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 |  موضوع: كتاب Petroleum Refining Design and Applications Handbook - Volume 2 الإثنين 07 مارس 2022, 5:39 pm | |
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Petroleum Refining Design and Applications Handbook - Volume 2
• Rules of Thumb • Process Planning,
Scheduling and
Flowsheet Design
• Process Piping
Design
• Pumps • Compressors • Process safety
Incidents
A. Kayode Coker
و المحتوى كما يلي :
Contents
Preface xv
Acknowledgements xvii
13 Rules of Thumb—Summary 1
13.0 Introduction 1
14 Process Planning, Scheduling, and Flowsheet Design 19
14.1 Introduction 19
14.2 Organizational Structure 20
14.2.1 Process Design Scope 21
14.3 Role of the Process Design Engineer 23
14.4 Computer-Aided Flowsheeting 24
14.5 Flowsheets—Types 26
14.5.1 Block Diagram 26
14.5.2 Process Flowsheet or Flow Diagram 26
14.5.3 Piping Flowsheet or Mechanical Flow Diagram, or Piping and Instrumentation Diagram
(P&ID) 27
14.5.4 Combined Process and Piping Flowsheet or Diagram 32
14.5.5 Utility Flowsheets or Diagrams (ULDs) 32
14.5.6 Special Flowsheets or Diagrams 36
14.5.7 Special or Supplemental Aids 36
14.6 Flowsheet Presentation 36
14.7 General Arrangements Guide 36
14.8 Computer-Aided Flowsheet Design/Drafting 38
14.9 Flowsheet Symbols 40
14.10 Line Symbols and Designations 43
14.11 Materials of Construction for Lines 46
14.12 Test Pressure for Lines 47
14.13 Working Schedules 56
14.14 Information Checklists 61
14.15 Basic Engineering and Front End Engineering Design (FEED) 63
References 64
15 Fluid Flow 65
15.1 Introduction 65
15.2 Flow of Fluids in Pipes 65
15.3 Scope 70
15.4 Basis 72
15.5 Incompressible Flow 72
15.6 Compressible Flow: Vapors and Gases 73
15.7 Important Pressure Level References 75
15.8 Factors of “Safety” for Design Basis 75
15.9 Pipe, Fittings, and Valves 75
15.10 Pipe 75x Contents
15.11 Total Line Pressure Drop 78
15.11.1 Relationship Between the Pipe Diameter and Pressure Drop (ΔP) 80
15.11.2 Economic Balance in Piping and Optimum Pipe Diameter 82
15.12 Reynolds Number, Re (Sometimes Used NRe) 83
15.13 Pipe Relative Roughness 85
15.14 Darcy Friction Factor, f 85
15.15 Friction Head Loss (Resistance) in Pipe, Fittings, and Connections 94
15.15.1 Pressure Drop in Straight Pipe: Incompressible Fluid 94
15.16 Oil System Piping 96
15.16.1 Density and Specific Gravity 97
15.16.2 Specific Gravity of Blended Products 98
15.16.3 Viscosity 98
15.16.4 Viscosity of Blended Products 100
15.16.5 Blending Index, H 101
15.16.6 Vapor Pressure 101
15.16.7 Velocity 101
15.16.8 Frictional Pressure Drop, ft of Liquid Head 104
15.16.9 Hazen–Williams Equation 105
15.16.10 Transmission Factor 107
15.16.11 Miller Equation 112
15.16.12 Shell–MIT Equation 113
15.17 Pressure Drop in Fittings, Valves, and Connections 116
15.17.1 Incompressible Fluid 116
15.17.2 Velocity and Velocity Head 116
15.17.3 Equivalent Lengths of Fittings 117
15.17.4 L/D Values in Laminar Region 120
15.17.5 Validity of K Values 122
15.17.6 Laminar Flow 122
