The Reciprocating Pump Theory, Design, And Use - John E. Miller 2nd Edition
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The Reciprocating Pump Theory, Design, And Use - John E. Miller 2nd Edition...
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THE RECIPR CATIN THEORY, DESIGN, ANO USE Second Edition
John E. Mmer White Rock Engineering, Inc. Dallas, Texas
KRIEGER PUBUSHING COMPANY MALABAR, FLORIDA 1995
PU P
Second Edition 1995 Printed and Published by KRIEGER PUBUSHING COMPANY
KRIEGER ORIVE MALABAR, FLORIDA 32950 Copyright © 1995 by Krieger Publishing Company Ali rights reserved. No par! of this book may be reproduced in any form or by any means, electronic or mechanical, including informa!ion storage and retrieval systems without permission in writing from the publisher. No liability is assumed with respecl lo the use of the iriformation contained herein. Printed in the United States of America.
FROM A DECLARATION OF PRINC!PLES JOINTLY ADOPTED BY ,A COMMITTEE OF THE AMERICAN BAR ASSOCIATION ANDA COMMITTEE OF PUBLISHERS: This publication is designed to provide accurate and authoritalive information in regard to the subject matter covered. lt is sold with the understanding that !he publisher is not engaged in rendering legal, accounting, or other professional service. lf legal advice or other expert assistance is required, the services of a competen! professional person should be sought
Library of Congress Cataloging-in-Pubiication Dala Miller, John E. (John Evans), 1909-
The reciprocating pump : theory, design, and use / John E. Miller.-2nd ed. p. cm. lncludes index. ISBN 0-89464-599-4 (allc paper) L Reciprocating pumps. L Titie. TJ901.M55 1995 62L6'5-dc20
94-46260 CIP
!098765432
PRE
CE T
SEC NO EDITI N
In the four years following the First Edition, 'The Reciprocating Pump; Theory Design and Use' it became evident that the confüsion between the Centrifuga! Pump and the Reciprocating Pump had greatly increased because of the increased interest in reciprocating pumps for highly technical applications and high to extremely high discharge pressures (l0,000 to !00,000 PSI) for such services as water purification by reverse osmosis, cutting and cleaning materials, food processing, etc. High discharge pressure requirements prompted a discussion of high-pressure pump design and the method of Autofrettage of pump liquid-ends in order to reduce corrosion-fatigue failures in high pressure use. Further experience with the use of multiple pump applications and how to these for mínimum cost is included. Additional experience in the complicated effects of suction requirements has led to a completely new approach to the problems. This Edition is dedicated to the memory of my loving Margaret, who away on April 16, 1991, after 56 years of companionship of the kind that gave me the encouragement to complete this book and who, with the ravages of Alzheimers, sat for hours with an autographed copy of the First Edition clasped to her breast. JOHN
E.
MILLER
PREFACE
The intent of this book is to bring together rnost of the aspects of reciprocating purnps, keeping in rnind the requirernents of designers, rnanufacturers, and users. For rnany years there has been sorne confusion in the rnatter of the effects of liquid dynarnics (ftow variation and acceleration) on the performance of reciprocating purnps. One possible reason is the great difference between reciprocating and centrifuga! purnps; those dealing with the two types are usually not confronted with the sarne types of disturbances. Another reason is the neglect that reciprocating purnp theory has experienced in the midst of an increase in the problerns resulting frorn high-speed operation as the result of rnanufacturers' frequent speed upratings applied over the years dueto the pressure of cornpetition and econornics. Many subjects in this book are covered by rneans of discussion, allowing the reader to better understand the cause and effect. In rnany cases, examples of calculations and derivations are given to support the explanation. Aside frorn the casual interest associated with the past history of purnps, such history is sornetirnes used to draw attention to discarded ideas so that reinvention of the wheel will be avoided. (And they rnay stirnulate new ideas.) A rather new and wide application of reciprocating purnps is in the transportation of solids in the form of a liquid-rnixed slurry. This subject is covered in sorne detail. In order to provide a cornprehensive encyclopedia of reciprocating purnps, Chapters 13 and 14 contain many useful tables, charts, and conversions. After expressing appreciation to Oilwell Division of U.S. Steel Corp. for their sharing of knowledge to the industry, the author wishes to thank several experts and institutions in the field of purnping who have rnade valuable contributions, acknowledged throughout this text. Special thanks to Mike Rizzone, Bob Crane, •• ¡¡
Viii
PREFACE
and my son Jim Miller, professional engineers, and my son Ben Miller. All are well experienced in the field of reciprocating pumps and have reviewed the manuscript and offered many worthy suggestions. My wife, Margaret, supplied the encouragement. JOHN Dallas, Texas
E.
MILLER
e
NTENTS
1. PUMP TYPES l.l l .2 1.3 l .4 1.5
Definitions I l Nomenclature and Definitions I 13 Double-Acting vs. Single-Acting Pumps / 23 Plunger vs. Piston Pumps I 33 Interna!. Gears / 34
2. DYNAMICS 2.1 2.2 2.3
2.4 2.5 2.6 2.7 2.8 2. 9 2.10 2.11 2.12 2.13
Introduction I 36 Standard Definitions / 36 Flow Variation I 37 Acceleration / 38 Derivation of Acceleration Pressure / 40 Derivation of Acceleration Pressure at Pump Inlet / 41 Critica! Suction Conditions I 42 Discharge Acceleration I 42 Hydraulic Flow and Pressure Waveforms / 44 Discussion of Ideal Waveforms I 44 Mean or Average Flow Rate I 46 Pump Displacement / 47 Graphics of Pump Performance / 51
SUCTION REQUIREMENTS 3.1. l 3.1.2
36
55
Introduction / 55 Analysis of Suction Requirements / 57 ix
X
CONTENTS
3.1.3 3.1.4 3.1.5 3.1.6 3. l. 7 3. 2 3.2. l 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2. 7 3.2.8 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.5 3.6 3. 7 3. 8 3.9 3.10
More on Suction Requirements / 58 Suction Requirement Factors / 63 Valve Leakage and Slip / 65 Typical Suction Pressure Waveforms / 67 Relation of Pressure Waves to Pump Cycle / 67 Performance Curves I 69 Method of Recording Actual Mechanical End-of-Stroke / 69 Performance-POSIVA and RPM / 69 Performance-Reduced Plunger Diameter / 72 Volumetric Efficiency Statistics / 72 Short vs. Long Suction Line / 73 Acceleration / 74 Computer Calculations / 75 Suction Stabilizer / 75 Testing Pumps for Suction Requirements / 80 Introduction / 80 TCP Required, (TCPR) ! 81 Procedure for Testing ! 82 The Myth of NPSH ! 82 Air and Gas Saturation of Liquids / 86 Dissolved Gas at Pump Inlet / 87 Notes Regarding TCP ! 88 Methods of Increasing TCP / 88 Cavitation / 89 Suction Systems / 89
4. PULSATION ANO SURGE CONTROL 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 4.1. 7 4.1.8 4.1.9 4.2 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5
Pulsation Types / 95 Type DV - Discharge-Velocity / 95 Type DO - Discharge-Valve Open / 100 Type DR101 - Discharge-Acceleration (P,ac) / 101 Type SV - Suction Velocity / 101 Type SA - Suction Acceleration / 101 Type SD - Suction Valve Opening (P,v0 ) I 101 Type VA - Vertical Acceleration / 10 l Type PS - Pulsation-Surge ! 101 (WH)-Water Hammer ! 102 Dampener Types / 103 Type G / 103 Type GCAE / 103 Type GUAE ! 104 Type GCDE ! 104 Type LNFA ! 104
95
CONTENTS
xi
Type GFFE I l05 Type DCFR I 105 Reporting Degree of Pulsation / l 08 Discharge Dampening / 109 Gas-Type Dampener Sizing I l 11 Gas-Type Dampener Sizing Equations I 112 Derivation of K ! 114 PASAFE Pulsation Control Sizing / ll4 Multiple Dampeners I 117 Precharging Gas-Type Dampeners I l l 8 4.lO Vaporization or "Heated" Dampeners / 118 4.11 Manifolded Multiple Pumps (Phasing) I l l 9 4.12 The Suction Stabilizer / 120 4.13 4.14 The Discharge System I 120 Dampener Facts / 121 4.15 Dampener Performance í 121 4.16 Acoustic Filters / 123 4.17 The Suction Stabilizer / 125 4.18 Surge Control in Water Systems I 127 4.19 4.19.l Methods of Surge Control in Water Systems / 131 4.19.2 Sizing of Surge Suppressors / l 35 4.19.3 Conclusion I 137 4.20 Sample Problem I 138
4.2.6 4.2.7 4.3 4.4 4.5 4.6 4.7 4.8 4.9
5. PUMP DESIGN 5.1 5.2 5.3
Rating Standards I 140 Family Planning I 142 Windows of Non-utilization I 143 5. 4 Piston Rod Load i 144 5.4. l Unusual Pressure in the Pump Cylinder / 145 5.5 Maximum Piston Diameter i 146 5.6 Stroke Length / 146 5.7 NumberofCylinders I 147 5.8 Speed I 147 5.9 Speed of Duplex and Similar Pumps 149 5.10 Speed of Multicylinder Pumps I 149 5. 11 Direction of Rotation I 150 5.11. l Rotation "Overrunning" / 150 5.11.2 Rofation "Underrunning" I 152 5.12 Offset Crankshaft I 152 5.13 Connecting Rod Forces / 153 5.13.1 Introduction I 153 5. 13. 2 Equations / 154 5.14 Crankshafl Bending Moments-Calculations I 159
140
XII
CONTENTS
5.15 5.16 5.17 5.17.1 5.17.2 5.17.3 5.18 5.18.1 5.18.2 5.18.3 5.19 5.20 5.21 5.22 5.23
Crankshaft Bending Stress-Calculations I 161 Crossheads I 162 Bearings / 163 Roller Bearing B-10 Life I 164 Roller Bearing Average Life / 164 Journal Bearings / 165 Lubrication / 166 Pressure Lubrication / 166 Oil Cleaning I 167 Oil Temperature / 167 Volumetric Efficiency (Eq. 2.26) / 167 Mechanical Efficiency / 168 Intermittent Service I 169 Continuous Service / 170 Reciprocating Pumps with High Suction Pressure / 171
6. LIQUID ENDS 6.1 6.2 6.2.1 6.3 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.5 6.6 6.7
Typical Liquid-end Manifold Configurations / 172 S-N Curve I 172 The Goodman Diagram / 174 Stress I 176 Stress Reduction Methods I 177 Strain Bolts / 177 Autofrettage Procedure for Liquid Ends / 178 Shot Peening I 186 Coating and Plating / 186 Ultra-high Pressure Pump Design / 187 Abrasive Jet Cutting / 190 The Intensifier / 191
7. EXPENDABLE PARTS 7 .1 7.2 7 .2.1 7 .3 7.4 7.4.1 7.4.2 7.5 7. 5 .1 7.5.2 7.5.3 7.5.4 7.5.5
172
API Standards for Slush Pump Components / 193 Pump Liners / 206 Liner Development / 207 Pistons I 207 Plungers I 211 Metal-to-metal Plungers / 212 Ceramic Plunger Construction / 213 Packing / 215 Introduction and History / 215 Packing Types I 216 Split Packing Rings I 218 Spring Loaded Packing / 218 Segmenta! Metal Packing / 218
193
CONTENTS
7.5.6 7.5.7 7.5.8 7.5.9 7.5.10 7.5.11 7.5.12 7.6 7.7 7.8 7.9 7.10 7.10.1 7.10.2 7.10.3 7.10.4 7.10.5 7 .11 7.12 7.13 7.14
Multiple Material Assemblies / 219 Double Stack Height Seal Rings / 220 Spiral Packings / 220 FLAT-BAK Vee Ring I ·222 Knitted Wire Mesh / 222 Packing "Dos" / 223 Packing "Don'ts" / 224 0-Rings / 225 Controlled-Compression Gaskets / 225 Basic Elastomers / 226 Elastomers in Carbon Dioxide / 227 Stuffing Box Brass or Trim / 228 Stuffing Box Wear / 228 Stuffing Box Design Criteria / 230 Gland Tightening (Screwed Gland) / 231 Packing Lubrication / 231 Lubrication by Lantern Ring / 232 Jacoby Leakage I ·232 Glossary of Terms / 234 Guidelines for Material Selection / 236 Titanium as a Pump Material / 239
8. VALVES 8.1 8.2 8.3 8.4 8.5 8.6 8.6.1 8.6.2 8.6.3 8.6.4 8.6.5 8.6.6 8.6.7 8.6.8 8.6.9 8. 7 8.8 8.9 8.10 8.11 8.12
xiii
Valve-Type Classification / 240 Pump Valves / 241 Valve Seats / 245 Valve Springs / 248 Valve Spring Design / 251 The Effect of Valve Design on Suction Requirements / 254 Determining Valve Efficiency / 255 Valve Tests / 256 Valve Combinations / 256 Velocity Through Valves I 256 Valve Through Area / 259 Required Valve Lift / 260 The Effect of Valve Weight / 260 Effect of Spring Load I 262 Summary / 262 Derivation of Val ve Velocity / 263 Unbalanced Valve Area I 264 Power-operated Valves / 265 Valves in Series / 266 Valves in Parallel / 266 Valve Flutter / 266
240
xiv
CONTENTS
8.13 8.14
Steady-State Flow Through Valves / 267 Valve Delay / 268
9. SLURRY PUMPING 9.1 9.2 9.2.1 9.2.2 9.2.3 9.2.4 9.2.5 9.2.6 9.2.7 9.2.8 9.2.9 9.3 9.4 9.5 9.5.1 9.5.2 9.5.3 9.6 9.7 9.7.1 9.7.2 9.7.3 9.7.4 9.7.5 9.8 9.8.1 9.8.2 9.8.3 9.8.4 9.8.5 9.8.6 9.8.7 9.8.8 9.8.9 9.8.10 9.8.11 9.8.12 9.9. 9.10 9.11
Slurry Properties / 270 Pumps for Slurry St>rvice / 271 Introduction / 271 Packing I 274 Plunger Flushing Methods / 276 Flushing Details / 278 Pistons I 280 Liners I 280 Piston Membrane Pumps / 280 Switch-Loop Pumping / 281 Other Methods / 281 Horizontal vs. Vertical Pumps for Slurry Service / 282 Suction Pressure for Slurry Puinps / 283 Coal Slurries / 284 Concentration of Solids l 284 Particle Size / 286 Concentration and Particle Size / 286 Valve Service for Slurry Pumping / 287 Slurry Erosion / 287 Introduction / 287 Slurry Wear Modes / 287 Effects of Wear / 289 Dry Abrasivity / 289 Conclusions / 289 Slurry Abrasion Testing / 293 Miller Number / 293 SAR Number (Slurry Abrasion Resistance) / 294 Test Equipment / 294 Procedure / 295 Calculation of Results / 295 Miller Number / 296 SAR Number / 296 A Miller Number System Overview I 297 Slurry Concentration, Particle Size, and Particle Shape / 299 Oil-Mixed Slurries / 300 Corrosion / 300 Corrosive Effect of Slurries / 301 The Gold Number for Low Abrasivity / 302 A Method for Locating a Plug in a Slurry Pipeline / 303 Black Mesa Pipeline / 304
270
CONTENTS
9 .12 9 .13
1
Savage River Mines I 305 Slurry Tables I 305
PARTS WEAR AND LIFE 10. i 10.Ll 10. l.2 10.l.3 10.1.4 10.l.5 10.2 10.3 l0.3. l 10.3.2 10.4 10.5 10.6 10.7 10.8 10.9 10. lO
316
The Mechanics of Wear in Pumps I 316 Introduction / 316 Wear Modes / 316 Effects of Wear I 320 Effect of Pump Stroke Reversa! Rate I 323 Piston Liner Clearance I 333 Phmgers I 333 Ceramic Plunger Pitting / 334 Causes I 335 Cures I 336 Theory of Ceramic Plunger Failure Mode I 336 Other Means of Reducing Wear Rate I 337 Slurry Abrasivity I 338 Examples of Parts Life in Hours I 338 Reducing DriHing Pump Parts Cost I 338 Danger of "Strainers" or "Filters" in the Suction Line I 340 Slurry Particle Size I 340
11. APPUCATIONS 1 Ll 11.Ll 11.1.2 l l. 1.3 11.l.4 11.2 ll.3 l l.3.1 11.3.2 11.3.3 11.3.4 11.3.5 11.3.6 11.4 11.5 11.5.l 11.5.2 11.5.3 11.5.4 11.5.5 11.5.6
XV
Effect of Liquid Compressibility I 342 Pump Hook-up / 343 Charging or "Booster" Pump I 345 Pump Valve Unloading System I 345 Suction System Loops I 345 Hydraulics Institute Standards of Application I 347 The Dynamics of Liquid Piping Systems I 367 Where does Vibration Come From? I 368 How Does the Pulsation Couple into the Piping? 368 Cakulating Mechanical Natural Frequency / 369 Making the Application to Actual Piping / 37 l What About Generalized Finite-Element Analysis? I 372 Design Philosophy / 373 High Suction Pressure / 375 Sizing Pumps for Pipelines / 376 Pump Cost / 377 Expendable Parts Cost I 378 Methods of Cost Projection I 378 Standby Pumps I 379 Procedure for Pump Selection I 380 Stations I 381
342
xvi
CONTENTS
11. 5. 7 Calculations I 383 11.5.8 Study Results I 384 11.6 Bolt Tightening Specifications I 384
12. INSTRUMENTATION 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8
Pressure Measurement Methods I 387 Vibration Measurement I 389 Typical Waveforms I 389 Miscellaneous Waveforms (Oscillographs) I 390 Optical Phaser I 402 Positioning Strain Gages to Monitor Torsional Loads I 403 Damped Pressure Gauge I 405 Measuring Pressure Drop by Oscilloscope / 405
13. THEORY OF FLOW IN PIPE 13. l 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 13.10 13.11 13.12 13.13 Appendix 1 Appendix 2 Appendix 3 Index / 462
387
408
Introduction I 408 Physical Properties of Fluids / 409 Nature of Flow in Pipe-Laminar and Turbulent / 412 General Energy Equation-Bernoulli's Theorem / 414 Measurement of Pressure I 415 Darcy's Formula-General Equation for Flow of Fluids I 416 Flow Through Nozzles and Orífices I 419 Pressure Drop and Velocity in Piping Systems I 420 Pipe Line Flow Problems I 422 Flow Through Orífice Meters I 424 Reference Figures and Tables I 427 Summary of Formulas / 445 Nomenclature / 450 Symbols and Nomenclature-Conversion / 451 Subscripts I 459 Abbreviations / 460
1 PUMPTYPES
DEFINITIONS RECIPROCATING PUMP. A mechanical device used to impart a pulsating, dynamic flow to a liquid and consisting of one or more single- or double-acting positivedisplacement elements (pistons or plungers). The elements in the liquid end are driven in a more or less harmonic motion by a rotating crank and connecting rod mechanism. The liquid flow generated by this reciprocating motion is directed from the pump inlet (suction) to the pump outlet (discharge) by the selective operation of self-acting check valves located at the inlet and outlet of each displacement element. HORIZONTAL PUMP. A pump in which the axial centerline ofthe cylinder, piston, piston rod, and CTO!'\Shead is horizontal. See Figure 1.1.
