Mann U. Principles of Chemical Reactor Analysis and Design: New Tools for Industrial Chemical Reactor Operations
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C.2 NUMERICAL INTEGRATION
Trapezoidal Rule The trapezoidal rule provides a first-order approximation of the
area of a function between two points:
I ¼
ð
x
2
x
1
f (x) dx ¼
x
2
x
1
2
[ f (x
1
) þ f (x
2
)] (C:4)
Simpson’s Rule This method is based on a second-order polynomial approxi-
mation of the function. For equally spaced points, the integral of the function
between x
0
and x
2
is
I ¼
ð
x
2
x
0
f (x) dx ¼
Dx
3
[ f (x
0
) þ 4f (x
1
) þ f (x
2
)] (C:5)
470 APPENDIX C
INDEX
Activation energy 86
Determination of 87
Activity coefficients 134
Adiabatic operations
Batch reactor 144, 165, 217, 224
CSTR 154, 321, 359, 364
Plug-flow reactor 153, 244,
284, 289
PFR with distributed feed 409
Recycle reactor 431
Semibatch reactor 387, 394
Adsorption 10
Arrhenius equation 86
Autocatalytic reactions 431
Batch-reactor 3, 29, 159– 230
Constant-volume 167–181
Variable-volume 181–189
Biological reactions see Enzymatic reactions
Bubble column reactor 7
Cascade of CSTRs 4, 336–341
Catalysis 10
Catalytic reactions 10, 257
Characteristic reaction time
Definition of 92
Determination of 93
Chemical formula 26
Co-current flow 282
Continuous stirred tank reactor (CSTR)
see Reactor
Conversion
Definition of 54
Relation to extent 54
Counter-current flow 282
Correction factor of heat capacity
Definition of 139, 150
for gas-phase reactions 142, 152
for liquid-phase reactions 142, 152
for distillation reactor 421
for PFR with distributed feed 405, 406
for recycle reactor 430
for semibatch reactor 386
Damkohler number 13
Dependent reactions 39
Relation to independent
reactions 43
Design equation see Reactor design
equation 43
Differential method 190 –192
Differential reactor 102
Diffusion coefficient 11
Diffusivity 9
Principles of Chemical Reactor Analysis and Design, Second Edition. By Uzi Mann
Copyright # 2009 John Wiley & Sons, Inc. All rights reserved.
471
Dimensionless variables, definition of
Activation energy 88
Extent 64
Heat 140
Heat of reaction 140
Heat transfer rate 153
Heat transfer number 140
Operating time 113
Space time 115
Distillation reactor 3, 416–425
Economics 441 –453
Effectiveness factor 10
Elementary reactions 26
Endothermic reactions 88
Energy of activation see Activation energy
Energy balance equation 15,
135– 156
for batch reactors 136– 145
for plug-flow reactor 150, 243
for steady flow reactors 147– 154
for CSTR 153, 320
for semibatch reactors 382– 384
for recycle reactor 429
for PFR with distributed feed 405
Enzymatic reactions 175, 331
Equilibrium constant 134
Ergun equation 301
Excess reactant 49
Exothermic reactions 88
Extent of reaction
Definition of 28
Experimental reactors 16
Fixed bed reactor see Packed-bed reactor
Fluidized bed reactor 5
Fluidized catalytic cracking 20
Formulation procedure
of design equations, batch reactor 199
of design equations, PFR 265
of design equations, CSTR 341
of energy balance equation, batch
reactor 216
of energy balance equation, PFR 283
of energy balance equation, CSTR 358
Fractional conversion see Conversion
Frequency factor see Pre-exponential factor
Friction factor 296
Gas–solid reactions 2, 12
Gaussian elimination 41
Generation rate 31
Global reaction rate 14, 91
Hatta number 13
Heat capacity
Dependence on composition 142
Dependence on temperature 143
of reference state or stream 141, 151
Heat of formation 131
Heat of reaction 131
Heat transfer coefficient 138
Heat transfer number (HTN)
Definition 140
Estimation of 165, 244, 321
Heterogeneous reactions 2
Homogeneous reactions 2
Hougen– Watson formulation 10
Independent chemical reactions 39–47
Determination of number of 40
Relation to dependent reactions 43
Selecting a set of 112
Independent species specifications 68–71
Interfacial area 82
Instantaneous HTN 165
Integral method 192
Intrinsic kinetics 91
Isothermal operations
of batch reactors 166–215
of plug-flow reactor 245– 281
of CSTR 322– 358
Kiln reactor 7
Kinetics 9, 81–97
Laminar flow 239
Langmuir– Hinshelwood formulation 10
Limiting reactant 48
Local HTN 244
Mass transfer 9
Michaelis– Menten rate expression 90
Molar flux 465
Momentum balance equation 15, 296
Moving bed reactor 6
Multiple steady-states 18
Nonideal flow 20
Nonisothermal operation
of batch reactors 216–230
of plug-flow reactor 281– 295
of CSTR 358– 370
of PFR with distributed feed 409
of recycle reactor 431
of semibatch reactors 387, 393
Numerical differentiation 469
472
INDEX
Optimization 441– 452
Order of reaction 89–90
Packed-bed reactor 6
Pore diffusion 2, 10
Porous catalyst 2
Power law rate expression 90
Pre-exponential factor 86 –90
Pressure drop 296 –308
Price of chemicals 443
Rate expression 86
Determination of 189 –193, 261, 333–334
Forms of 90
Rate of reaction 82– 84
Rate of species formation 81– 82
Rate law see Rate expression
Rate limiting step 10
Reaction intermediates 26
Reaction operating curve 117
Reaction pathway 26
Reaction rate constant 86
Reaction rates 83
Reactor
Batch 159– 230
Continuous stirred tank 317– 370
Distillation 416 –425
Plug-flow 239– 309
PFR with distributed feed 400–416
Recycle 425– 434
Semibatch 377– 400
Reactor design equation
Dimensionless forms 113–116
Reaction-based 107–112
Species-based 102 –107
Reference state 113
Reference stream 114
Resident time 20, 114
Residence time distribution 20
Reynolds number 9
Schmidt number 9
Second law of thermodynamics 300
Selectivity 59
Sherwood number 9
Shrinking core model 12
Shrinking particle model 12
Simpson rule 470
Sound velocity 300
Space time 114
Space velocity 114
Species balance equations 14, 101–107
Macroscopic form 102–104
Microscopic form 465 –469
Species continuity equations 465
Species formation rate 81
Species operating curves 117
Stirred tank reactor see CSTR
Stoichiometric coefficients 27
Stoichiometric proportion 48
Stoichiometric relationships, table of 456
Surface reactions 2
Thiele modulus 10
Transport limitations 9, 91
Trickle-bed reactor 5
Tubular reactor see Plug-flow reactor
Turbulent flow 239
Yield, definition of 58
INDEX 473