15.17.7 Expressing All Pipe Sizes in Terms of One Diameter 124
15.17.8 Loss Coefficient 128
15.17.9 Sudden Enlargement or Contraction 134
15.17.10 For Sudden Contractions 134
15.17.11 Piping Systems 136
15.18 Resistance of Valves 136
15.19 Flow Coefficients for Valves, C
v
137
15.20 Flow Meters 138
15.20.1 Process Design of Orifice Meter 138
15.20.2 Nozzles and Orifices 142
Conclusion 167
15.21 Estimation of Pressure Loss Across Control Valves 169
15.22 The Direct Design of a Control Valve 173
15.23 Water Hammer 173
15.24 Friction Pressure Drop for Compressible Fluid Flow 175
15.24.1 Compressible Fluid Flow in Pipes 176
15.24.2 Maximum Flow and Pressure Drop 177
15.24.3 Sonic Conditions Limiting Flow of Gases and Vapors 177
15.24.4 The Mach Number, Ma 182
15.24.5 Critical Pressure Ratio 197
15.24.6 Adiabatic Flow 200
15.24.7 The Expansion Factor, Y 201
15.24.8 Misleading Rules of Thumb for Compressible Fluid Flow 203Contents xi
15.24.9 Other Simplified Compressible Flow Methods 204
15.24.10 Friction Drop for Flow of Vapors, Gases and Steam 205
15.25 Darcy Rational Relation for Compressible Vapors and Gases 213
15.26 Velocity of Compressible Fluids in Pipe 215
15.27 Procedure 228
15.28 Friction Drop for Compressible Natural Gas in Long Pipe Lines 231
15.29 Panhandle-A Gas Flow Formula 235
15.30 Modified Panhandle Flow Formula 237
15.31 American Gas Association (AGA) Dry Gas Method 237
15.32 Complex Pipe Systems Handling Natural (or Similar) Gas 237
15.33 Two-Phase Liquid and Gas Flow in Process Piping 239
15.33.1 Flow Patterns 239
15.33.2 Flow Regimes 242
15.33.3 Pressure Drop 243
15.33.4 Erosion–Corrosion 248
15.33.5 Total System Pressure Drop 250
15.33.6 Pipe Sizing Rules 257
15.33.7 A Solution for All Two-Phase Problems 261
15.33.8 Gas–Liquid Two-Phase Vertical Down Flow 270
15.33.9 Pressure Drop in Vacuum Systems 277
15.33.10 Low Absolute Pressure Systems for Air 279
15.33.11 Vacuum for Other Gases and Vapors 281
15.33.12 Pressure Drop for Flashing Liquids 284
15.33.13 Sizing Condensate Return Lines 286
15.34 UniSim Design PIPESYS 295
15.35 Pipe Line Safety 300
15.36 Mitigating Pipeline Hazards 301
15.37 Examples of Safety Design Concerns 301
15.38 Safety Incidents Related With Pipeworks and Materials of Construction 303
15.39 Lessons Learned From Piping Designs 319
15.40 Design of Safer Piping 320
15.40.1 Best Practices for Process Piping 320
15.40.2 Designing Liquid Piping 321
15.40.3 Best Practices for Liquid Piping 322
Nomenclature 324
Greek Symbols 326
Subscripts 327
References 327
16 Pumps 331
16.1 Pumping of Liquids 331
16.2 Pump Design Standardization 336
16.3 Basic Parts of a Centrifugal Pump 336
16.4 Centrifugal Pump Selection 341
16.5 Hydraulic Characteristics for Centrifugal Pumps 359
16.6 Suction Head or Suction Lift, h
s
367
16.7 Discharge Head, hd 369
16.8 Velocity Head 369
16.9 Friction 370
16.10 Net Positive Suction Head (NPSH) and Pump Suction 370
16.11 General Suction System 378xii Contents
16.12 Reductions in NPSH
R 384