A pump in which the axial centerline of the cylinder, plunger, extension rod, and crosshead is vertical. See Figures 1.2-1.3.
VERTICAL PUMP.
This arrangement allows, in effect, a single-acting pump to perform like a double-acting, thereby eliminating the usual half-stroke period of no delivery. The delivery is divided into two reduced and equal flow rates per stroke, thereby permitting improved pulsation control with a dampener of smaller size. This is accomplished by making the ratio of diameters SIMPLEX SINGLE·DOUBLE-ACTING PUMP.
(1.1)
The uneven displacement generated by the piston rod of a conventional doubleacting pump is avoided. See Figure 1.4.
Figure 1.1. 1700 BHP duplex double-acting piston pump. (Courtesy Oilwell Division, U.S. Steel.)
Figure 1.2. Vertical triplex single-acting plunger pump. (Courtesy Worthington Pump Division, Dresser Industries.)
2
1.1
DEFINITIONS
3
Vertical triplex single-acting plunger pump. (Courtesy Wo1thington Pump Division, Dresser Industries.)
A pump in which the liquid in each cylinder is discharged only during a head-end or crank-end stroke during one half of a revolution. See Figure 1.5.
S!NGLE-ACTING PUMP.
DOUBLE-ACTING PUMP. A pump in which the liquid in each cylinder is discharged during both a head-end and a crank-end stroke during one full tevolution. See Figure 1.6.
1
ON
- + - - - • - .....,_._
1
Simplex single-double-acting pump. (Courtesy American Spray Industries, American Power Equipment Co.)
.¡:.
Figure 1.5. Horizontal quintuplex single-acting plunger pump. (Courtesy Oilwell Division, U.S. Steel.)
Fabricated Steel Power Frame Double Extended Pinion Shaft Screw-Type Valve Covers
@
/ Hl-HARD Piston Rods Liner Retention
Super Dl-HARD Liners Abrasion-Resistant Slurry-Type Pistons
Roller Bearings Throughout
Figure 1.6. 1700 BHP duplex double-acting piston pump. (Courtesy Oilwell Division, U.S. Steel.) en
6
PUMPTYPES
Figure 1.7. 1700 BHP triplex single-acting piston pump. (Courtesy Oilwell Division, U.S. Steel.)
PISTON PUMP.
A pump in which the liquid is displaced by pistons. See Figure 1. 7.
PLUNGER PUMP.
A pump in which the liquid is displaced by plungers. See Figures
1.8 and 1.9.
Figure 1.8. Horizontal single-acting plunger Pump. (Courtesy Worthington Pump Division, Dresser Industries)
Figure 1.9. Horizontal triplex single-acting plunger pump. (Courtesy Oilwell Division, U.S. Steel.) ....,¡
8
PUMPTYPES
1" to 2" Plunger by 2'h" Stroke Simplex
Figure 1.10. Simplex horizontal single-acting plunger pump. (Courtesy Kerr Machine Co. Ada, OK.) SIMPLEX PUMP. A pump consisting of a single cylinder. Contains one piston or its equivalent, that is, a single- or double-acting piston. See Figure 1.10.
pump consisting of two cylinders. Contains two pistons or their equivalent, that is, single- or double-acting pistons. See Figures 1.1 and 1.6.
DUPLEX PUMP. A
pump consisting of three or more cylinders. Contains more than two pistons or their equivalent, that is, single- or double-acting. See Figures 1.11 and 1.12.
MUL TICYLINDER PUMP. A
Figure 1.11. Horizontal triplex single-acting plunger pump. (Courtesy Oilwell Division, U.S. Steel.)
1.1
DEFINITIONS
9
Figure 1.12. Horizontal quintuplex single-acting plunger pump. (Courtesy Oilwell Division, U .S. Steel.)
ARTICULATED PUMP. A double-acting design attained by driving an opposed set of single-acting cylinders by means of articulated connecting rods that drive the opposed crossheads, giving the character of a single-acting pump in a doubleacting action. See Figure l. 13.
OPPOSED PUMP. A doubie-acting design attained by driving an opposed set of
single-acting cylinders by means of crankshaft-straddling connecting bars that drive the opposed crossheads, giving the character of a single-acting pump in a doubleacting action. See Figures 1.13 and 1.14. The membrane pump, (sometimes erroneously referred to as a "diaphragm" pump) differs from the diaphragm pump in that clean liquid displaced by a conventional piston pump is used in tum to ''pulse'' an isolated membrane of rather large diameter and of great placed in a chamber between the piston liquid end and the "dirty" or abrasive pumped liquid on the opposite side. See Figure l.15 and l.16. MEMBRANE PUMP.
Figure 1.13. Horizontal triplex articulated piston pump. (Courtesy Worthington Pump Division, Dresser Industries.)
10
PUMP TYPES
Figure 1.14. 3200 BHP opposed triplex piston slurry pump. (Courtesy Worthington Pump Division, Dresser Industries.)
DIAPHRAGM PUMP. A single-acting or double acting reciprocating pump with the displacing piston being replaced with a fixed-edge flexible diaphragm being reciprocated by a piston-rod connected to the center of the diaphragm. This arrangement eliminates the actual wear and leakage path between a moving piston and the liner. Positive displacement is obtained by the alternating "pulses" of the diaphragm. These pumps were developed for low-pressure high-volume handling of abrasive liquids. See Figure l. !A. Neither the membrane nor the diaphragm pump will isolate the valves from the liquid being pumped. DUAL-DISC PUMP. Two tough rubber discs reciprocate in opposition to each other. A Iarge cavity is created between them at one end of the stroke, producing a positive suction and discharge sequence, resulting in a smooth positive pumping action. See Figure l .2A.
The end of the liquid end farthest from the crankshaft. Sometimes called the cylinder head end in horizontal pumps.
HEAD END (HE) OF LIQUID END.
CRANK END (CE) OF LIQUID END.
The end of the liquid end closest to the crank-
shaft. HEAD-END STROKE.
Travel of the piston toward the head end.
CRANK-END STROKE.
Travel of the piston toward the crankshaft.
UPPER OR OUTSIDE CROSSHEAD. An additional crosshead located outside the power end of the pump at the head end and usually driven by rods connected to the interna! crosshead. In such pumps the plunger travels toward the crankshaft on the delivery stroke. Most vertical pumps use this feature. The upper crosshead is
"'(¡;
O>
~"'
-~~
Cl >
11
DISCHARGE
1
FLEXIBLE DIAPHRAGM
VAL VE
RECIPRDCATING RDD VAL VE
SUCT ION Figure l.lA Diaphragm pump
Figure l.2A Dual-disc pump (Courtesy MPL Pumps Limited, Victoria Road, Feltham Middlesex TW13 7DS)
1.2
NOMENCLATURE AND DEFINITIONS
13
,,,.----$>-
' 1 1
!_\__~~~~~~~~~~~~-~~~~~~
-------"--
Figure 1.16. Piston membrane pump, sectional, Hquid end. Wearing parts: (6) valve eones, (7) valve seats, (8) valve rubbers, (9) pump membranes. (Courtesy GEHO Pumps, Holthuis b.v., Venlo, Holland.)
noted for its ability to keep leaking liquid from entering the power end and tends to minimize plunger misalignment that can result from intemal crosshead misalignment.
to refer to plunger pumps in which the displacement element (plunger) runs through a stuffing box extemally accessed.
OUTSIDE-PACKED. A term usually used
1.2
NOMENCLATURE ANO DEFINITIONS
The text and illustrations of this section are taken from Hydraulic lnstitute Standards, 1983, by courtesy ofthe Hydraulic Institute. The Institute is an organization of pump manufacturers that has been in existence in the U nited States since 1917.
14
PUMP TYPES
It has been successful in setting up engineering standards for pumps of ali types
and continues to contribute to the industry through close association with most pump manufacturers.
Purpose The nomenclature and definitions in these Standards were prepared to provide a means for identifying the various pump components covered by these Standards and also to serve as a common language for all who
"' "'e D.
o
2500
15
~
·g
12 11 10
03
>
2000
1500 3.4
25
50 75 100 125 Pipe inside diameter/Pipe wall thickness
150
Figure 4.23 Pressure wave velocity, water. Numbers to right of curves indicate modulus. of elasticity in millions of PSI units. C, = 0.91.
the slower the valve closure should be. However, one can readily see that this. does not o:ffer a very practical or accurate solution. The second method to reduce waterhammer is a simple bypass or a relief device (Fig. 4.23). These devices basically relieve the excessive pressure by discharging the decelerating water volume either to the atmosphere or into the piping down- • stream ofthe rapidly closing valve. In sorne cases, the water is discharged into the supply tank through a line connecting the relief valve to the tank. This method not very reliable and requires frequent inspection and maintenance. Air chambers also offer a solution for the waterhammer problem. An air -·.,~·-· .. ., .• ber is simply a tank or a large pipe with its top closed to prevent the release of entrapped above the water level (Fig. 4.24). Air within the chamber occupies only
4.19
SURGE CONTROL IN WATER SYSTEMS
133
wlOOO~~~-.-~~~.,-~~--.-~~~·..-~~--.
:; Vl
ti)
~
Q.
~ 800F=~~--+-~~~+-~~--1-~~---1 :;¡
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'5 :;¡
]
6001--~~-+~-=""""......=='---+~~~-i--~~--1
iñ
~
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~
400r-~~-r-~~-=-¡-~~-t~~~T-~~--i
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E
"'
tí
~
2001--~~-+-~~~+-~~-1-~~~+-~~--1
E :::l E
·x
"'
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o
30
60
80
120
Water ilow pressure, PSI
Figure 4.24 Maximum system pressure. A = 15 ft/s, B = IO ft/s, C = 5 ft/s.
25 or 20% of the total chamber volume, depending on the water system pressure. The air inside the aír chamber accommodates the kinetic energy i.n the system by compressing. Kinetic energy is thus converted to potential energy. However, if the system pressure reduces below the design pressure, trapped air in the air chamber will discharge into the system, thus rendering the entire device ineffective. In addition, the compressed air in direct contact with the water tends to slowly dissolve into the water, which also diminishes the device's surge-dampening capability. Then, when the system pressure is reduced, the dissolved air resumes its gaseous fonn, causing undesirable sponginess in the system and possible damage to the system components. The shortcomings and deficiencies of air chambers are e:ffectively eliminated in gas-loaded, flexible, separator-type surge suppressors (Fig. 4.25). Gas confined inside a flexible bladder separator provides an efficient means of transfonning the system's kinetic energy into potential energy. A gas-filled separator-type surge suppressor is installed upstream and close to the valve, which is the source of the waterhammer (Fig. 4.26). In the event ofthe valve's sudden closure, the suppres~ sor accommodates the abruptly stopping column of water immediately adjacent to the valve (Fig. 4.27). As the system pressure increases after quick valve closure, the gas, which is indirectly in contact with the water through the flexibie bladder, is compressed, thereby absorbing and suppressing the high-pressure surges that would otherwise be dissipated only after they had been detrimental to the system's piping, components, and ultimate performance.
134
PUMP PULSATION ANO CONTROL
Relief val ve By-pass line
Tank Quick-Closing valve
Figure 4.25 Relief valve upstream of the shutoff valve.
Air-pressurizing valve connection
Gas charging valve Bladder: BUNA N
Shell: Alloy steel
Figure 4.26 Nonseparator-type surge suppressor.
Figure 4.27 Gas-loaded flexible type surge suppressor.
separator~
135
4.19 SURGE CONTROL IN WATER SYSTEMS*
4.19.2
Sizing of Surge Suppressors
The size of a surge suppressor must be properly calculated, taking into account all the effective system parameters, if the unit is to perform with optimum efficiency. The following simplified explanation illustrates the method of determining the surge suppressor capacity for water systems. The analysis is based on two assumptions: (1) friction losses are small and may be disregarded and (2) the energy absorbed by compressing the column of water and expanding the pipeline is very small compared to the energy stored and absorbed by the surge suppressor and, consequently, is also a negligible factor. The sizing of the surge suppressor, based on these assumptions, offers a conservative answer, which is desirable since all the system variables cannot be known or taken into account. The water ftowing in a pipeline possesses a finite amount of kinetic energy (KE) which can be expressed as KE
wALv 212g
(4.29)
where
= specific weight of water, 62 .4 lb/ ft 3 A = effective area of pipe, ft2 v = initial velocity of water at normal ftow, L = length of pipe, ft g = acceleration due to gravity, 32.2 ft/s
w
ft/s
When the system ftow is stopped abruptly, this kinetic energy has to be transferred to the gas inside the separator. The gas follows Boyle's law: (4.30)
= = = V2 = n =
P1 P2 V1
initial gas pressure (precharge), the same as system pressure, PSIA allowable surge pressure, PSIA surge suppressor volume (gas volume inside suppressor), in3 gas volume at the allowable surge pressure, in3 polytropic exponent of expansion of the gas ( nitrogen = 1.4)
Therefore, to achieve energy balance in the system before and after the valve closure, the k:inetic energy of the system before the valve closure is equal to the energy stored in the suppressor gas volume V1 between the pressure limits P 1 and Pz. Hence, (4.31)
136
PUMP PULSATION AND CONTROL
Surge suppressor
Valve open
Figure 4.28 Free-flow surge suppressor installed in line.
