an optimum batch size, or optimum cycle time, that will give the minimum cost per

unit of production.

For some processes, though they would not be classified as batch processes, the period

of continuous production will be limited by gradual changes in process conditions; such

as, the deactivation of catalysts or the fouling of heat-exchange surfaces. Production will

be lost during the periods when the plant is shut down for catalyst renewal or equipment

clean-up, and, as with batch process, there will be an optimum cycle time to give the

minimum production cost.

The optimum time between shut-downs can be found by determining the relationship

between cycle time and cost per unit of production (the objective function) and using one

of the optimisation techniques outlined in this section to find the minimum.

With discontinuous processes, the period between shut-downs will usually be a function

of equipment size. Increasing the size of critical equipment will extend the production

period, but at the expense of increased capital cost. The designer must strike a balance

between the savings gained by reducing the non-productive period and the increased

investment required.

1.11. REFERENCES

ALLEN, D. H. (1971) Brit. Chem. Eng. 16, 685. Linear programming models.

ARIS, R. (1963) Discrete Dynamic Programming (Blaisdell).

BAASEL, W. D. (1965) Chem. Eng., NY 72 (Oct. 25th) 147. Exploring response surfaces to establish optimum

conditions.

BAASEL, W. D. (1974) Preliminary Chemical Engineering Plant Design (Elsevier).

BEIGHTLER, C. S. and WILDE, D. J. (1967) Foundations of Optimisation (Prentice-Hall).

BELLMAN, R. (1957) Dynamic Programming (Princeton University, New York).

BERGE, C. (1962) Theory of Graphs and its Applications (Wiley).

BEVERIDGE, G. S. G. and SCHECHTER, R. S. (1970) Optimisation: Theory and Practice (McGraw-Hill).

BOAS, A. H. (1963a) Chem. Eng., NY 70 (Jan. 7th) 95. How to use Lagrange multipliers.

BOAS, A. H. (1963b) Chem. Eng., NY 70 (Feb. 4th) 105. How search methods locate optimum in univariate

problems.

BURKLIN, C. R. (1979) The Process Plant Designers Pocket Handbook of Codes and Standards (Gulf).

CASEY, R. J. and FRAZER, M. J. (1984) Problem Solving in the Chemical Industry (Pitman).

CHADDOCK, D. H. (1975) Paper read to S. Wales Branch, Institution of Mechanical Engineers (Feb. 27th).

Thought structure, or what makes a designer tick.

solving approach.

DANO, S. (1965) Linear Programming in Industry (Springer-Verlag).

DANTZIG, G. B. (1963) Linear Programming and Extensions (Princeton University Press).

DRIEBEEK, N. J. (1969) Applied Linear Programming (Addison-Wesley).

EDGAR, T. E. and HIMMELBLAU, D. M., 2nd edn (2001) Optimization of Chemical Processes (McGraw-Hill).

HENLEY, E. J. and ROSEN, E. M. (1969) Material and Energy Balance Computations (Wiley).

HIMMELBLAU, D. M. (1963) Ind. Eng. Chem. Process Design and Development 2, 296. Process optimisation by

search techniques.

JONES, C. J. (1970) Design Methods: Seeds of Human Futures (Wiley).

KWAUK, M. (1956) AIChE Jl 2, 240. A system for counting variables in separation processes.

LEE, W. CHRISTENSEN J. H. and RUDD, D. F. (1966): AIChE Jl 12, 1104. Design variable selection to simplify

process calculations.

LEE, W. and RUDD, D. F. (1966) AIChE Jl 12, 1185. On the ordering of recycle calculations.

NEMHAUSER, G. L. (1966) Introduction to Dynamic Programming (Wiley).

PETERS, M. S. and TIMMERHAUS, K. D. (1991) Plant Design and Economics for Chemical Engineers, 4th edn

(McGraw-Hill).

POLYA, G. (1957) How to Solve It, 2nd edn (Doubleday).

RASE H. F and BARROW, M. H. (1964) Project Engineering (Wiley).

RUDD, D. F. and WATSON, C. C. (1968) Strategy of Process Design (Wiley).

SMITH, B. D. (1963) Design of Equilibrium Stage Processes (McGraw-Hill).

STOECKER, W. F. (1989) Design of Thermal Systems 3rd edn (McGraw-Hill).

URBANIEC, K. (1986) Optimal Design of Process Equipment (Ellis Horwood).

WELLS, G. L. (1973) Process Engineering with Economic Objective (Leonard Hill).