16.13 Charting NPSHR Values of Pumps 384
16.14 Net Positive Suction Head (NPSH) 386
16.15 NPSH Requirement for Liquids Saturation With Dissolved Gases 388
16.16 Specific Speed 390
16.17 Rotative Speed 394
16.18 Pumping Systems and Performance 395
16.19 Power Requirements for Pumping Through Process Lines 399
16.20 Affinity Laws 405
16.21 Centrifugal Pump Efficiency 417
16.22 Effects of Viscosity 421
16.23 Temperature Rise and Minimum Flow 436
16.24 Centrifugal Pump Specifications 440
16.25 Number of Pumping Units 441
16.26 Rotary Pumps 448
16.27 Reciprocating Pumps 452
16.28 Pump Selection 456
16.29 Selection Rules-of-Thumb 456
16.30 Case Studies 459
16.31 Pump Cavitations 464
16.32 Pump Fundamentals 474
16.33 Operating Philosophy 475
16.34 Piping 485
16.35 Troubleshooting Checklist for Centrifugal Pumps 485
Nomenclature 493
Subscripts 494
Greek Symbols 495
References 495
17 Compression Equipment 497
17.1 Introduction 497
17.2 General Application Guide 498
17.3 Specification Guides 499
17.4 General Considerations for Any Type of Compressor Flow Conditions 501
17.4.1 Fluid Properties 501
17.4.2 Compressibility 502
17.4.3 Corrosive Nature 502
17.4.4 Moisture 502
17.4.5 Special Conditions 502
17.5 Reciprocating Compression 503
17.6 Suction and Discharge Valves 514
17.7 Specification Sheet 523
17.8 Performance Considerations 524
17.9 Compressor Performance Characteristics 557
17.10 Hydrogen Use in the Refinery 594
17.10.1 IsoTherming Technology for Kerosene, Vacuum Gas Oil, and Diesel
Hydroprocessing 595
Nomenclature 829
Greek Symbols 832Contents xiii
Subscripts 832
References 833
Glossary of Petroleum and Technical Terminology 837
Appendix D 929
Appendix E 1005
Index 1019
About the Author
Index
Abrasion, 349
Abrasiveness, 175
Absorber, 28
Absorption, 1, 4, 6
Accumulator, 159
Adiabatic, 73, 185, 200, 205, 207, 244
ADIP, 158
Adsorbent, 269
Aftercooler, 149–151, 154–156
AGA, 237
Alignment, 13
Alkylation, 99, 312–316, 478
Allowable, 348, 438
Altercooler, 153, 159
Annular, 240
ANSI, 76, 122, 322
API, 97–98, 126, 307, 310, 313, 320, 323
Axial, 173, 312, 332, 347, 390, 458
Backplate, 163
Bearing, 345–346, 489, 491
Bearings, 174, 189, 245
Bellows, 339
Below, 87
Bernoulli, 73, 140, 148, 201
Bhp, 419–420, 452
Block, 26, 34, 52
Blowdown, 45, 52
Blower, 42, 44, 51
Brake, 438
Breaker, 374–375, 379, 485
Bubble, 240
Bubbles, 368, 370–374
Bushing, 182
Cameron, 75, 120, 225, 295, 324, 327, 366, 381,
397, 495
CAPCOST, 1, 4, 6
Cavitating, 373–374, 407, 420, 468
Centifugal, 187
Centistokes, 100, 295, 422, 425–426
Centrifugal, 1, 42, 44, 58–59, 101, 157
Chattering, 326
Checklist, 61
Chen, 91–92, 94, 251, 284, 327
Chenoweth, 328
Choke, 200
Churchill, 91–92
Clearance, 136, 312
Code, 322–323
Codes, 23, 40, 43, 50, 52–53
Coker, 65–66, 243, 327–3281020 Index
Colebrook, 87, 91, 107–109, 114, 130, 231, 327
Combustion, 495
Compressibility, 6, 31, 40–66, 68, 78, 87, 144,
146–147, 186, 226, 249, 280, 326, 337
Compression, 33, 79–84, 86–89, 298, 312
Compressor, 41–42, 44–45, 51, 295, 320–321