Surge suppressor
Quickly closed valve
Figure 4.29 Sudden stoppage of flow (suppression of waterhammer).
4.19
1.4
1.2
SURGE CONTROL IN WATER SYSTEMS
137
l
\
1.0 .8
i
\
\
e .6
.4 .2
~
""'!--_
!----__
o 1.00 1.251.50 1.75 2.00
3.00
3.50
4.00
Figure 4.30 Pressure constant C curve.
For the water system, 4.65ALv 2
(4.32)
To reduce mathematical computations, this formula can be further simplified to (4.33) The value of C, based on the pressure ratio Pi/ P¡, can be readily determined from Figure 4.28. A cakulation illustrating the use of the above formula is given at the end of this discussion.
4.19.3
Conclusion
One aspect of surge control not directly connected with maintenance cost savings bears mention. Because of new safety codes and noise control laws and regulations, surge control in water systems may soon become a necessity. Thus, water system engineers and designers should become thoroughly familiar with pending legislation a:ifecting their current and future efforts. Such legislation is an expression of the growing concern over noise pollution and industrial safety, and costly retrofit programs may be avoided by careful consideration of surge control during the initial system design.
138
PUMP PULSATION ANO CONTROL
4.20
SAMPLE PROBlEM
Problem. Determine the surge suppressor capacity required to Hmit the maximum surge pressure to 125 PSIA in a water supply system with the following parameters: Pipe length, 1200 ft; pipe size, 8 in, schedule 40 Pump flow rate, 1500 GPM System pressure prior to valve closure, 80 PSIA Liquid pumped, water at ambient temperature Valve closure time, 0.4 s Solution. The necessary surge suppressor size is determined by the equation (4.10): 4.65ALv 2
·
where V1 = surge suppressor capacity, in3 L = 1200 ft A = 0.348 ft 2
v
flow velocity = flow rate / ftow area = 1500 X 232 / 50 = 9.67 FPS P 1 = normal system pressure = 80 PSIA =
X
720
Pmax = maximum shock pressure = 53.8v + P 1 P2 = maximum allowable surge pressure = 125 PSIA te= critical time= 2L/a = 2 X 1200/4000 = 0.6 s Since the valve closure time is less than the critical time, this condition can be treated as an instantaneous valve closure (the valve doses before the pressure wave retums to the valve).
p max
= 53.8
X
9.67
4.65
X
0.348
+
150
=
670 PSI
Therefore, X
1200
80[(125/80)"
Vi=
286
16,690 in 3 (72 gal)
An 80-gal capacity surge suppressor is required.
X -
(9.7/ 1]
4.20 SAMPLE PROBLEMS
139
lternate Method. The size of the necessary surge suppressor can also be determined by equation (4 .11)
(4.35) bere C is the pressure constant determined from Figure 4.28 for a corresponding tío of P2 /P 1 • When Pi/P 1 = 1.56, C = 0.54. Therefore, V¡
= 62.4
X
0.348
X
1200
X
93.5
X
0.54 /80
= 16,690 in3 (72 gal) n 80-gal capacity surge suppressor is required.
FINAL IMPORTANT NOTES word about the most severe type of pulsation in the discharge of a reciprocatg pump-the 'flow-variation-induced' pulsations inherent in the pump itself. gure 4.2. Gas-type dampeners work on the principie that they prevent the foration of pulsations in the entire system, including the pump, by the simple cess of 'smoothing' out the entire discharge system ftow-variations themselves that the cause of pulsation is removed. Pure 'acoustic' type dampeners not only allow the pulsations to be formed, n to be partly 'filtered' out of the downsteam side of the system only-they metimes add resistance to that flow in the form of chokes ·and 'tu bes' to be ded to the power load of the pump. Such devices must be large with respect the pump.
PUMP DESI N
5.1
RATING STANDARDS*
The following definitions are reprinted from Hydraulic Institute Standards, 1985, by courtesy of the Hydraulic Institute. The purpose of this section is to define terms used in pump ratings. These ratings are characteristics of pump design and not conditions of the specific application. One complete uni-directional motion of piston or plunger. Stroke length is expressed in inches.
STROKE.
PUMP CAPACITY (Q). The capacity of a reciprocating pump is the total volume through-put per unit of time at suction conditions. It includes both liquid and any dissolved or entrained gases at the stated operating conditions. The standard unit of pump capacity is the U. S. gallon per minute.
The displacement of a reciprocating pump is the volume swept by all pistons or plungers per unit time. Deduction for piston rod volume is made on. double-acting piston-type pumps when cakulating displacement. The standard unit of pump displacement is the U.S. gallon per minute. For single-acting pumps:
PUMP DISPLACEMENT (D).
Asnm
D=-231
*Nomenclature in Section 5.1 may not be consistent with that in the main text.
140
(5.1)
5.1
141
RATING STANDARDS
For double-acting piston pumps with no tail-rod(s): (2A - a)snm
D
=
231
(5.2)
where A
= plunger or piston area, square inch
a
= = = =
s n m
piston rod cross-sectional area, square inch (double-acting pumps) stroke length, inch RPM of crankshaft number of pistons or plungers
PLUNGER OR PISTON SPEED (v). The plunger or piston speed is the average speed of the plunger or piston. lt is expressed in feet per minute.
ns V= -
PRESSURES.
6
(5.3)
The standard unit of pressure is the pound force per square inch.
Discharge pressure ( Pd ). discharge port. Suction pressure ( Ps ).
The liquid pressure at the centerline of the pump
The liquid pressure at the centerline of the suction port.
Differentia/ pressure ( Ptd ). sure and suction pressure.
The difference between the liquid discharge pres-
Net positive suctiOfJ head required (NPSHR). The amount of suction pressure, over vapor pressure, required by the pump to obtain satisfactory volumetric efficiency and prevent excessive cavitation. The pump manufacturer determines (by test) the net positive suction head required by the pump at the specified operating conditions. NPSHR is related to losses in the suction valves of the pump and frictional losses in the pump suction manifold and pumping chambers. Required NPSH does not include system acceleration head, which is a system-related factor.
s ). Slip of a reciprocating pump is the loss of capacity, expressed as a fraction or percent of displacement, dueto leaks past the valves (including the backfiow through the valves caused by delayed closing) and past double-acting pistons. Slip. does not include fluid compressibility or leaks from the liquid end. SLIP (
Pump power input (P¡ )-The mechanical power delivered to a pump input shaft, at the specified operating conditions. Input horsepower may be calculated as follows:
POWER (P).
142
PUMP DESIGN
P; =
Q X
Pu1
--~-
1714
X Y/p
(5.4)
Pump power output ( P0 ) - The hydraulic power imparted to the liquid by the pump, at the specified operating conditions. Output horsepower may be cakulated as follows:
p
=
Q
()
X P1c1
1714
(5.5)
The standard unit for power is the horsepower. EFFICIENCIES ( 11 ). Pump efficíency ( r¡P), (also called pump mechanical efficiency)-The ratio of the pump power output to the pump power input.
pº P;
(5.6)
Volumetric efficiency ( r¡ v ) -The ratio of the pump capacity to displacement.
r¡,. =
Q
/5
(5.7)
PLUNGER LOAD (SINGLE-ACTING PUMP). The computed axial hydraulic load, act-
ing u pon one plunger during the discharge portion of the stroke is the plunger load. It is the product of plunger area and the gauge discharge pressure. It is expressed in pounds force. PISTON ROD LOAD (DOUBLE-ACTING PUMP). The computed axial hydraulic load,
acting upon one piston rod during the forward stroke (toward head end) is the piston rod load. It is the product of piston area and discharge pressure, less the product of net piston area (rod area deducted) and suction pressure. It is expressed in pounds force.
5.2
FAMllY PLANNING
It is usually anticipated that a family of pumps of any one type wiU be produced in a series of horsepower sizes. The éhoice of sizes should follow sorne order of progression, and the geometric series seems desirable. For example,
n, nr1 , nr 2 , nr 3 , nr4 ; etc. where
n r
=
=
base horsepower (BHP) progression ratio
(5.8)
5.3
WINDOWS OF NONUTILIZAT!ON
143
TABLE 5.1. Geometric Si:ze Progression
= 100 BHP
n = 100
n4
= 100 X 5.1
=
510
n 1 = 100 X 1.5 = l 50
n5 = 100 x 7.6 = 760
n 2 = 100 X 2.3 = 230 n3 = 100 X 3.4 = 340
n6
= 100 X 11.4 = 1140 n1 = 100 X 17. l = 17 10
TABLE 5.2. Arithmetic Si:ze Progresslcm
n = n 1 = 100 !12 = 200 n3 = 300
= BHP = 200
+ 100 + 100 + 100
=
300
= 400
n4 = 400 n5 = 500 11.5 = 600 !17 = 70.0
+ + + +
100 100 100 100
500 600 = 700 = 800 = =
With a base of 100 BHP anda progression ratio of 1.5, each term is 50% larger than the previous term (see Table 5.1). An arithmetic series may sometimes be desirable. This is
n; n 1
= n + d;
n2
= n1 + d;
= n2 + d;
n4
=
n3
+ d; etc.
(5.9)
where n d
= base horsepower (BHP) = progression difference
Table 5.2 illustrates the first seven members of an arithmetic series with a basen of 100 BHP anda difference d of 100.
5.3
WINDOWS OF NONUTIUZATION
.Predictable pumping requirements include a wide order of displacement and pressure pararneters. This unavoidably large variation of and mandatory economic limit on the number of pumps in a family contribute to the complexity of the familysize selection process. Sometimes a project may warrant the design and manufacture of a pump of a particular size to exactly fit that project. This is true in the long slurry pipeline that entails a great number of large pumps and a long lead time from conception to completion. Nevertheless, there are unavoidable gaps or "windows of nonutilization" in the overlapping pump specifications, as shown in Figure 5.L These are regions in the typical pressure vs. displacement curve for each pump of a family where operation is impossible on account of the pump overload. The chart shows the in-
144
PUMP DESIGN
Maximum pump pressure (minimum piston diameter)
1500 1400
1200
800
600 5001----L~~--:'-_.__._..___.__,___;,,._....L...l-,--~""""~....i.~~-L.::,,,_--I
Minimum pump pressure (maximum piston diameter)
100
200
300
400
500
600
700
800
900
GPM
Figure 5.1. Performance characteristics of a typical family of reciprocating pumps. Win dows of nonutilization (shaded areas).
herent disparity in displacement vs. pressure characteristics of a family of fo* similar pumps of any practica! progression. For example, if a pump requirement falls at point A (280 GPM at 1300 PSÍ just outside the 210-BHP envelope, one would be forced to choose a 320-BH pump ( point B) and accept a certain amount of first-cost penalty of excess installe power. ~;
5.4
f;
PISTON ROO LOAD
There is no absolute rule for selecting the piston rod load (PRL) for a particul pump design. However, the nature ofthe mechanism associated with reciprocaf pumps of all types along with past practices dictate that the PRL be directly rela to the hydraulic horsepower (HHP) in about the following ratio: 192 X BHP PRL=---n where n = number of cylinders An exception to this rule is the case of multicylinder plunger pumps where same reciprocating parts, both power-end and liquid-end, are used for econom advantage in all of the cylinders of the triplex, quintuplex, septuplex, and non plex. In those instances, the PRL is based on the original triplex design and i
5.4
PISTON ROD LOAD
145
TYPICAL FASTENING r----".--~~~~~~--~~~~------¡
SMALL PIN FDR RETURN STRDKE
/
1
_J
DIRECTIDN DF LOAD - - - CONNECTI NG ROD
END OF CONNECTING RDD GROUND TO BEARING
BEARING
FINISH.
Means of Increasing Crosshead Pin Bearing Load on Single Acting Pumps
used for the other multicylinder pumps. The horsepower increase in each succeeding increase in the number of cylinders comes from this addition of cylinders rather than from an increase in PRL. The PRL is a function of piston area AP and the discharge pressure: (5.1 l) where Pd
= maximum allowable pressure,
PSI
In double-acting pumps, the piston-rod diameter reduces the effective area of the piston on the cmnk-end stroke. The pump must be designed on the maximum PRL seen on the head end of the piston where the full area is subjected to the discharge pressure. A high suction pressure on a double-acting pump will tend t0>reduce the PRL, but this should not inftuence the design of the pump, because the actual suction pressure cannot be predicted or guaranteed.
Unusual Pressure in the Pump Cyiinder Naturnlly, any excessive pressure in the pump cy!inder will show up in excessive bearing loads and the question arises as to what maximum pressures can normally be expected. An investigation started about 35 years ago on the failure of íluid ends on pumps due to corrosion-fatigue, with sorne statements that, "Pressure as high as seven times the average discharge (design) pressure have been measured". This led first to a study of the best means of measuring these pressures and the conclusion was that the strain gauge type of pressure transducer
146
PUMP DESIGN
with a small, ftush, sensing diaphragm mounted directly into the pump cylinder head without any connecting pipes, valves, etc., is required. Then the pressure read-out should be by means of an oscilloscope to eliminate any mechanical (inertial) effects associated with any strip-chart type of recorder. With literally thousands of oscillographs taken in the cylinder of 1· BHP to 1700 BHP pump in every conceivable service, it can be said that the normal cylinder over-pressure seldom exceeds 10% at the beginning of each pressure stroke. Now there are occasions when a poor suction system or other contributions can cause an increased over-pressure but ·even then, the worst that has been observed is about 100% and in those cases corrective measures had to be taken. While on this subject, it is important to note that a typical cylinder pressure is theoretically a "good" square wave which means that the cylinder (and the associated bearings) "see" the full discharge pressure for almost ali of the 180 degrees of discharge stoke. This is a departure from the less severe pressure waveform seen in gas compressors and interna! combustion engines. lt is also of interest that the "overshoot" pressure, sometimes seen in the cylinder, is usually not seen in the discharge pressure waveform. A good example is shown in Figure 4.3, Parts A and B. Never-the-less, the crankshaft and bearings "see" this elevated pressure load.
5.5
MAXIMUM PISTON DIAMETER
There must be sorne size limit to the piston diameter, but here again there is no absolute rule. One guideline is that the practica! diameter of the piston should be no greater than the pump stroke length s, thus setting the ratio of maximum displacement to maximum pressure limits: Dmax
=S
A pump with such a piston diameter is known as a '' square'' pump. With pump~ having a range of replaceable and multisize liners and pistons, the PRL /MAP relation must be maintained. The design approach in that case is to assume an arbitrary piston diameter of approximately half-stroke length: Dave
= s/2
Maximum limits of PRL dictate that for extremely high pressure pumps (abov~ 10,000 PSI MAP), a drastic reduction in the plunger size/stroke length ratio is required.
5.6
STROKE LENGTH
The selection of a design stroke length is roughly related to accepted past practices, dictated by the mechanisms associated with reciprocating pumps, usually resulting
5.8 SPEED
147
TABLE 5.3. Pl1mp Stroke length
PumpBHP
Stroke, in
Pump BHP
Stroke, in ----~--
50 100 200
4
400
5
800 1600
7
10 13 18
in the "square" pump limitation previously with the maximum stmke about equal to the piston diameter. St.roke length is more closely related to pump horsepower in the arbitrary manner:
s
=
0.7(BHP)°" 44
(5.14)
But sorne departure will be encountered. This relation is illustrated in Table 5.3 for sorne common pump horsepower values. See also the relation of pump RPM to stroke in Sections 5.9 and 5.10.