WILDE, D. J. (1964) Optimum Seeking Methods (Prentice-Hall).

WILLIAMS, N. (1967) Linear and Non-linear Programming in Industry (Pitman).

1.12. NOMENCLATURE

Dimensions

in MLTq

C

Number of components

D

Diameter

L

F

Stream flow rate

MT1

f

General function

fi

General function (design relationship)

f1, f2 ... General functions (design relationships)

L

Length

L

Nd

Degrees of freedom in a design problem

N0d

Degrees of freedom (variables free to be selected as design variables)

Nr

Number of design relationships

Nv

Number of variables

P

Pressure

ML1T2

Pp

Inequality constraints

q

Heat input, flash distillation

ML2T3

T

Temperature

q

vj

Variables

v1, v2 ... Variables

x1,x2 ... Variables

Equality constraint function

Inequality constraint function

Suffixes

1

Inlet, flash distillation

2

Vapour outlet, flash distillation

3

Liquid outlet, flash distillation

1.1. Given that 1 in D 25.4 mm; 1 lbm D 0.4536 kg; 1 ŽF D 0.556 ŽC; 1 cal D 4.1868 J;

g D 9.807 m s2, calculate conversion factors to SI units for the following

terms:

i. feet

ii. pounds mass

iii. pounds force

iv. horse power (1 HP D 550 foot pounds per second)

v. psi (pounds per square inch)

vi. lb ft1 s1 (viscosity)

vii. poise (gm cm1 s1)

viii. Btu (British Thermal Unit)

ix. CHU (Centigrade Heat Unit) also known as PCU (Pound Centigrade Unit)

x. Btu ft2 h1 ŽF1 (heat transfer coefficient).

1.2. Determine the degrees of freedom available in the design of a simple heat

exchanger. Take the exchanger as a double-pipe exchanger transferring heat

between two single-phase streams.

1.3. A separator divides a process stream into three phases: a liquid organic stream, a

liquid aqueous stream, and a gas stream. The feed stream contains three compo-

nents, all of which are present to some extent in the separated steams. The compo-

sition and flowrate of the feed stream are known. All the streams will be at the same

temperature and pressure. The phase equilibria for the three phases is available.

How many design variables need to be specified in order to calculate the output

stream compositions and flow rates?

1.4. A rectangular tank with a square base is constructed from 5 mm steel plates. If

the capacity required is eight cubic metres determine the optimum dimensions if

the tank has:

i. a closed top

ii. an open top.

1.5. Estimate the optimum thickness of insulation for the roof of a house, given the

following information. The insulation will be installed flat on the attic floor.

Overall heat transfer coefficient for the insulation as a function of thickness, U

values (see Chapter 12):

thickness, mm

0

25

50

100

150

200

250

U, Wm2 ŽC1

20

0.9

0.7

0.3

0.25

0.20

0.15

Average temperature difference between inside and outside of house 10 ŽC; heating

period 200 days in a year.

Cost of insulation, including installation, £70/m3. Capital charges (see Chapter 6)

15 per cent per year. Cost of fuel, allowing for the efficiency of the heating

system, 6p/MJ.

Note: the rate at which heat is being lost is given by U ðT, W/m2, where U

is the overall coefficient and T the temperature difference; see Chapter 12.

given the following information. The insulation will be installed flat on the attic

floor.

Overall heat transfer coefficient for the insulation as a function of thickness, U

values (see Chapter 12):

thickness, mm

0

25

50

100

150

200

250

U, Wm2 ŽC1

20

0.9

0.7

0.3

0.25

0.20

0.15

Average temperature difference between inside and outside of house 12 ŽC; heating

period 250 days in a year. Cost of insulation, including installation, $120/m3.

Capital charges (see chapter 6) 20 per cent per year. Cost of fuel, allowing for the

efficiency of the heating system, 9c/MJ.

Note: the rate at which heat is being lost is given by UðT, W/m2, where U

is the overall coefficient and T the temperature difference; see Chapter 12.

1.7. What is the optimum practical shape for a dwelling, to minimise the heat losses

through the building fabric?

Why is this optimum shape seldom used?

What people do use the optimum shape for their winter dwellings? Is heat retention

their only consideration in their selection of this shape?

1.8. You are part of the design team working on a project for the manufacture of

cyclohexane.

The chief engineer calls you into his office and asks you to prepare an outline

design for an inert gas purging and blanketing system for the reactors and other

equipment, on shutdown. This request arises from a report into an explosion and

fire at another site manufacturing a similar product.