Compressors, 1, 4, 6, 86, 173, 244
Computer, 23–24, 38–39
Condensable, 6, 229, 298, 336
Control, 178, 197, 200, 281, 300, 317, 338–339
Conveyor, 1, 4, 6
Cooler, 121, 178, 259, 268
Cooling, 28, 76, 152, 158, 186, 329
Corrosion, 55–56, 75, 248, 300, 349, 416, 418,
473, 482
Corrosive, 6
Corrosiveness, 6, 175
Cracked, 309
Cracking, 101, 104, 196, 269
Crane, 130
Crankcase, 322
Crankshaft, 327
Crude, 27, 35
Cryogenic, 1, 338
Cyclone, 41
Cyclones, 1, 4, 6
Damping, 315
Darby, 435
Debottleneck, 269
Debutaniser, 473, 476
Debutanizer, 158–159
Desulfurization, 28
Desulphurization, 103
Dew, 151
Dewpoint, 315
Diesel, 99, 102–104
Discharge, 80, 146, 152, 157, 160, 216–217, 225, 324,
342, 416, 418, 450
Dispersed, 240–242, 246, 250, 258, 273
Distillation, 20, 23
Downflow, 258, 270, 276
Driver, 58–59
Drivers, 1, 4, 6, 30, 338
Drum, 1, 4, 6, 43, 51
Drying, 1, 315, 324, 329
Dukler, 261–263, 268, 290, 328
Economic, 19, 23, 25–26, 63
Efficiency, 416–418, 422, 440, 463–464, 493, 495
Ejector, 1, 4, 5, 6, 45, 51, 176
Ejectors, 278–281, 328
Embrittlement, 161
Emergency, 329
Enthalpy, 31–33, 39–40, 87, 108, 121, 123, 211–212,
214, 217–218, 220, 283, 290–291, 334
Entrainment, 309, 325, 328, 485
Entropy, 40, 215, 291, 337
Environmental, 490
Equipment, 19–21, 23–27, 36, 38, 41, 43, 47, 50–51,
53, 58, 63
Erosion, 310, 416, 418
Exchanger, 1, 4, 6
Exchangers, 27, 58
Exhaust, 151, 153–155
Expanders, 86
Explosion, 478
Factors, 72, 75, 117, 127, 171, 202, 219, 278, 327, 424,
427
Failure, 327, 329
Fan, 1, 4, 6
Fanning, 68, 72–73, 86, 94, 201, 253, 324
Fatalities, 303, 307, 317
Fatigue, 18–19, 26
Fenske, 1, 4, 6
Fittings, 54–55
Flammable, 16, 316, 479
Flashing, 284–286, 289, 329, 373–374, 485
Flixborough, 316–317
Flowsheet, 19, 21, 24–27, 36, 38–39, 43–44, 50–52, 56,
298, 459
Flowsheeting, 24–25, 64
Fluidization, 1, 4, 6
Fluorocarbon, 168–169
Fouling, 1, 4, 6
Friction, 280
Froth, 240, 274
Froude, 270, 273–276
Furnace, 293
Gas, 158
Gasoline, 96–97, 105–106, 109, 126, 303, 307, 309
Gear, 332, 449
Gearbox, 158, 320, 402, 405
Geometrically, 227, 278, 390, 406
Governor, 188, 283
Guidelines, 456
Hazard, 23, 63, 303, 310, 313–314, 318–321
Hazardous, 24, 36, 58, 480, 492
Hazards, 441, 480Index 1021
HAZOP, 23, 40, 316
Heptane, 256, 462
Heuristics, 1, 167
Hexane, 69–71, 261, 461
Homogeneous, 265, 327
Hooper, 129–132, 136, 327
Horsepower, 347–348, 353, 402, 405, 407, 422, 428, 456
Horsepowers, 204, 288
Hydraulic, 212
Hydrocarbon, 40, 64
Hydrocarbonprocessing, 496
Hydrocracker, 26
Hydrocracking, 99, 101
Hydrofluoric, 478, 482
Hydrogenation, 13, 99
Hydroprocessing, 99
Hydrotreater, 28
Hydrotreating, 103–104
Impeller, 162, 173, 333, 391
Incidents, 487
Incompressible, 96, 140, 143, 148, 201, 203, 459
Index, 101, 248
Inherent, 171, 315, 320
Inherently, 102, 310, 318
Instrument, 27, 39–40, 42, 46, 52
Insulation, 23–24, 27, 58, 176, 249, 302
Integrity, 481
Intercooler, 75, 152
Intermittent, 261
Interstage, 76, 157–158, 162, 164, 191, 271
Isenthalpic, 290
Isentropic, 73, 86, 198, 200–201
Isentropically, 81
Isoamylene, 70