5. 7
NUMBER OF CYUNDERS
Duplex double-acting pumps with four pressure strokes per cyde would naturally require 90º crank angle spacing of the two throws to generate a tolerable flow variation pattem. Multicylinder pumps can be designed with any number of cylinders, but for most efficient distribution of flow variations per cycle, the use of an odd number of cylinders, namely 3, 5, 7, or 9, is desired. Even numbers of cylinders result in superjacency of two or more flow pattems per cylinder, which in turn result in emphasized peaks that generate greater pressure pulsations. Sometimes the main reason for using a multicylinder pump is its more desirable flow pattem, with lower values of flow valiation and subsequent pulsation. As illustrated in Table 5.4, even-numbered cylinders have an inherently greater valiation.
5.8
SPEED
There is a great temptation to increase the horsepower rating of pumps by simply increasing the speed. An existing pump can be uprated only slightly in speed. At a higher speed the liquid velocity through the valves may be greatly exceeded, to the extent that hydraulic difficulties would be encountered. The. valves in an existing pump were probably designed for a practica! maximum velocity as determined for its original rated pump speed and piston size.
...
t
TABLE 5.4. Pump Type flow Variation
Pump Type Simplex SA Simplex DA Duplex SA Duplex DA Triplex SA Triplex SA (0) Triplex SA (30) Triplex SA (60) Triplex DA Quadruplex SA Quadruplex DA Quintuplex SA Quintuplex DA Sextuplex SA Sextuplex DA Septuplex SA Septuplex DA Octuplex SA Octuplex DA No1mplex SA Nonuplex DA
--
Numb Cyls
Crank Angle
A(I)
B(2)
1 1 2 2
360 180 180 90 120 120 120 120 120 90 90 72 72 60 60 51.4 51.4 45 45 40 40
0.58 0.29 0.29 0.24 0.06 0.062 0.061 0.05 0.06 0.11 0.11 0.02 0.02 0.06 0.06 0.012 0.012 0.026 0.026 0.006 0.006
1 1 l 0.22 0.17 0.17 0.12 0.09 0.17 0.22 0.22 0.05 0.05 0.17 0.17 0.026 0.026 0.052 0.052 0.002 0.002
3 3 3 3 3 4 4 5 5 6 6 7 7 8 8 9 9
Total(3) Percent 158 129 129 46 23 23 18 14 23 33 33 7 "7 1
23 23 3.8 3.8 8 8 2.1 2.1
K(4) 0.684 1.368 0.558 0.199 0.100 O.lOO 0.078 0.06! 0.200 0.143 0.286 0.030 0.076 0.100 0.200 0.016 0.032 0.035 0.070 0.009 0.018
Max Press Percent(5) 250 166
166 93 43 44 35 27 43 62 62 14 14 43 43 8 8 15 15 2 2
NOTES; (1) - "A" Flow variation above average, decimal.
(2) - "B" Flow variation below average, decimal. (3) - Flow variation, total percenl (4) - K Factor for calculation of dampener size (Equation 4.5)
(5) - Maxirnum pressure variation (pulsation) without dampener, percent. (0) - Fixed phase angle of two pumps compounded. (30) - Fixed phase angle of two pumps compounded. (60) - Fixed phase angle of two pumps compounded.
5.10
SPEED OF MULTICYLINDER PUMPS
149
TABLE 5.5. RPM of Dup!ex Pumps
Stroke, in
,.,,_ 4 6 8 10
RPM
Stroke, in
RPM
600 300 200
12 14 16 18
100 86 75 67
150
120
However, dueto competition and economic reasons, there has been a tendency to design greater speed into pumps, and the hydraulic limit has probably been reached. Greater speeds will no doubt require drastic design approaches, such as positively actuated valves, tending to offset any economic advantages associated with the speed. The greater the pump speed (RPM), regardless of stroke length, the greater the detrimental effect of high acceleration pressure at the pump suction and discharge. In other words, maintaining a constant piston speed (FPM) by choice of RPM vs. stroke length results in constant displacement in GPM, but the short-stroke highspeed pump suffers most from acceleration problems. It has also been shown that liquid-end parts life is exponentially reduced by increases in RPM and/or in number of reversals. See Chapter 10, Parts Wear and Life.
5.9
SPEED OF DUPLEX AND SIMILAR PUMPS
Aside from the hydraulic limiting factors affecting maximum RPM, the imbalance of pump crankshafts with nonsymmetrical throws, such as the duplex double-acting with two throws at 90º separation, creates intolerable rotary imbalance. Such pumps must be limited to a relatively low RPM, because the e:ffects of the unbalanced forces (centrifuga!) increase to the power 2 with rotating speed. Accordingly, a practical speed rating for such pumps is
(5.15) where FPMd
= 200
Table 5.5 was constructed on that basis.
5.10
SPEED OF MULTICYLINDER PUMPS
Pumps with symmetrical crankshafts (equally crank angles) such as a duplex single-acting and all multicylinder pumps can be operated at much higher
150
PUMP DESIGN
TABLE 5.6. RPM of Multi-Cylinder Pumps
Stroke, in
2 4 6 8 10
RPM
Stroke, in
RPM
600ª
12 14 16 18
130 112
450 300
225 180
160
100
ªNote: An arbitrary limit has been set at 600 RPM for stroke of 3-in. or less.
speeds because of the inherent static balance of the crankshaft, but now being limited by the hydraulics. Liquid flow or friction pressure increases directly with velocity. Liquid acceleration pressure increases as the second power of crankshaft rotating speed. Both of these factors affect the volumetric efficiency of the pump, and there must be sorne limit to the maximum speed at which the pump can operate. Due to economic factors and competition, the industry has seen a gradual increase in the maximum allowable speed (MAS) for multicy linder pumps. lt appears that a limit has been reached beyond which the problems associated with high speed cannot be tolerated. In fact, sorne manufacturers have followed a trend to lower speeds. Speed reduction is desirable in many cases where suction conditions are minimal. See Chapter 2, Dynamics. An acceptable range of basic speeds for multicylinder pumps is determined by the following formula, based on a constant piston speed of 300 FPM: RPMMax. = FPMs/(2s/12) where FPM5
(5.16)
= 300
Table 5.6 illustrates this relationship. For further discussion of the effects of pump speed see Section 10.1.4 Chapter 10. Parts Wear and Life.
5.11 5.11.1
DIRECTION OF ROTATION Rotation "Overrunning"
In an overrunning pump the crank rotation is such that the crank approaches the crosshead from the top of the rotation circle as shown in Figure 5.2. This motion is preferred for horizontal pumps because the connecting rod force component R and the weight component W are always directed downward. To resist the normally high crosshead forces, more rigidity can be built into the lower crosshead guide,
Head end
Crank end
(a)
(b)
Figure 5.2. Direction of rotation. (a) Overrunning. (b) Underruning. l'lhl -
PIN
.. LIJAD?~···················
BEARING CRDSSHEAD PIN ANO BEARING ASSEMBLY VITH CLEARANCE DBTAINED VITH PARTS OF DIFFERENT SHDVING CEXAGGERATED J THE ºLINE CDNTACTº PRESSURE RESULTING IN EXTREMELY HIGH CDMPRESSIDN STRESS FRDM APPLIED LDADS. THE MDDULUS DF ELASTICITY DF THE METALS DF BDTH PARTS CTHAT OF THE BEARING BEING THE LDVEST J ALLOVS AN ºAREA CDNTACT . TO BE GENERATED
Figure 5.2A. Oscillating Crosshead Bearing Arrangement. 151
152
PUMP DESIGN
since it is tied into the base of the power end. Overrunning also minimizes cross' head slap or knock.
5.11.2
Rotation "Undem.mning"
Rotating in the opposite direction, an underrunning purnp, in Figure 5.2(b) has force component R that is always directed upward while the weight component is always downward. These altemating forces can cause crosshead slap or kno Extremely close crosshead and guide clearances must therefore be incorporated.
5.12
OFFSET CRANKSHAFT
As described in Section 5 .11, all crosshead forces or loads are usually direct downward in a horizontal reciprocating pump. The offset crankshaft (Fig. 5. causes a modification of these loads in such a manner that the maximum downw · load at the center of the stroke is reduced by an amount that is transferred to · upper guide at the beginning and end of the stroke (Fig. 5.4). A slight impro ment in mechanical efficiency should be expected, but there is the possibility' crosshead slap or knock at the points of load reversal. The offset crankshaft offers little if any advantage with respect to the standpoint. The acceleration at the ends of each stroke is not altered, and the pattern change is almost undiscemible. The following special formulas apply to the offset crankshaft: X=
a
=
r(l - cos 8) + (r sin()+ h) 2/2Lc arctan [ ( r sin ()
+
h) /
~L~
- ( r sin ()
w
h
e
90°
Figure 5.3. Offset crankshaft.
+ h) 2 ]
5.13 CONNECTING ROD FORCES
153
UPPER GUIDE ~UNNING
CLEARANCE
SH1JE
LO\.JER GUIDE UPPER CLEARANCE ¡ EXAGGERATED J
RIGHT
IJRDNG SHOES TURNED
TO
SH!JES TURNEO TO
D!AMETER LESS THAN
'"-----'
Sl\ME D l AME TER AS
GUIDE Dll\METER
CR!JSSHEAD !lDRE .
RESULTS IN L!NE
RESUL TS lN 1007.
CONTAtH
BEAP.INu CONTACT.
Figure 5.3A. Shim-Adjusted Crosshead Shoe and Guide Fits
w
= 27íN /60 r 12
V=-w
sin ( ()
(5. l 9)
+ o:)
.
(5.20)
sin (1.57 - a)
a = 0.084rw 2 ( cos ()
r
h
\
Le
Le
/
+ - cos 2e + - sin fJ)
R = (tan a)PRL
(5.2l) (5.22)
CONNECTING ROO FORCES
lntroduction fundamental mechanism of the power end of a reciprocating pump is the crank-
nnecting rod-crosshead system. The design of a crankshaft provides single or
154
PUMP DESIGN
2" Offset crankshaft Underrunning
~
c.
....~+-~+--~I----+~--+~~ .!+1--~~,.......+~--+~-+-....,...'"+--~ to ~
al
e
"'
;::
l=----l~---l-...::::,,....¡.~::::..¡_~--1--~-t=-~J-~-l------ll-----l-~---+~-I
b8 No offset Overrunning
180 210
240
270
300 330
180
210
240 270
300
330 360
Crank angle, deg
Figure 5.4. Offset crankshaft, crosshead loads.
multiple throws or crank pins, the axis of which are on the desired distance (radiu from the axis of the main shaft. Many forms of crankshaft configuration are used, most representing differen methods of manufacture such as forged, cast and machined-from-billet and eve bolted assemblies. Figure 5.5 shows the general shape of several crankshaft de signs, all having opinionated features. The basic geometry of a crank-connecting rod-crosshead system is shown i Figure 5.6. The pump mechanism forces are shown in Figure 5.7 for a conven tional crank mechanism and in Figure 5.8 for an articulated mechanism.
5.13.2
Formulas
The following formulas are used to calculate the crank mechanism forces and a example is shown in Figure 5. 9. Example: Triplex Single-Acting; Type 111 Crankshaft
See Figure 5. 7. r
=
3 in; Le
=
18 in; PRL
=
Pd = 1415 PSI; Ps = 100 PSI
10,000 lb
~ Bearing ~ Frame
V
Cast eccentric Multicylinder Single- or double-acting
Gear
Barrel type Duplex only VI
11
Gear
Shaft-eccentric Multicylinder Single- or double-acting
111
Overhung crank Duplex only VII
Cast marine type Multicylinder Single- or double-acting Optional full or half "back-up" journals
Forged marine type Multicylinder Single- or double-acting
Modular eccentric Multicylinder Single- or double-acting VIII
lntermediat.e journal
Figure 5.5. Crankshaft types.
155
StrokeS, in
Outlet connection pipe size, in
270° Piston diameter, in
180°
90° pipe size, in
Figure 5.6. Pump geometry.
e 5Peed upwar ~tribute to a rapid drop in volumetric efficiency. ect starts to ca
ª
5.20
MECHANICAl EFFICIENCy
Introduction Mechanical Efficiency (ME) of a pump is ge of input horsepower (BHP) or energy imparted to the liquid be¡ the percenta ng pumped; ME = (HHP/BHP) (5.46) X: 100
HHP = (gpm X PSi)/(17¡4 X ¡v1J3) (5.47) With modem pump design and construct¡0 ·cal efficiency of 85% in double-acting pumps and 90% in single-act~' mechalll 0 be expected. The horsepower required for a double-a. l~g pumps cahould be calculated from formula (5.39), Section 5.22. Cting pump 5 For the same reason that a single-actin~ . bigh suction pressure has higher stresses in the power end, all the be P~mp with ore heavily loaded in relation to the work being done and therefore ªn.ngs are '1'.cal efficiency is reduced. the mechalll
ª
5.21
INTERMITTENT SERVICE
169
Q.,"
;;:~ 0.6 , _ _ - - - - + - - - - + - - - - + -........- - - - - - - -
º
~ ~
:::J
"' 0.4 t-----+-----+----+-----i\-------1
~
Q_
o
0.2
0.4
0.6
0.8
0.9
1.0
Mech¡mical efficiency ME
Figure 5.12. Single-acting pump mechanical efficiency vs. suction pressure / discharge pressure. To determine BHP: Calculate pressure ratio; determine mechanical efficiency from curve; substitute in: BHP = (Pd - P,) x GPM/1714
X
ME
(5.48)
where Pd = discharge pressure, PSI; and P, = suction pressure, PSI.
lt has been determined by test that the relation shown in Figure 5.12 exists. There-
fore, for a single-acting pump the required horsepower is derived from formula (5.40) Section 5.22. Since the manifestation of low mechanical efficiency is sensible heat generation, higher power-end temperatures will be expected with high suction pressure.
5.21
INTERMITTENT SERVICE
Any pump can be overloaded by a reasonable amount for a few minutes of operation at rare time intervals by increasing either the pressure or speed or both. And any pump can probably be operated at extremely slow speed for a short period without harm. Spurred by the need for the greatest amount of power packed in a small space for portable use in the oil fields for sand fracturing, acidizing, and cementing, most manufacturers offer such pumps for this and other services. By increasing the
170
PUMP DESIGN
GPM
o
30
60
90
120
150
180
210
0 01--~2~5~-..Jso'--~7~5~-1~00~~12~5~-1~5-0~1~7-5~--'
0
RPM Curve Curve Curve Curve
ABCO-
lntermittent service, constant horsepower Continuous service, proportional horsepower lntermittent service, proportional pressure Continuous service, constant pressure
Figure 5.13. Continuous vs. intennittent duty.
design piston rod load (PRL) three- or fourfold and increasing the maximum speed about twofold, pumps with a threefold reduction in weight per horsepower have been produced. These so-called constant-horsepower pumps are rated for intermittent service and typically Iimit the duty to l 1/2 hours per day. Figure 5.13 shows the performance curve of two pumps of this type with equal design horse" · power. lt is obvious that such pumps will require more frequent replacement of · bearings and parts.
5.22
CONTINUOUS SERVICE
Continuous service denotes operation at rated conditions of speed and pressure for 24 hours a day. Basically, this is a constant-torque operation with a 'speed turndown of about 50% allowed, such turndown usually being limited by the types of bearings and the lubrication system provided. Antifriction (roller) bearings throughout the power end will allow a greater turndown than journal or plain bearings. The design criteria incorporated into this text apply to continuous service ºP" eration.
5.23
171
RECIPROCATING PUMPS WITH HIGH SUCTION PRESSURE
5.23 RECIPROCATING PUMPS WITH HIGH SUCTION PRESSURE For Double-Acting Pumps 0.85
(5.49)
- P,) X GPM/1714 X ME*
(5.50)
= pd + !P, = Pd + ~P, = Pd + iP, = Pd + ~P,
(5.51)
BHP = (Pd - P,)
X
GPM/1714
X
For Single-Acting Pumps BHP
= (Pd
Triplex pumps
p
Quintuplex pumps
P
Septuplex pumps
P
Nonuplex pumps
P
P
(5.52) (5.53) (5.54)
= artificial discharge pressure upon which plunger/piston is selected when suction pressure is in excess of 5 % of discharge pressure
Pd P,
BHP GPM *ME
= actual discharge pressure = actual suction pressure = input brake horsepower = actual U.S. gal/min = mechanical efficiency from Figure 5.12
·
Example A certain triplex pump rated at 1000 PSI with 3-in plungers ( PRL 7200 lb) would have to be equipped with 2i-in plungers ( 1250 PSI at PRL 7200 lb) to pump at actual 1000 PSI with 500 PSI suction pressure.
