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
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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 10
3 m3
4.5461 ð 10
3
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
Composition
1
1
Enthalpy
2
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
3
CC 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 relationships
2
C
Equilibrium still restriction
3
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:
fi
vj D 0
where j D 1, 2, 3,..., Nv,
i D 1, 2, 3,..., Nr
Consider the following set of such equations:
f1
v1, v2 D 0
f2
v1, v2, v3, v5 D 0
f4
v2, v4, v5, v6 D 0
f5
v5, 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, p
f1 D 2, and at the v5 node it is 3,
p
v5 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:
fi
v1, 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.
f1
x1,x2 D 0
f2
x1,x3,x4 D 0
f3
x2,x3,x4,x5,x6 D 0
f4
x4,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:
f
D 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
f
D 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 f
v1, 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 m
v1, v2, v3,. .., vn D 0

1.3
Others as inequality constraints:
p D p
v1, 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
MT
1
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
ML
1T
2
Pp
Inequality constraints
q
Heat input, flash distillation
ML2T
3
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 s
2, 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 ft
1 s
1 (viscosity)
vii. poise (gm cm
1 s
1)
viii. Btu (British Thermal Unit)
ix. CHU (Centigrade Heat Unit) also known as PCU (Pound Centigrade Unit)
x. Btu ft
2 h
1 ŽF
1 (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, Wm
2 ŽC
1
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 ðT, 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, Wm
2 ŽC
1
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 UðT, 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 10
4 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.