Isobaric, 31
Isobutane, , 63–64, 313–314, 316
Isolation, 478
Isometric, 168, 469
Isometrics, 22, 39
Isopentane, 249
Isothermal, 31–32, 75, 176, 183, 185, 196, 201, 205,
215, 328
Jacket, 312
Kinetics, 1, 4, 6
Knockout, 1
Labyrinth, 182, 216
Laminar, 72, 99, 120, 122
Lapple, 328
Leakage, 101, 182, 313, 321
Leaks, 300, 317, 322
Liquefied, 157, 323
Lockhart, 243–244, 246, 257, 260–261
Louvar, 319, 329
Lubricant, 489
Lubricants, 6, 99
Mach, 180, 182–183, 185, 187, 188, 190, 194–195,
197–198, 204, 227, 228–229, 275, 289, 308, 334
Machine, 178, 202, 244
Machinery, 480
Maintenance, 82, 249, 302–303, 307–308, 312, 316,
318–320, 349, 495–496
Malfunctions, 485
Manufacturers, 23, 52
Martinelli, 243–244, 246–248, 252, 257, 260–261, 328
Material, 19, 21, 23, 25–27, 40, 42, 47, 50, 61, 63
Materials, 303, 311
Mechanical, 19, 21–23, 26–27, 32, 36, 39–41, 50, 58,
87–89, 292, 333, 336, 340, 444–445, 456, 479,
481, 488–489, 495
Metallurgical, 304, 308
Misalignment, 488–489
Mixing, 2, 4, 6
Model, 68, 265, 297–298, 313
Modeling, 469
Modulus, 174, 244–248, 257–258, 260–261
Moisture, 154
Monograph, 231, 233–235, 237, 328
Moody, 70, 72–74, 85–87, 91–92, 94, 107–108, 112,
115, 117, 120, 127–128, 153, 156, 162, 165,
235–236, 251, 253, 284, 324, 327
Mpeller, 187
Multicomponent, 2, 248
Multiphase, 328
Naphtha, 26, 151–152, 303
Nelson, 181
Nitrobenzene, 168
NPSH, 2, 4, 6, 117
NPSHA, 80, 331, 345, 371–374, 376–388, 390, 394,
411, 438, 440, 456, 464, 468–469, 471, 473–475,
477, 485, 487–489, 492
NPSHr, 470–471
NPHSR, 371
Operations, 19, 21, 39–41
Optimization, 24–25
Organization, 19–211022 Index
Orifice, 42, 44, 53, 432, 464
Orifices, 68, 142–145, 176, 201, 207, 210, 217,
221–226, 324, 326
OSHA, 40, 305, 485, 496
Overpressure, 302, 448
Packing, 15
Packings, 495
Panhandle, 73, 231, 235–237, 253
Patterns, 239–241, 257, 265, 270, 273, 285
Petrochemical, 331, 344, 359, 492
Petroleum, 2, 4, 6, 19–20, 22, 24, 26, 28, 30, 32, 34, 36,
38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64,
96–103, 105–107, 138, 157, 300–301, 303, 320,
322–323
PFD, 63, 459, 462, 464
PHA, 320
Pigging, 297–298, 300
Pipeline, 184, 253, 298, 300–301, 321, 329, 417
Pipesys, 295, 297–299, 328, 464
Pipework, 65, 168, 316–318
Piping, 2, 4, 6, 21, 23–25, 27, 32, 34, 36, 38–39, 45, 47,
50, 52–56, 58
Plug, 121, 132, 134, 240–242, 244, 252, 258, 261, 265,
273, 313, 316
Plunger, 326, 332, 452, 454
Polyatomic, 57
Polymerization, 63, 92, 241, 308
Polytropic, 33, 175, 207, 244, 270, 291
Power, 416, 418
Pressure, 342, 383
Process, 19–23, 25–29, 31–33, 35, 37, 39–43, 45–51,
53, 55–64
Propane, 190, 195, 309, 311
Propeller, 2
PSHA, 488
Pulsating, 80, 273
Pulsation, 196, 303, 310, 485
Pump, 36, 51–52, 58–59, 158–159, 342, 416, 418, 455
Pumps, 2, 4, 6
Purge, 8, 28
Radial, 337, 458
Ratings, 350
Reaction, 36, 52
Reactor, 2, 4, 6
Reactors, 27, 104, 307, 316–318
Reboiler, 120, 242, 246
Reciprocating, 2, 4, 6, 454, 458
Refineries, 96, 303, 305, 309–310, 313–314, 320
Refining, 2, 19–20, 22, 24, 26, 28, 30, 32, 34, 36, 38,