P
=
1000
+ 500 /2 = 1250 PSI
6 LIQUID ENDS
6.1
TYPICAL LIQUID-END MANIFOLD CONFIGURATIONS
The valve-over-valve configuration for multicylinder pumps is probably the m efficient from the standpoint of suction problems and efficiency and ease of mai tenance (Figure 6. la). Pumps with long suction and discharge passages, called surge legs (b) and is lation leg (e), where the valves are placed a great distance from the cylinder · the dubious reason of isolating the piston from abrasive materials in the liqti often exhibit poor hydraulic performance. These long passages tend to mag the acceleration and ftow problems because of the greater mass of liquid that m be moved from a "dead-stopped" condition. The large volumetric clearance the isolation-leg design results in low volumetric efficiency and contributes to ni? and rough running. This is particularly true if air, gas, or vapor is present in liquid. The inverted configuration (d) has been considered for slurry services on contention that the solids would "naturally" fall through the liquid end with danger of plugging and stacking. But its shortcomings include the inability to p itself of air or gas, and valve replacement would be ext~emely awkward.
6.2
S-N CURVE
As shown in the S-N curve (stress vs. number of cycles) of Figure 6.2, if maximum stresses are kept lower than 35 ,000 PSI there should never be failu air. In water, a stress of about 15,000 PSI would be the limit. 172
Minimal length (a) NORMAL -
Sign ificant length
VALVE-OVER-VALVE
(b) SURGE-LEG
(d) INVERTED (e) ISOLATION LEG
Figure 6.1. Liquid-end configurations. (a) Normal, valve-over-valve. (b) Surge leg. (e) Isolation leg. (d) Inverted.
50
.te §...
40
-= 30
rr.ie en en Q)
...
ti 20 E :::1 E ·;;e
...
:E
B
10
105
106 107 Fatigue life N, cycles
loB
Figure 6.2. S-N curve. Exposure of steel to water greatly reduces fatigue life. Salt water and hydrogen sulfide still further reduce life .. Curve A, dry fatigue life; curve B, wet fatigue life. 173
174
LIQUID ENDS
MOD IFI ED GOODMi\N DIAGRAM ........ . .:......... .. ;..... .. .. .. .: .. ........ .: ...........:.... ...... .: .. . . .. .. ... ... .. . . ..
11l0 •....•... 180 . ...•••.. 140 ...••••. ··~ . ... •....
~ •••••
~
.. ~
100 .. . ....... ; . .....
80
.
•••.•••••• j •••••• . . •• • ..•.••. •• • ;. ••.•..• . • ·:. . . . . . . . . •
..
. ...
..
... .
... .
• ••.. • • •••
·r·· ······ ··········!··········:··········:···········¡···········: ................ ..
8á~¿··[ ..........:······ ·· ·· ·········· >·······[··········:··········[···········¡·········· ··········
80 . . .•..... · [ .. ..... .. ·\·. .. . . . . ..
. 40 ·· ·· · ·····:·········
20 · · · ···· ··
. .. ~w.1.m.·······-r········ ........
·1 · · ·····r·······-:--······· :·······. r........·········· 80
100
120
JNJTIAL STRESS, 1000 PSI
140
160
180
200
Figure 6.IA
The results to be expected with the material being stress cyded in even a slightly corrosive liquid (pure water with dissolved air, for example) differ greatly; the stresses that would allow extended life are far below those in air. In figure 6-2, a stress level of about 17 ,000 PSI would offer a fair amount of additional life, but it is now believed that the corrosion-fatigue curve never flattens out and that such stressed parts will have a finite life (hopefully beyond the life of the unit of which they are a part). Liquid ends and expendable parts of all pumps are subject to corrosion-fatigue failure, and therefore it is important to consider this in their design. Where corrosion fatigue is expected, the logical approach would be to design for the lowest possible stress. In parts with associated stress-risers (intersecting bores in liquid ends, notches, pitting, machining marks, sharp shoulders, and drastic change in cross section being the most important), steps can be taken to reduce stresses or protect the point of stress concentration.
6.2.1
The Goodman Diagram
In the design of repeatedly-stressed parts or devices, such as valve springs, with a material in question one can take advantage of the fact that most materials exhibit a trait that if the stress range is limited by a certain minimum stress of higher value than zero, fatigue strength can be substantially increased as shown in Figure 6.2A.
6.2 S-N CURVE
175
YIELD 115.000 psi
'
-
--210.000 psi
CD1nens1on X" .. ) DIA
...
o::
o::
CI
CI
cu o:: cu u
AD
D2R2 A1R2 AlRI A
D cu
-
cu o:: cu <
111
-
cu
--i:
111
111
o::
cu <
Q:
cu
o::
u
e
RADIUS 1\LL BDRE INTERSECTlDHS t 1/4' l. ADD THAf RADIUS/4 1 .061 TD BDRE RADIUS "ID OBTAIN RI.
CIRI CIR2
1
o::
B2Rl B2R2 aj
a:
lLI
e
IJIA
1 BC
"'osed Pressure Range Act• al Pressure Applied Instrument Styrain Reading Calculated Stress (O x 30) Lam40
Figure 6.5A. Autofrettage Analysis-Piotted Data
AUTOFRETTAGE ROSETIE CALCULA T!ON
::::::::::::~:~:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::~:~::::..:::::.. ....... .,
/ .................................. j···· ..
·+·····.. ····............... j
:::::::::::::::~::::::::::::::::::::::::··7·!...... :::::. ::::::::::. :::::::::::::: ................................
···:::::::::. .~:::::::::t:::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::·:::::::::::::::::::::::::::::::·:::::: :::::::::::::::::::::::: 60000
40,664
100000
68.,445
200000
150000
STRESS, PSl
171 ~ 000
211,664
Figure 6.6A. Autofrettage Analysis-Rosette Gage Data
250000
186
LIQUID ENDS
k
=
Concentration Factor (Approx. 2. 75, Cakulated 3. 7)
Rl
Bore Radius, in. R2 = Outside radius or shortest distance to outside wall.
6.4.2.7
CAlCUlATIOlllS FROM TEST DATA (See Figure 6.5A)
This method is preferred because it utilizes strain gage differential readings averaging, superior to a single actual residual strain gage reading at fin;¡ with the pressure released. [ l] Calculate SLOPE of Proportional Curve; Se!ect an Applied Pressure
low the yield and positively on the Curve, for example, at (20,000) PSI, , could apply greater accuracy by averaging severa! points on that line. Slope
=
Stress/Pressure
=
(2911) x 30 (20,000)
=
(4.37)
[2] Project Proportional Curve to Maximum Applied Pressure;
Projected Stress
=
Slope
= 4.37
x Maximum Applied Pressure x 50,000
=
218,500 PSI
[3] Select Actual Indicated Stress at Maximum Applied Pressure, (269,640, [4] Determine Stress Difference;
Delta Stress = [3] - [2] = 269,640 - 218,500
51,140 PSI
[5] Calculate New Allowable Working Pressure; Project line from Maximum Applied Pressure Stress (269,640) par¡i Proportional (Slope = 4.37), through [4] (51, 140) to intersect zero (Ó sure abscissa at the New Working Pressure; New Working Pressure = (51,140)/(4.37) = 11,750 PSI without tensile stress at the critica! point in the working pressure range.
6.4.3
Shot Peening
Shot peening is usually scientifically applied to the critica! areas in a liquid bombarding them with glass beads. The shot particles in effect "peen" the layer, compressing the "skin" surface and in tum protecting against có fatigue.
6.4.4
Coating and Plating
Coating and plating have been used as protection against corrosion (subse against corrosion fatigue), but because of the strict requirements for comple erage (no "holidays") and the fragility of such coatings, they are seldom ~,
6.5
ULTRA-HIGH PRESSURE PUMP DESIGN
187
WATER COMPRESSIBILITY
r·\·T . . . :....... .......... :. · · ."[' ...... f.. . T..... ·: ................ . FACTOR ll
2·9
~
1
....,
:
:
:
r::¡ :~~; T !
. .
:
:
TI < , ., .
'·ut··········¡···········'~···>···················:
···.-·········:·····················:··········:
:J l I t?;LJ~~l~J__· .• "!·········· ........ -······· ....................................................•..........· 2.2
o
10000
2000!l
30000
40000
50000 6000!) PRESS\JRE, PSI
70000
60000
90000
100000
Water Compressibifüy Compressibility Factor jj, x I0- 6 Contraction in Unit Volume per PSI Pressure tCompressibility from 14.7 PSIA at 68º F.
UlTRAmHIGH PRESSURE PUMP DESIGN requirements for hydraulic pressures extending into the 100,000 psi range '~"·u~'"'"' and the most severe problem in pumping at high pressure liquids resulting from excessive clearance-volume in a pump, that volume of liq.aining in the cylinder between the suction and discharge valves after the ement element (piston or plunger) has completed its delivery stroke. Typimp design involves significant ammmts of clearance volume, as a percentf displacement, in the order of l 00 to 200 percent, an ammmt that does not t a serious problem below about 5000 PSI. basic reason that a high clearance volume contributes to the poor perforof a reciprocating pump is because of the compressibility of liquids, FigPicture a cylinder ful! of high pressure "compressed" just as unger starts its return (suction) stroke. Before the suction valve can open, ble movement of the plunger is required to allow the compressed liquid to the suction pressure. A part of the useful stroke is forever lost as a of completely filling the cylinder and the ful! capability of the pump is re 6.8A shows proposed suction valve design which takes advantage of a feature of reversing the suction valve spring from the cylinder side, or
188
LIQUID ENDS
LIOUIO ENO
/777777:_:/ f\IN!f\Uf\ CLEARANCE VOLUf\E NOTE STYLE OF VALVE ANO PLACEf\ENT Figure 6.SA. Ultra High Pressure Suction Valve.
UHP PUf\P !ULTRA HIGH PRESSUREJ FEATURES:
LIOUID ENO BLOCK
ASSISTED SUCTIDN VALVE CLDSURE 'ZERD ' CLEARANCE VOLU/\E
Figure 6.9A.
top, of the valve to the suction or bottom side, thereby removing a volume occupied by the spring and its associated mechanism from t side, resulting in the ability for the displacing element to sweep almos cent of the cylinder volume. Another feature, not formerly recognized, that will improve hig pump performance is the "augmented" closing force on the suction sulting from the pressure surge created by the reversal of the plunger of its delivery stroke, by placing the suction valve directly in front of:
6.5
ULTRA-HIGH PRESSURE PUMP DESIGN
189
nger. That pressure surge is aimed directly toward the open suction valve, the closing force of the valve spring at the instant when rapid valve s desired to minimize delay and leakage through a partially closed valve. mp design places the suction valve in positions whereby such assisting greatly attenuated by turns and restrictions in the path from the end lunger to the valve. (Quick-closing of the discharge valve is also desirable an be obtained by the use of an extremely strong spring load without g the pump cylinder filling problems). See Figure 6.9A. understood that a single-acting multi-cylinder (probably a triplex) plunger ould be selected because of the inherent and desirable anti-extrusion efpacking friction counteracting the hydraulic pressure extrusion effect. See 'NGER VERSUS PISTON PUMP. s 6. lOA and 6.1 IA are examples of "high-pressure" pumps now on the
A power pump liquid end for operation at pressures up to 30,000 psi. ght Kobe, /ne. Used with permission.)
190
LIQUID ENDS
11 =
Suction water
1
= High-pressure water
IJ
= Suction valve
=
Pump pistan
Courtesy
Paul Hammelmann Maschinenfabrik GmbH Zum Sur.dem 13-21 · Post Box 3309 0·4740 Oelde · W.-Germany Phone 02522176-0 ·Telex 89455
Figure 6.HA. Ultra-high Pressure Pump
6.6
ABRASIVE JET CUTTING "NOTHING ON EARTH IS SO YIELDING AS WATER, BUT FOR BREAKING DOWN THE FIRM AND STRONG IT HAS NO EQUAL" -Lao Tzu 600 BC.
Many industries are looking at the use of a high-velocity water jet as a cutti tooL In order to generate the high velocity required, high pressure and low vq ume are the parameters needed. Pressure in the order of 60,000 PSI or more used. For cutting metal, an abrasive like fine silica sand is introduced into t jet stream at the sapphire cutting tip or nozzle. Several years ago a drilling contractor ran a test oil weU drilling rig whereb the formation rock was disintegrated by the use of 10,000 PSI drilling m charged with chilled steel shot as the abrasive medium. The high pressure m was pumped through typical roller bearing rock bits equipped with special sm diameter nozzles, the disintegration of the formation being purely the result impingement of the shot-laden mud. Here again, intensifier type of pressure ge eration was used. This system compromised on the pressure-volume relations on account of the relatively high circulating rate of mud to carry the rock cutti. to the surface. Incidentally, the drilling rate in hard rock was increased about fold but the overall operating cost was found to be prohibitive.
6.7 THE INTENSIFIER
191
POVER-OPERATED FOU.-VAY VALVEI
_,. .....- ......
J X 1 11UM.D' llta.I ..
10· X 24º 100 GPW
P~
C'Yl.IN>ER
5000 PS 1
7• X 24• HIOH·PRESSlRE C'Yl.IN'.>ER 43 OPM
HIGH·PRESSlRE LIQUID Tf.H<
11.:1110 PSI
Figure 6.12A. Typical Single-Cylinder Intensifier
THE INTENSIFIER e intensifier is an ingenious but rather costly way of generating low-volume 'gh-pressure services for such applications as cutting materials, liquid sandlasting, autofrettaging and oil well formation fracturing and cementing, or other uirements for extremely high pressure to about 100,000 PSI. The principie usually involves the output of a medium-high pressure reciproting pump of about 5000 PSI to operate a differential tandem direct-acting draulic pump-a large diameter piston and cylinder connected by a common ·ston-rod to aoother small diameter piston in a cylinder. The pressure magnifition being directly. related to the square of the two piston diameters. Figure 6.12A shows the basic principie involved in a typical intensifier. lt ould be noted that the delivery or ftow-variation generated pulsations of the imary pump will .not be reftected and magnified by the same percentage. lt is portant that the primary pump be well dampened in order to protect the system om shock-pressure waveforms generated at the intensifier reversals. In order to eliminate the inherent zero delivery pressure occurring at each end the piston stroke, sometimes two or three such units are operated in parallel, e stroking being phased by sequential operation of the four-way valves being grammed by end-of-stroke detecting switches (micro or proximity). A severe rge problem can arise from improperly timed valves. Why not generate the ultra-high pressure directly with a typical multi-cylinder wer pump? The problem of handling a high-concentration of abrasive solids, ch as used for "sand fracing" oil well formations (the high pressure separating
192
LIOUID ENDS
the formation layers with the sand grains acting as a "propping" agent stimulating the rate of oil flow to the well bore), takes advantage of th~ long-stroke and low stroke-reversal-rate of the intensifier. Por other appli with clean liquids, properly designed multi-cylinder pumps could be use conserving cost and space. A discussion on the design of ultra-high p liquid ends is covered in Section 6.5.
7 EXPENDABLE PARTS
API STANDARDS FOR SLUSH PUMP COMPONENTS* The American Petroleum lnstitute (API) has rendered a valuable service to the oilwell drilling industry in promoting standards for mud (and sorne slurry) pumps, pistons, and piston rods, liners, valve pots, and extension rods. Standardization has made it possible to use such parts interchangeably in any malee of pump. Such standards also serve as a guideline in the design of nonstandard parts. The API Standards on Parts in the following pages are reprinted here by permission from the American Petroleum Institute, 211 N. Ervay, Suite 1700, Dallas, Texas 75201. Figure, table, and paragraph numbers have been changed to be consistent with the rest of this volume.