Following the steps given in Figure 1.2, find what you consider the best solution

to this design problem.

CHAPTER 2

Fundamentals of Material Balances

2.1. INTRODUCTION

Material balances are the basis of process design. A material balance taken over the

complete process will determine the quantities of raw materials required and products

produced. Balances over individual process units set the process stream flows and

compositions.

A good understanding of material balance calculations is essential in process design.

In this chapter the fundamentals of the subject are covered, using simple examples to

illustrate each topic. Practice is needed to develop expertise in handling what can often

become very involved calculations. More examples and a more detailed discussion of the

subject can be found in the numerous specialist books written on material and energy

balance computations. Several suitable texts are listed under the heading of “Further

Reading” at the end of this chapter.

The application of material balances to more complex problems is discussed in “Flow-

sheeting”, Chapter 4.

Material balances are also useful tools for the study of plant operation and trouble

shooting. They can be used to check performance against design; to extend the often

limited data available from the plant instrumentation; to check instrument calibrations;

and to locate sources of material loss.

2.2. THE EQUIVALENCE OF MASS AND ENERGY

Einstein showed that mass and energy are equivalent. Energy can be converted into mass,

and mass into energy. They are related by Einstein’s equation:

E D mc2

2.1

where E D energy, J,

m D mass, kg,

c D the speed of light in vacuo, 3 ð 108 m/s.

The loss of mass associated with the production of energy is significant only in nuclear

reactions. Energy and matter are always considered to be separately conserved in chemical

reactions.

2.3. CONSERVATION OF MASS

The general conservation equation for any process system can be written as:

Material out D Material in C Generation Consumption Accumulation

34

mass is neither generated nor consumed; but if a chemical reaction takes place a particular

chemical species may be formed or consumed in the process. If there is no chemical

reaction the steady-state balance reduces to

Material out D Material in

A balance equation can be written for each separately identifiable species present, elements,

compounds or radicals; and for the total material.

Example 2.1

2000 kg of a 5 per cent slurry of calcium hydroxide in water is to be prepared by diluting

a 20 per cent slurry. Calculate the quantities required. The percentages are by weight.

Solution

Let the unknown quantities of the 20% slurry and water be X and Y respectively.

Material balance on Ca(OH)2

In

Out

X

20

100

D 2000 ð 5

100

a

Balance on water

X

100 20

100

C Y D 2000 100 5

100

b

From equation a X D 500 kg.

Substituting into equation b gives Y D 1500 kg

Check material balance on total quantity:

XC Y D 2000

500 C 1500 D 2000, correct

2.4. UNITS USED TO EXPRESS COMPOSITIONS

When specifying a composition as a percentage it is important to state clearly the basis:

weight, molar or volume.

The abbreviations w/w and v/v are used to designate weight basis and volume basis.

Example 2.2

Technical grade hydrochloric acid has a strength of 28 per cent w/w, express this as a

mol fraction.

Basis of calculation 100 kg of 28 per cent w/w acid.

Molecular mass: water 18, HCl 36.5

Mass HCl D 100 ð 0.28 D 28 kg

Mass water D 100 ð 0.72 D 72 kg

kmol HCl D 28

36.5

D 0.77

kmol water D 72

18

D 4.00

Total mols

D 4.77

mol fraction HCl D 0.77

4.77

D 0.16

mol fraction water D 4.00

4.77

D 0.84

Check total

1.00

Within the accuracy needed for technical calculations, volume fractions can be taken

as equivalent to mol fractions for gases, up to moderate pressures (say 25 bar).

Trace quantities are often expressed as parts per million (ppm). The basis, weight or

volume, needs to be stated.

ppm D quantity of component

total quantity

ð 106

Note. 1 ppm D 104 per cent.

Minute quantities are sometimes quoted in ppb, parts per billion. Care is needed here,

as the billion is usually an American billion (109), not the UK billion (1012).

2.5. STOICHIOMETRY

Stoichiometry (from the Greek stoikeion

element) is the practical application of the

law of multiple proportions. The stoichiometric equation for a chemical reaction states

unambiguously the number of molecules of the reactants and products that take part; from

which the quantities can be calculated. The equation must balance.

With simple reactions it is usually possible to balance the stoichiometric equation by

inspection, or by trial and error calculations. If difficulty is experienced in balancing

complex equations, the problem can always be solved by writing a balance for each

element present. The procedure is illustrated in Example 2.3.

Example 2.3

Write out and balance the overall equation for the manufacture of vinyl chloride from

ethylene, chlorine and oxygen.