40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 82,
307, 313
Reforming, 20, 191
Refrigeration, 191, 324
Regenerators, 2
Regime, 83, 240, 242–246, 248, 250, 260–262, 265, 270
Relief, 177–178, 239, 302, 317, 319–321, 323, 326, 329,
448, 450, 492
Retainer, 186
Retrofti, 339
Reynolds, 280, 334
Rotary, 2, 4, 6, 332, 383, 391–392, 424, 427, 448–449,
495
Rotating, 178, 338, 451, 488
Rotor, 449–451
Roughness, 72, 85–88, 327
Rupture, 175, 249, 304, 307, 321, 492
Ruskin, 289–290, 329
Safeguards, 479
Safer, 320, 329
Safety, 75, 80, 169, 177–178, 249, 257, 287, 300, 303,
307, 312, 318–321, 323, 341, 416, 418, 481–482,
485, 496
Sarco, 71, 287–288, 328
Saturated, 85, 118, 179, 217, 326
Saturation, 284
Saybolt, 100–101
Schedule, 122, 214–215, 254, 297
Schedules, 23, 50, 58, 61
Scope, 20–22, 26, 61
Sealing, 416, 418
Sealless, 332
Seals, 161–162, 175, 181, 189, 338
Segregated, 261
Separator, 120, 239
Separators, 23, 51
Sequence, 26, 32, 36, 47, 50, 63
Sequestration, 318
Serghides, 93
Shaft, 333, 342–343
Shutdowns, 489
Simulation, 24, 63, 459–462, 464
Size, 78, 218, 296–297
Slug, 240, 274
Slugging, 297–298
Slugs, 328
Sonic, 177, 181, 187, 194, 202, 228, 282, 326
Sour, 157, 416, 418Index 1023
Specifications, 22–23, 27, 36, 50, 52–56, 58
Spirax, 288, 328
Stagnation, 198, 203–204
Standard, 34, 40, 54
Stationary, 186–187, 336, 339–341, 452
Stator, 4, 101, 293, 295
Steam, 5, 19, 30, 185, 187–188, 320
Stirrer, 2
Stonewall, 198, 272
Storage, 34, 41–42
Strain, 328
Strainer, 45, 51, 90, 415–418, 479
Stratified, 240–242, 245, 252, 258, 261
Streamlined, 277, 280
Strokes, 452, 456
Stuffing, 336, 339, 489
Subcooling, 372
Subsonic, 185
Suction, 80, 101, 117, 119–120, 151, 153, 157,
161–162, 165–166, 179, 245, 277, 284
Sulfidation, 304
Sulfuric, 118, 168
Superheatsteam, 218
Supersonic, 182
Surge, 198–199, 302
Surging, 197, 200
Sustainable, 101
Synthesis, 24–25
Tailpipes, 319
Technology 48–50, 58–62
Tesoro, 304
Texas, 307, 309
Thermodynamic, 72
Throat, 339
Throttle, 468
Throttling, 336, 376, 378, 419, 479
Thumb, 2, 4, 6
Toxic, 16, 299
Transmission, 107–109, 211, 231–232, 251–253, 321, 324
Traps, 249, 287–288, 319
Troubleshooting, 1, 19, 40, 290, 322, 328, 485,
488–489, 495
Turbine, 2, 320, 332, 334, 495
Turbocompressors, 338
Turbomachinery, 271
Turbulence, 446–447, 492
Underwood, 2
Upstream, 399, 478
Vacuum, 70–71, 75, 177, 181, 250, 277, 281–285, 310,
324–325, 380–382, 477
Valve, 90, 158, 177, 315
Vapor, 383
Vapors, 75, 118–119, 122, 137, 173, 175–177, 181,
220–223, 225
Vaporization, 325, 371
Vaporizing, 371
Vent, 170, 177, 185, 317, 319, 342
Vents, 32, 38
Venting, 177, 273, 276, 307, 317
Venturi, 44, 138, 140, 201
Vessel, 2, 4, 6, 379–381, 476
Vessels, 116, 123, 136, 260, 277, 319, 323
Vibration, 174, 182, 270, 275–276, 322–324, 489,
491
Vibrations, 227, 330
Visbreaker, 26
Viscosity, 342, 424, 427
Vortexing, 374, 446, 485
Washdown, 157
Washer, 333
Wastewater, 61
Water, 34, 43, 62, 64
Wave, 240–242, 245, 258
Wavy, 261
Workflow, 63
Worksheet, 32
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