S/ush Pump Piston Rod and Piston Body Bore, Fluid End 7. 1 Sizes and Dimensions. Fluid ends of slush-pump piston rods and piston body bores shall be in accordance with Table 7 .1 and Figs. 7 .1 and 7 .2 for doubleacting pumps and Table 7 .2 and Fig. 7 .3 for single-acting pumps. 7.2 Threads. Threads on rod ends and in retainer nuts shall conform to the dimensions given in Tables 7 .1 and 7 .2, and shall be controlled by class X gages conforming to the stipulations in ANSI Bl.2: Screw Thread Gages and Gaging. If supplementary production or working gages are used, they shall be accurate copies of the master gages.
*Nomenclature used in Section 7 .1 may not agree with that used in the main text. 193
194
EXPENDABLE PARTS
TABLE 7.1. Fluid End of Double-Actlng Slush Pump Plston Rods and Plston Body Bores (All dlmenslons are in lnches. See Flgs. 7.1and7.2.) 2
3
7
6
4
8
Piaton Rod. Plotoa
.Diamet.er
TaNo.
A
11
13
Taper, In. Per Ft. on Diam•
a......
1 -lñ l'Á - lH a 1'1.i - lH 4 l'!!i-2ñ 5 2'Á - 211 6 2114 - 2H 5HP** 2114 - 3'1.i 6HP 3 - 3'1.i
12
Pilt:on .. Rod
Rod
.. Rod
1 2
10
9 ~iat.ou
±•···· K
3'!!! 5'1.i 7'1.i 8 8% 9% 8% 9%
1.000 1.250 1.500 1.875 2.250 2.750 2.225 2.725
1'1.i 2'1.i 2% 4 4 4'1.i 3% 4'Á
lU
2n
0.979 1.229 1.474 1.854 2.229 2.729 2.229 2.729
u 1,i. ls\ l/r lU 2% lU 2%
1% 1 '!!i 2tt 2U 2U 2U 2U 2U
1.000 1.000 1.250 1.000 1.000 1.000 1.000 1.000
'Á 'Á 'Á 'Á 'Á 'Á 0.041 0.113 0.041 0.113
·~.~jjrfn:~~meter tolerancea for API rod numbers 1 and 2:+0.0l0¡-().005 inch. For rod number 3 and larger:
+
••Recommended aa a substitute for API 6HP piston for reduced liner sizes only. H•Dimeneion G, column 8, relates to dimension S, min. only (column 12).
J
~t
PISTON (HANOTIGHT)
/¿R OR
~~------
!.........,_.................,~.~·
_ TAPER K
~~O~L~tiNOCCURS _J t-4-----D~ __
1
1
~
r--E
i---------- 8---
Figure 7.1. Tapers 1 through 6.
7.3 High Pressure Pistons and Rods. Shoulder faces M and N of pisto rods numbered 5HP and 6HP shall be square to the taper within 0.001 inc indicator reading (TIR). Shoulder face P shall be square to the taper within . inch TIR. 7.4 High Pressure Piston lnstallation lnstructions.
a b. c. d. e.
Clean rod and piston tapers and assemble (oíl free). Piston must stand off from rod shoulder when made up handtight. Apply lubricant on thread and nut faceto prevent galling. Draw piston to rod shoulder with nut. After initial shoulder contact, mark relative position of both nut and p with punch marks or paint stripe. Continue tightening 60 to 72 deg
7.1
'-._BREAK
195
API STANDARDS FOR SLUSH PUMP COMPONENTS
b, MAX ~
MAX-j
-~1
FlLLETS a ÜÑDERCUT DIA TO BE PRESTRESSED BY COLDWORK!NG
UNDERCUT DETAil
. . ,._________ ª Figure i .2. Tapers 5HP and 6HP.
TABLE 7.2. Fluid End of Single-Acting Slush Pump Pistan Rods ami Pistan Body Sores (A!I dimensions are in inches. See Fig. 7.3.) 2
3
Piston andRod Connection No. SA-2 SA-4
Connection Diamete:r~
nominal
1
l'h
Rod
Diamete:r,
4
Length Rod End,
±,¡..
5 Piston Rod Start of Thread from Shoulder, maximum
e
A
B
0.997-0.999 1.497-1.499
4i'.
1~
5t.
2%
6
7
g
Piston
..-----... Shoulder Diameter
Bo:re
±-h
Thread Designation
2 3%
l-8UNC-2A l'h-8UN -2A
D
1.000-1.003 1.500-1.503
2~ splines for API 5 locknut with 12 splines and 2~ to 3 splines for API 6 locknut with 15 splines).
Markíng
a. Pistons, Double Acting. Pistons with a taper confonning to this specification shall be marked with the manufacturer's name or mark, the API monogram, and the taper number. High pressure pistons number 5HP and 6HP are di-
196
EXPENDABLE PARTS
Figure 7 .3. Fluid end of single-acting slush pump piston rod and piston body bore. See Table 7.2.
mensionally interchangeable with pistons 5 and 6. It is permissible to stamp both tapers on shoulder P. b. Pistons, Single Acting. Pistons with straight bores conforming to this spec~. ification shall be marked with the manufacturer' s name or mark, the API monogram, and the connection number. c. Rods, Double Acting. Piston rods conforming to this specification shall be marked with the manufacturer's name or mark, the API monogram, and the taper number. The crosshead extension end of the piston rod shall be marked · with the API monogram and the taper thread number or the straight thread number from Table 7.3 or 7.4. d. Rods, Single Acting. Piston rods conforming to this specification on the flui end shall be marked with the manufacturer's name or mark, the API mono gram, and the connection number. If the crosshead extension end of the· piston rod conforms to Par. 7 .6 or 7 .9, this end shall be marked with the API monogram and the taper thread number or the straight thread numbe from Table 7.3 or 7.4. Slush Pump Crosshead, Crosshead Extension, and Piston Rod Connections-Tapered Thread Type
7.6 Sizes. Tapered thread type connections between crossheads, crosshead extensions, and piston rods shall be 8 TPI, Series UN, Class 2A-2B modified, in th sizes given in Table 7 .3.
7.1
API STANDARDS FOR SLUSH PUMP COMPONENTS
197
TABLE 7.3. Crosshead, Crosshead Extenslon, and Plston Rod Connectlons-Tapered Thread Type (All dlmenslons are In lnches. See Flg. 7.4.)
1 Taper Thread Number Tl T2 T3 T4 T5 T6 T7 TS T9 TlO Tll T12 Tl3 T14 T15 Tl6 T17 T18 T19 T20
2 Nominal Size,* A 1 1% 1% 1% 11h 1% 1% 1% 2 2% 2% 2% 3 3% 31h 4 4% 5 51h 6
3
Length of Taper Thread, B 1%
lU
1-h
lit
1% 2n 2-ilr 2H 21h 2U 3% 3* 3% 4ñr 4% 5 5% 6% 6% 7%
4 Length of Straight Thread, Min
e
1 1 1 1
H~
1% 1% 1% 11h 1% 1% 1% 2 2 2% 2% 2% 21~
2% 2%
5
Locknut Thickness, D
%. %.
% %
1 1 1% 1% 1% 1% 1% 1% 1%. 1% 2 2 2 2 2 2
*Ali threads are 8 TPI, Series UN, Class 2A-2B modified.
7. 7 Thread Dímensíons and Tolerances. Tapered thread type connections shall conform to dimensions given in Table 7 .3, Figs. 7.4 and 7 .5, and the following tolerances: a. Taper. Tapered threads shall have a taper of 2 in. per ft on pitch cone di-
Figure 7 .4. Crosshead, crosshead extension, and piston rod connections-tapered thread type. See Table 7 .3.
198
EXPENDABLE PARTS
TABLE 7.4. Crosshead, Crosshead Extension, and Piston Rod Connections-Straight Thread Type {All dimensicms are in inches. See Fig. 7.7.)
1
Straight Thread Number Sl
82
S3 S4 S5 S6 S7
SS 89
S10
2
3
4
Le~¡th
Nominal Size A*
Length of Internal Thread B
1
1% 1% 1%
11h
1% 1% 1% 2
2% 21h
S11 S12 S13 $14 S15
3'.lh
S17
41h
819 S20
51h
S16 S18
2% 3
3%
4
5
6
1%
lH l/ir
lH
1%
2ñ 2-h 2U 21h 2ii 3% 3.[g
3%.
4-fr
4% 5 5% 6% 6%
71h
5 Locknut
Externa! Thread
e
Thickness Min. D
2%
%.
2ii 2/ir 2H 3%
3S\i
3i«
3U
4
41'\r
4% 5i\5%
6~
6% 7% 7% 81h
9%
9%
1 1
*%%
1% 1% 1% 1% 11h 1% 1% 1% 2 2 2
2
2 2
*All thr!'ad111 are 8 TPI, Series UN, Class 2A-2B.
ameter with a tolerance of +0.000, -0.020 in. for intemal threads and +0.020, -0.000 in. for externa! threads. b. Concentricity. Within limitations of good practice, threads shall be concentrie with rod design axis. Angular misalignment of thread axis with rod design axis shall not exceed 0.0005 in. per in. of length. ---0-
Figure 7.5. Tapered thread form. See Par. 7.7,
7.1
API STANDARDS FOR SLUSH PUMP COMPür~ENTS
199
B = 1.25.A. c. Length. Total length of externa! threads = B + d. Perpendicularity. Face of intemal thread member shall be perpendicular to thread axis within 0.001 in. per in. of face diameter.
e. Lead. Lcad tolerance shall be ±0.0022 in. per in. Cumulative lead tolerance shall be ±0.0022 in. f. Thread Angle. Half angle tolerance of thread angle shall be ± l deg. g. Truncation. Crest on both intemal and externa! threads shall be truncated parallel to taper to produce a fiat 0.030 in. wide. Root on both interna! and external threads shall be truncated paraUel to thread axis to produce a flat 0.015 in. wide. Root of interna! threads may be trnncated parallel to taper of thread at option of manufacturer. Straight threads truncated same as tapered threads. h. Pitch Diameter. Pitch diameter and pitch diameter tolerance of straight threads shall be as designated in [111] ANSI B 1.1: Unified Screw Threads. L Standoff. In gaging tapered threads, stando:ff of product from plain and threaded plug and ring gages shall be maintained within a tolerance of ± 1/16 in. CAUTION TO USER: Threads must not be damaged, as damage will cause misalignment and failure.
TB Lock Nuts. Crosshead extension and piston rod lock nuts shall be fumished in accordance with Par. 7 .12. Slush Pump Crosshead, Crosshead Extension, and Piston Rod Cormections-Straight Thread Type 7. 9 Sizes. Straight thread type connections between crossheads,' crosshead extensions, and pistan rods shall be 8 TPI, Series UN, Class 2A-2B modified, in the sizes given in T~ble 7 .4. 7. 10 Thread Dimensions and Tolera.neas. Straight thread type connections shall conform to the dimensions and tolerances given in Table 7.4, Figs. 7 .6 and 7. 7 and ANSI B 1.1: Unified Screw Threads, and shall be gaged in accordance with ANSI Bl.2: Screw Thread Gages and Gaging. The following requirements are also applicable: a. Concentricity. Within limitations of good practice, threads shall be concentric with rod design axis. Angular misalignment of thread axis with rod design axis shall not exceed 0.0005 in. per in. of length. b. Length. Interna!: B = 1.25A Extemal: C = B + D
+ 0.25
200
EXPENDABLE PARTS
INTERNAL THREAD
EXTERNAL THRE'AD
TH~EAD
_J'v'~I"
AXIS7
.
~ltr'
/ PITOH--i
•
-.___¡_______ -.J.-__L
Figure 7.6. Straight thread form. See Par. 7.10.
c. Perpendicularity. Face of interna! thread member shall be perpendicular to thread axis within 0.001 in. per in. of face diameter. 7. 11 Lock Nuts. Crosshead extension and piston rod lock nuts shall be fumished in accordance with Par. 7 .12. 7. 12 Lock Nuts. Crosshead extension and piston rod lock nuts shall be fumished in accordance with Fig. 7 .8. 7. 13 Taper Threads. Locknut threads for the taper type connection shall form to the requirements of Par. 7. 7.
con~
7. 14 Threads. Locknut threads for the straight type connection shall confo to the requirements of Par. 7. 1O.
} ct-L ·:
CROSSHEAD EXTENSION
LOCKNUT
PISTON
Figure 7. 7. Crosshead, crosshead extension, and piston rod connections-straight threa type. See Table 7.4.
7,1
API STANDARDS FOR SLUSH PUMP COMPONENTS
201
Figure 7 .8. Crosshead extension and piston rod lock nut.
Slush Pump Valve Pots 7. 15 Sizes and Dimensions. Slush pump valve pots shaH be fumished in the sizes and dimensions given in Table 7.5 and Fig. 7.9, as specified on the purchase order. API valve pots for caged valves shall provide a minimum G dimension (see Table 7 .5) for cage clearance.
A.BLE 7.5. Slush Pump Valve Pots ;(All dimensions are in inches. See Fig. 7.9 for explanation of dimensional symbols. 'oimensions for pot sizes 1, 2, and 3 are tentative.) 1
3
4
B
e
2
1
2% 3% 3%
2 2 2
Pis
4%
2
1%
5
2 2 2 2 2 2 2 2
5% 5% 6% 7 7%
8'11. 9%
6
7
8
9
F 1%
G
J
Solid
21,4
3% 33114
2%
10
Valve Pot Dimensions
,---------
A
5
1%.
D
314 3% 41,4
1 \/2
4%. 5%
1%
5% 6
1% 2 2',i 2%
2Vs
31,1,
6%
E So lid
u u u
lf.
Ho
1·i'c. l1i1
7~~
11:;1.i
s~;g
lf.
8% 9%
u. H,
*Dimensions for these pot sizes are tentative.
2%
2%
2* 3 3%
3%. 3%
3%. 4 41,4 4%
41/s 4%
514 51,4
5% 6
6"',g 6% 7'/s
21,~
2%. 3% 3% 3% 3% 3% 41/g
4%
5%
12 11 Sp:ring Mounting Dimensions
r---~
3
N 2 112 314
3
3%
3 3%.
3%
L
M
1 1% 1%
2%
2 2% 2%. 2%.
2%, 2% 2% 2% 2%
4% 4%
3% 3% 3%. 3% 3%
5%
3%.
5 1h
3%
4% 4%,
5 5%.
202
EXPENDABLE PARTS
~
,jr JT,n· CM••
t L
,i
.//, r---B lTAPER r'ER FOOT
.:!_:':
ON
L_.___ .L ___
DIAME+-~[R) --
1
______ JMINIMUM CLEARANCE
Figure 7.9. Slush pump valve pot. See Table 7.5 for dimensions.
7. 16 Spring Mounting Dimensions. Valve pot spring mounting dimensions · shall conform to dimensions L, M, and Nin Fig. 7.9 aild Table 7.5. 7. 17 Marking. Slush pump valve pots fumished to this specification shall b marked with the manufacturer's name or mark, the API monogram, and the valv pot size number. Markings shall be cast or die stamped on the fluid cylinder applied to a plate securely affixed to the fluid cylinder. Markings shall be applie in a location visible after installation of the fluid cylinder on the pump and ma be applied to either pot. For pumps having divided fluid ends, each section sh be marked. Slush Pump Pistons
7. 18 Sizes and Dimensions. Slush pump pistons shall be bored to fit the st . dard taper of piston rods as given in Fig. 7 .1 and Table 7 .1. Piston outside di ameters shall be suitable for use in liners or cylinders having increments of di ameter change noted in Fig. 7 .10. 7. 19 Marking. Pistons conforming to this specification shall be marked with th manufacturer's name or mark, the API monogram, the corresponding API number, and standard bore. Markings shall be stamped in letters ~-in. high on t end face of the piston core at the large end of the piston-rod hole.
7.1
API STANDARDS FOR SLUSH PUMP COMPONENTS
203
Slush Pump Liners 7.20 Uner Bares. Bores of slush pump liners shall be gíven in one-fourth inch increments and with tolerance as noted in Fig. 7 .10 and as specified on the purchase order.
7.21
The inside edge of the piston be chamfered as shown in Fig. 7.10.
end of slush pump liners
Marking. Slush pump liners confonning to this specification shall be marked with the manufacturer's name or mark, the API monogram, and the size (standard bore) of the liner. Markings shall be stamped in letters ~ in. high on the retainer end (outer end) of the liner.
Slush Pump Gear Ratings Provisions. Gear ratings as given herein are derived from AGMA Std 424.0l · Standard Practice for the of Helical and Gearing far Oilfield Mud Pumps. Ratings are based on surface durability (which is mn'""''n" of pítch). However, the gear manufacturer shall as sume responsibility for selecting a pitch sufficiently coarse to provide adequate tooth strength. 7.24 Design. Gears shall be single reduction, either helical or herringbone. Gear materials to be in accordance with AGMA Std 241.01: Gear Materials-Steel. While field experience in the use of nodular iron as a gear material in slush pumps
PIS TON ENTERING
END
!'
~:W4-1 __\_A /
/.
1/8" MIN
A= Noml1111I Diameter in one-fourth ind1 incremenh, toleruc:e plus O.O 1O inchas, minus 0.000 iru:luu.
Figure 7.10. Slush pump Hner.
204
EXPENDABLE PARTS
is limited, it does, to indicate this matelial can be used. Tentative use nodular iron is permissible for gears only (not pinion), providing it is in accordanc~ with AGMA Std 244.01: Nodular !ron Gear Materials. Use the steel hardne curves of Fig. 7 .12 to obtain Kr values. Any practica! combination of tooth height; pressure angle, or helix angle may be used. However, American Gear Manufac: turers Association standards are recommended. The slush pump manufacturer shaU be responsible for adequate shafting and support to maintain proper alignment derload. 7. 25 Rating Formulas. The horsepower rating for surface durability shall determined from the following formula:
F;KrDs
P=-where
F;
.65F. Combined factor for face width and inbuilt factor (where F = face width in inches.) F, = rating factor, see Fig. 7 .11. Kr = combined factor for materials, tooth form, and ratio, see Fig. 7 .12. Ds = combined factor for pinion rpm, pitch diameter, and velocity factor, using Fig. 3 of AGMA Std 211.01: Surface Durability of Helical and · Herringbone Gears, or the following formula: =
v;cvn
D =--s 126,000
1. 7
l-----+---+---f--__,l-----'----1---1----l
-
r,= 16 ·-
._
HP
5000
"-.i.6 le:-'-'!---+--_,, USE RATING FACTOR OF 1.4 ON ~ 1 PUMPS 1000 HP a HIGHER
t;
1
e;: 1.5
1
1
1
~ z
i
Si 1.4
>----+----+-,--1---J--~¡.....-.¡....._...¡.._....¡
a:: 1. 3
_,__--+-----+----<
1---~-L_,__,___ 1
o
1
2
4 6 8 10 12. 14 16 INPUT HORSEPOWER RATING OF PUMP, IN HUNDREDS
Figure 7.11. Gear rating chart for mud pumps. See Par. 7.25.
7.1
API STANDARDS FOR SLUSH PUMP COMPONENTS
205
600
500
......."' o
u
,. 400
300
STANDARD HARDNESS COMBINATIONI AS SHOWN ARE llU:COMMENDED. WHEN NON•STANDARD HAADNEll
COMllNATIONS .U:E USED 1 THAT CURVE SATISFVING IOTH GEAR a PINION HARDNESIES SHALL APPLV •
NO INTERPOLATION IS PERNITTED.
3
4
5
6
7
RATIO OF GEAR TO PINION
8
s
10 11
IEiiJ
Figure 7.12. Variation of K, factor with gear ratio. See Par. 7.25.
DP
= pinion pitch diameter, inches. With enlarged pinions, a value equal to outside diameter minus two standard addendums, may be used.
Cv 78/(78 + ./V) v = pitch line velocity in fpm (do not use enlarged value of Dp). n ·= pinion rpm. 7.26 Name Plate Ra.ting. The name plate rating of a slush pump shall not exceed the API rating of the gear.
205
EXPENDABLE PARTS
7.2
PUMP LINERS
In the 1920s, the cylinders of reciprocating pumps were either an integral part of
the liquid end or employed a pressed-in bronze or cast-iron sleeve that requirecf time-consuming and usually difficult rernoval using hammer and chisel to split the sleeve. The use of double-acting reciprocating steam pumps and then power pumps for ~ circulating drilling mud (and later slurries), usually a severely abrasive service requiring frequent replacement, led to the adoption of a "quick-change" renewable cylinder or ''liner.'' The loose-fitting liner was equipped with a shoulder that engaged with a short rubber sleeve to serve as a slug packing, being forced against the packing in its recess by mechanical means such as set screws in an internal . cage or through the cylinder head. Such an arrangement did not necessarily lend itself to easy removal of liners. Corrosion and packed sand and mud between the loose-fitting Iiner and the liquid-end bore often made necessary the use of mechanical or hydraulic jack arrangements either with a puller head that gripped the inside of the liner by expanding serrated jaws or with a toggled head that engaged the rear end ofthe liner. Such a puller required two jacks working against a "strong back'' spanning the two jacks. As a matter of historical interest, the jenny jack (so·. named after the female jackass) was developed with an open center hole that could be slipped over the single puller rod. Another objection to this liner-retention arrangement was the lateral movement or "working" of the liner against the relatively compressible packing rubber, caused by the pulsating pressure on the exposed end areas of the metallic liner. The relative motion between liner and liquid-end bore in the presence of abrasive sands resulted in rather rapid destructive wear of the liner bores in the liquid end. This was overcome by the use of an additional shoulder on the liner to enable it to make metal-to-metal contact with the liquid end. Opposed lip-type packing rings were placed in the original packing space with the lips facing each other and with a metal lantern ring between them to provide a small amount of compression for an initial seal, the final seal being provided by the pump pressure. An improved liner packing arrangement was developed in 1970 whereby the opposed pressureactivated lip-type packing rings were installed in a packing space that extended throughout the length of the liner, this space being filled with pressurized oil. This resulted in complete. protection against corrosion and packed sand and also provided the desirable pack-o:ff against clean oil rather than abrasive mud or slurry. With the .introduction of the single-acting piston-type pump in drilling and slurry service, the means of packing and clamping the renewable liner required a di:fferent approach. The usual practice was to install the liner through the cradle opening · and force the liner end against a rather hard, fabric-reinforced packing ring in a recess provided in the liquid end. The bolted or screwed clamp sometimes works against a shoulder or fiange as an integral part of the liner. At other times the clamp may work against the outside end of a straíght cylinder liner. Ease of installation and simplification of the clamping arrangement can be had
7.3
PISTONS
207
designing the liquid end to receive a flanged liner through the cylinder head. This precludes the need for clamping against the high hydraulic ram effect working on any since the hydraulic forces tend to hold the liner against its shoulder.
7.2.1
Liner Development
The value of any liner is the wear resistance of the inside diameter against which the piston runs. Thís surface must be compatible with the chemical constituents of the pumped liquid and the abrasivity of the solids that may be deliberately added as in the case of drilling mud and slurry. The first typical "quick-removable" mud-pump linern were of single-metal construction-cast iron, hardened carbon steel, and chrome-plated steeL Bimetal liners with centrifugally castor spun hard metals were introduced later. However, about 1950, a trend to 27% chrome iron was recognized by all pump liner manufacturers. Sometimes this hard metal is centrifugally cast into a liner shell, but other liners consist of a sleeve of the hard metal centrifugally cast and machined and shrunk into a mild steel or carbon steel shell. This construction results in a liner with greater hoop strength because of the prestressed liner and shell. On the other hand, the sleeve construction limits the maximum size of liner to a diameter considerably less than a spun liner because of the loss of thickness of the supporting shell. A spun-in hard facing is usually much thinner than a shrunk-in sleeve and contributes little to the strength of the unit. Of significance is the "rebirth" of the chrome-plated liner. Tests show that a properly plated liner will surpass one of 27% chrome iron. The reason for the demise of the early chrome-plated liner was the poor plating technique and application of a minimal thickness of chromium. Old liners (and piston rods) hada limit of about 0.010-0.015-in thickness of plate. As this relatively thin coating wore away, the base metal would become exposed, and the edge of the wom chrome plate acted as a knife to quickly decimate a piston rubber (or rod packing). The improved plating technique and the thicker plating (which allows the acceptable maximum w.ear off¡, in in diameter) results in a superior product.
7.3
PISTONS
The following discourse on the introduction of an "improved" piston for drilling mud service will provide information on the physical action of a piston and reveal sorne of the pitfalls that should be avoided. Examples of current piston designare shown in Figures 7 .13 and 7 .14. A piston with a solid steel back-up plate bonded to the fabric heel was marketed with the contention that it offered the ability to use several sizes of rubbers on a single size piston body (a dubious advantage) and it al so provided a clearancerenewable feature in that with each new rubber installation the liner clearance was
208
EXPENDABLE PARTS
Figure 7.13. Mud and slurry pistons. (Courtesy Fluid King.)
brought back to the "new" piston condition (Fig. 7 .15). Sorne detrimental effe of having a "floating" back-up plate were observed. (Even though it was bond to the rubber, it was rather free to float radially.) The first evidence of trouble w the galling that appeared in 27% chrome-iron liners. No thought was given at t time to the possibility of excessive plate "shifting" (Fig. 7 .16), but there w concem for the damage to the liner. lt was determined that the galling produced "fish-scale" surface on the liner that was extremely hard on rubber pistons. T
(a)
(b)
Figure 7.14. Typical pistons. (a) Double-acting. (b) Single-acting. (Courtesy Fluid Kin
7.3
PISTONS
209
Pistan body
Figure 7.15. Piston with "back-up" plate.
fact that any steel piston Figures 7 .17 and 7 .18, without plates could still result in the same injury with the steel body galling on the liner tended to dispel any worry about back-up plate shift. during the development of a large piston ( 12-in diameter) for coal · slun-y pumping service, it was dramatically shown that the back-up plate shift was undesirable. Figure 7.16 shows how the shifüng of the back-up plate generates liner and piston wear on the opposite side from the clearance gap due to the high unit loading of the back-up plate against the liner. The suggestion that the back-up plate be split into segments and unbonded so that it would expand equally with the rubber is not practical, because the rule
-EPressure Fabric extrusion into clearance results in rapid failure o! heel, and wedging efíect produces force on back-up plate
t
This generates wear on back-up plate, and the failure mode regene~ra.,.,te~s~.-;-1,
11111
¡:11¡
1
Hydraulic pressure bulges rubber to help center piston but provides no centering
to ring.
Figure 7.16. Piston with "back-up" plate. Reaction to pressure.
210
EXPENDABLE PARTS
'i¡i
111,111 111111
Figure 7.17. Typical piston.
applying to any packing system is that the packing ring next to the clearance gap performs all of the packing effects-the remaining multiple rings become pressure :: balanced and perform no work except to wear out from the initial interference buil{ into the ring. The argument that any piston (Fig. 7 .17) can be ''kicked'' over by the wedging action of the fabric into the clearance gap (Fig. 7 .18) is true, but the ability of solid piston to resist this force is so great that there is hardly any regeneration. , The solid piston takes this force on both rubbers and a much wider metal face (body fiange). The hydraulic pressure on the working rubber tends to "bulge" it out to liner size for the entire circumference, thereby acting as a centering forc.'
Fabric extrusion into clearance produces force
But force is counteracted by "rigid" rubbers and steel flange in contact with liner. Otters greater bearing area with reduced wear rate. ~
Hydraulic pressure bulges rubber, provides additional force to "center" piston.
Figure 7 .18. Typical piston reaction to pressure.
7.4
11111!1ll1
51
PLUNGERS
211
1 l l l 1!11111
Figure 7 .19. Improved piston (patented). Controlled expansion (by bonding or vulcanizing to fabric section), high-modulus, gap-closing, compatible-with-liner, anti-extrusion ring. (Courtesy Chromium Corporation.)
for the entire piston, overcoming the side force produced by extrusion. Such a centering force is lacking in intensity in the "back-up plate" piston. Accordingly, it appears that the use of any one-piece metal or high-modulus back-up plate is of doubtful value. lt is surprising to observe that in the mid- l 950s, drilling mud pump piston construction including the calandered 18 X 18 cotton-duck fabric plied into about 20 plies (later improved by stacking the plies with the warp and woof at random angles) is practically the same as its original design. This is great testimony to the sanctity of the fabric with its special properties-probably due to the ability of the fibers to absorb liquid and provide lubrication against the liner on the high pressure stroke, not an attribute of most synthetic fabrics. Of interest is a new concept in piston design, Figure 7 .19, whereby the clearance gap is kept at zero by the controlled expansion of a high-modulus segmenta}, step-cut anti-extrusion ring. Because failure of a piston begins with the deterioration of the fabric heel at the clearance gap, this means of reducing the gap will extend the life ofthe piston. See Chapter 10, Sec. 10.1.5.
7.4
PLUNGERS
Plungers are made in a wide variety of materials, the most common being solid ceramic, sprayed ceramic, and spray-welded Colmonoy 6. For clean water service, solid ceramic offers the best performance, lasting many years with no discernible wear. However, it is subject to damage from abrasive liquids, rough handling, and thermal shock. Spray-welded Colmonoy 6 is probably the most popular plunger
212
EXPENDABLE PARTS
Figure 7 .20. Plungers, val ves, and packing for typical multicylinder pump. (Courtesy Fluid King.)
material, resisting corrosion and abrasion fairly weH, and having none of the ceramic disadvantages. Refer to Figure 7 .20. There are many other plunger materials, including sprayed ceramic, stainless steel, and even hardened carbon steel. Plunger construction varies with size. For plungers up to about 3 in in diameter, solid base metals are usually used. Those of larger diameter are usually of hollow or sleeve construction, which reduces weight and cost. In horizontal pumps, most plungers have short, quick-connect ends to allow plunger change without opening the power end for access to the crosshead. An extension rod working through the diaphragrn packing has sorne sort of grooved clamping arrangement to allow the plunger to be fastened by working through the cradle opening, using a clamp of sorne sort. In order to ensure plunger alignment, the stub end should use a pilot-fit pin and socket. Early attempts to use a so-called self-aligning connection without a pilot fit resulted in disaster because of the care needed to assure that the plunger was aligned before clamping. Sorne clamps actually forced the plunger out of alignment during the tightening process. The outside crossheads used on most vertical pumps contribute to good plunger alignment because of their freedom of movement.
7.4.1
Metal-to Metal Plungers 0
With clean oil or with water and soluble oils, metal-to-metal close-füting plungers running in an appropriate sleeve, both parts being honed and lapped to extremely close clearance, are rather popular in smaller high-pressure pumps. Plungers can
7.4
PLUNGERS
213
be of hardened (nitrided) steel or chome An 0-ring is sometimes placed in a groove in the sleeve near the atmospheric end. This prolongs the useful life of the plunger by the additional seal afforded as clearance develops from wear. For an estímate of the leakage rate to be expected with such a close-fitting plunger, use the formula below. Of course, the leakage into the cradle would have to be disposed of by drainage ora scavenger pump.
where
Q Dp Pd
leakage rate per plunger, GPM = plunger diameter, in = discharge pressure, PSI e = diametric clearance, in µ = absolute viscosity, cP L = length of plunger, sleeve contact, in =
Example For a triplex single-acting pump with
= l in = 5000 PSI e= 0.001 in
DP
µ =
L
=
3 cP 6 in
Q
7.4.2
=
29,308
X
1
X
5000
X
0.001 3
X
6
X
3* = 0.024 GPM
Ceramic Plunger Construction (See Fig. 7.21)
The original supplier of solid ceramic plungers utilized the typical constru... : · 'Jn of a solid ceramic body with a reduced diameter neck or shank epoAy-c.:.:nepted into a metal adapter for fastening to the extension rod (Fig. 7.21a). After 's 1arge numthe cemer.tL.: connection ber of "pullouts" or bond failures, an effort to by deepening the socket of the adapter to provide greater bonding area was tried (Fig. 7.2lb). Loss of adapter strength '°rmn such removal of metal resulted in numerous cases of adapter failure from fatigue. Another manufacturer obtained better results by following the same design except that the adapter was heat-shrunk onto the ceramic shank. A superior ceramic plunger construction is the hollow "thimble" of solid ce-
*For three cylinders.
214
EXPENDABLE PARTS
a
cjfl:"' &, 1
"Pullout" due to failure of cement
Breakage of cerarnic due to mishandling or misalignment of pump
1
Breakage of ceramic due to thermal shock. Craze-cracking usually evident
Heat - shrink adapter
---+-
b
Adapter fails by fatigue at either location
e
c[J(
Ceramic failure same as above
___
)
/=(~)'" ~
T\./O BOL T CLA/"\P .
---~
d
PLUNGER
¡
l •
. ()
·~··
..
) 1
Plunger clamp connection
Figure 7.21. Ceramic plunger construction. (a) "Old" design. (b) "New" design. ( "Improved" design. Adapter with integral stinger provides strength of bond and reduc. stresses. (d) Typical Groove-and-Clamp Connection.
ramic cemented toan all-metal adapter with an extended "stinger" that provid strength and reduction of stresses (Fig. 7.21c). Aside from the screwed method of attaching the plunger to the extension r another popular method is the 'groove-and-clamp' scheme shown in Figure 21~ Note that a pilot-fit boss assures absolute axial alignment.
7.5
7.5 7.5. 1
Pl\CKING
215
PACKING lntroduction and History
The terms "packing" or "seals" are sometimes used to describe two distinctly different applications; namely, "dynamic" packing that usually refers to tha! used on a moving piston or plunger and to a stuffing box through which a plunger or piston-rod reciprocates (or rotates in the case of a centrifuga! or rotary pump). Then there is the term "static" packing, generally called "gaskets", that are used to sea! the gap between two fixed or stationary parts, typically pipe flanges, pump cylinder heads and valve pot covers or any other opening that must be permanently or temporarily sealed. Many packing types or shapes (lip-type rings, homogeneous or braided, flat, 0-rings, metal-segmenta!, etc.) are used in either application with al! types in both applications being subject to extrusion into the gap between the two parts but it will be seen that the mechanics of sealing are entirely different in the two applications-the dynamic packing being subjected to the additional friction forces and wear not encountered in static application and the greater ''gap'' necessary between moving parts. A discussion of plunger pumps and packing must be preceded by an explanation of why they differ from piston-type pumps, particularly in the matter of stuffing boxes and packing. With the common duplex double-acting piston pump, typical design requires an increase in piston rod strength, in both tension and compression, in sorne proportion to the increase in pump discharge pressure. Therefore, a point is reached where the piston rod diameter theoretically becomes so large that the pump, in eftect, approaches a single-acting duplex, the discharge characte1istics of which are extremely ''rough. '' Accordingly, single-acting pump design dictates three, five, or more cylinders, and multiplex single-acting pumps inherently have smoother discharge characteristics, even over a small-piston-rod duplex doubleacting pump. Of extreme importance is the often overlooked fact that the packing action of an outside packed plunger pump is completely opposite to that of any piston type, including a multiplex single-acting piston pump. In a plunger pump (Fig. 9.3), the plunger, during the pressure stroke, is traveling to the right out of the pressure-loaded packing into the liquid, and during the suction stroke the plunger is traveling to the left out of the dirty liquid into the relaxed packing. Conversely, in a piston-type pump (Fig. 9.4) (with both the piston and the piston rod packing), on the pressure stroke the piston is traveling to the left into_the pressure, and on the suction stroke it is tmveling to the right away from the liquid. With the piston rod packing, the same action is seen: on the pressure stroke the rod is traveling into the packing, which is loaded by hydraulic pressure. The purpose of packing ·is simply to close up the clearance gap between the moving plunger and it associated parts, particularly the gland bushing, in the
216
EXPENDABLE PARTS
stuffing box or the piston and its cylinder, and the pistan rod and its stuffing box' parts. With ordinary packing this is accomplished by the use of material with con~ siderable resiliency. The mechanics of ali packing are such that regardless of the general shape the sealíng member, the hydraulic pressure tends to force the member through the, clearance gap. Accordingly, practically ali of the sealing and subsequent wear extrusion take place at the "heel" (Figs. 9.3 and 9.4). It can be seen that the action in a plunger pump (Fig. 9 .3) is such that on the pressure stroke the heel is being "dragged" away from the clearance gap, thereb greatly overcoming the force produced by the hydraulic pressure that causes trusion through the clearance gap, a benefit in high-pressure service. With piston-rod packing (Fig. 9.4), the heel is being dragged into the clearance gap both the motion and the hydraulic pressure, accelerating wear of the packing. Lubrication of packing is extremely important in high-pressure service. It be seen that only with the plunger pump can a lubricant be applied to the plung as it is entering the hydraulically loaded packing, when it is most needed. This i another benefit in high-pressure service. Any attempt to lubricate a piston or piston rod is not as effective, since th. lubricated moving parts enter the packing only on the unloaded or suction strok when lubrication is not required. The l 940s saw an intensive search for an improved packing. Early styles of ing went through a period of popularity due to a false impression that one packi was better than another, when in reality a "different" unworn packing would seal for a while in a "different" location in the stuffing box, away from the wash'-~ boarded area caused by the previous packing. is justas important for a packi · to sea! on the inside surface of the stuffing box as for it to seal on the rod plunger.) ... All of the packings at that time were more or less adjustable in that gland ening caused the packing to squeeze with great force against the rod. An excepti· was packing with altemate metal spacer rings with pins extending through hol in the packing rings, the gland force being transmitted through these pins. Thi was a fairly successful packing, but trouble was encountered in high pressure the pins would crush and distort under the high load. At that time a development program was carried on, and as a result the füsf truly "nonadjustable" packing was made available. This is a lip-type packing wit~ a fairly hard, fl.at center section that will withstand considerable gland load withou.t affei:-~ing the lip load on the rod (Fig. 7 .22).
7 .5.2
Packing Types
The type of service in which a pump operates determines the type of packing t be used. The choice is not always simple, but in order to have a guide to t selection of packing, a discussion of each type follows. General Servíce. A nonadjustable packing set composed of rather hard phenoH bottom and top adapters in combination with nonadjustable seal rings, The
7.5
•
PACKING
217
J
Figure 7.22. Nonadjustable packing style 0740. (Courtesy Utex Industries, Inc.)
ring has a phenolic core, and the sealing lipis composed of Buna-N and fabric or bther materials. It is recommended for general service on water, oils, hydrocarbons, alcohols, glycols, and amines. Depending on local service conditions and maintenance, it will perform satisfactorily at pressures up to 5000 PSI and temperatures to 200ºF. See Figure 7.22. Acid Service. Same design and configuration as general service except that the sealing lipis homogeneous Buna-N. TJ:iis packing must be lubricated to give satisfactory service in well service pumps. Again rock drill or steam cylinder oil is recommended. Since most well service applications are intermittent, the packing. will perform up to 15,000 PSI and will give satisfactory service in the fluids commonly used in well service operations. Occasionally it is necessary to use this packing in services that are highly abrasive due to slurries or sand content. Organic Service. Same design and configuration as general service. The sealing lipis Buna-N, nylon, and Teflon. Organic service packing is recommended when problems are encountered dueto corrosion or organic action on the composition. The addition of Teflon offers sorne resistance to corrosive and organic action in such services as lean oil, sulfur concentrations in water and oil, and sorne amines. This is recommended only in isolated instances.
A molded duck and synthetic oil- and water-resistant composition packing, recommended for fluid rods on pumps handling oil and water-base muds. The packing is designed with noncrushable features, and thus excessive gland or fluid pressure will not cause the usual crushing action of the packing with resultant undue wear on packing and rods. However, the packing may be adjusted to adopt to rods that are undersize. High-Pressure Service. An adjustable packing composed of die-formed lead, die-formed flax, and molded phenolic bearing rings. This is recommended as an alternative to general service packing in local areas where combinations of pressures, temperatures, and maintenance practices dictate a change in styles. It will
218
EXPENDABLE PARTS
be serviceable up to 8000 PSI and at temperatures up to 240ºF. Since it is adjus able, it is subject to human error. lt is recommended for the same broad classi cation as general service packing and can be used as an altemative in applicatio where the customer cannot use lubrication.
Power Oil Service. This is a die-formed Tefton filament packing with bro end rings. The classification is misleading, since the packing can be used on myriad of services. The Tefton is very susceptible to adjustment due to the expansion, and it has not been too successful due to this. Continua! and judi gland adjustment is required. ·
7.5.3
Split Packing Rings
An age-old practice is the use of cut-ring packing that can be installed in a pu without removing the rod or plunger. Whenever possible, pumps should be .. signed with readily removable rods or plungers. The use of solid or uncut pac . .•. rings will repay the user in extended life. Split rings present a leakage path t. sometimes requires excessive gland tightening to stop the leakage.
7.5.4
Spring-Loaded Packing
The use of springs to load or activate packing rings is not new. However, advent of new materials coupled with a better understanding of the mechanical hydraulic functions of the stuffing box have regenerated considerable interes this concept. ... Sorne of the advantages are: There is no need for additional adjustment; des· and assemblies are possible to accommodate corrosive, hot, and extreme p applications. The main disadvantage is that the packing cannot be adjusted to a small leak for a short time until repacking can be accomplished. However, ing failure is not catastrophic, so this is not too severe a problem. lt is the opi in sorne circles that eventually the federal OHSA regulations will not allow ing to be adjusted while the pump is moving. In this eventuality, the spring-loa¡ concept will be very practica!. See Figure 7.23.
7.5.5
Segmenta! Metal Packing
In an environment of hot or cold and surgically clean liquids and steam, seg tal metal packing, Figure 7. IA, has performed with outstanding service. The piston-ring principie is utilized to allow the liquid to force the segm activated by a gentle garter spring, against the piston rod. The tangential-cut (A) performs the sealing, the tangential cut allowing the segments to mov wards the rod to compensate for rod and packing wear. The leakage gap a segmental-cuts are sealed by a radial-cut segmental ring (B) positioned ove above gap. Typical arrangements used for example, three pairs of rings, a a enclosed in solid cages ali stacked on each other. lt can be seen that precl machining is required to produce this packing and obviously adds to its cost
7.5
PACKING
219
Spring-loaded packing style 0805-4. (Courtesy Utex Industries, Inc.)
THREE RADIAL CUTS
~
~;::Y //c2...__,___ __,____,9 GAIHER SPRlNG
A
9..._~_ ___,___,(; B
/
??,,
ÓA 91-~B'-'-----==9-'---l
R!NG A B B STACKED
Figure 7.1A. Segmenta! Metallic Packing
Multiple Material Assemblies ea! assemblies using real rings of different materials is a common practice. me reasons for this practice are abrasive conditions, corrosive materials, exreme temperature environments, and local requirements on ieakage or emissions. One of the most common assemblies is that of alternating rings of homogeous and fabric reinforced rings. These are generally used for abrasive condins or low pressure leakage; however, multiple materials and designs can be sembled for myriads of service conditions. They combine the strengths and of various materials and designs into a synergy that improves perforon the whole. For instance, the use of an ali TFE set can be enhanced with the addition of itable homogeneous or fabric reinforced rings. Obviousiy, the additional ma-
220
EXPENDABLE PARTS
terial needs to be generally compatible with the pumpage, but it can be plac in the set so as to perform without exposure to the ful! extent of the strea The addition of this ring will keep the TFE pressure rings from reforming/ molding or "slugging" up and allow the rings to perform as individual rings. The same type of situation can be used for high temperature, low t perature, and other applications that require additional engineering to prov· assemblies for satisfactory service.
7.5.7
Double Stack Height Seal Rings
Sea! rings and/or pressure rings in vee packing sets do not have standard heig that are common between manufacturers in the sea! industry. There is sorne fort into this with a ne standard for homogeneous and fabric reinforced ri for hydraulic cylinders and the hydraulic industry. These rings and JIC dim sions are generally very thin or short so as to provide a short assembly for t hydraulic cylinder market. The high pressure, industrial pump service market requires sea! rings and ; semblies of a different design and/or dimensions. The generally accepted m of failure is a wearing or fretting away of the pressure ring material until m of it is gone, and the pressure ring cannot deform and ''heal'' itself. When t happens, failure occurs; therefore, the design of a "double stack" height or "t stack" height rings adds material bulk to the sea! ring. This additional material must be added in such a manner as to enhance t performance rather than hinder. Also, additional attention should be given · lubrication since the thicker or taller rings have more material rubbing on t rod shaft and this must be compensated for by more lubrication. Generally rings are recommended; however, one double stack or tall stack ring will suf in most cases.
7.5.8
Spiral Packings
The use of braided materials cut into rings and formed around the shaft of pump or the stem of a valve is a common practice. The features of this practí are the ease of repacking and less inventory since the bulk material is on a s or in a coi!. It can be used in an emergency. The disadvantages of cut rings incorrect size due to inaccurate measurements or stretching, ragged and matched joints, and in general dirty or poor housekeeping associated with ins lation. Also, each joint provides a leak path for fluid or gas to escape. The use of dieformed rings of braided materials will remedy sorne of problems associated with cut rings. Measurements can be made correctly. Joi. can be cut cleanly and the packing kept clean; however, the joint problem the leakage problem through the joint still remains. For instance, in four sets there are four joints or potential leak paths for fluid to escape. The spiral combines the features of the ease of manufacture from brai stock with the dieformed features and goes further in that it eliminates the jó problem. The spiral is made from one continuous length of braided material s
7.5 PACKING
221
ed around a plug the proper ID, then cut and dieformed. The ends are properly riented so as to provide a spiral with no excess or slight of material. It provides n endless packing ring with no joints or Ieak paths and can be installed much e same as one ring of packing. Cut rings can be installed either spring Ioaded or hand adjusted. In either case e joints must be staggered. When spring loading cut rings, it is necessary to e the spring in a compressed manner so the cut rings can be installed into the x. lf not, it is very difficult due to the cut rings not holding shape. The spiral liminates this problem since it is endless and can be installed as a simple one ·ng packing set. lt can be used with either a metal coil spring or with the new astomer spring concept. FEATURES OF THE SPIRAL l . Endless construction-no leak path. 2. Ease of installation.
3. Precision height and length.
PROBLEMS OF THE SPIRAL l. Must be made in the factory.
2. Un-spirals at times unless special packing design. 3. Customer resistance due to appearance.
STYLE 242 SPIRAL UNITIZED PACKING SET Figure 7.2A
CONVENTIONAL MULTIPLE RING SET Figure 7.3A
222
7.5.9
EXPENDABLE PARTS
FLAT-BAK Vee Ring
Vee ring technology, with the exception of material improvements, has remai unchanged for years. One manufacturer has now significantly changed the seali capabilities of the vee ring with the creation of the FLAT-BAK vee ring. T FLAT-BAK vee ring is applicable to any area where vees are used especially~ reciprocating sealing applications. The ordinary vee ring design with its vee shape on the face and heel side the ring has to have sorne type of adapter that is vee shaped on one side and on the other. The FLAT-BAK vee ring replaces this adapter with the additio capability of sealing pressure. Another significant improvement which results in increased seal life is t heavy duty construction as well as the optimum anti-extrusion capability. Flat-Bak Vee Ring is molded to twice the height of the standard vee ring. T along with the flat backed feature allows for a significant increase in the volu of material available for wear and extrusion resistance. The standard vee rí with its shallow height, has a much shorter distance for an extrusion or w zone to travel before a completed Jeak path occurs (See Fig. 1). The FLAT-B vee ring increases this distance over two times (>2X), resulting in significan increased sea! set life. The flat back feature now permits the full utilization of fabric reinforcem capabilities. The standard vee forces a flat fabric into the vee shape quite oft causing interna! or external folds in the ring. With the FLAT-BAK vee, t fabric plies are now in the optimum wear and extrusion resistant position in t heel of the ring. An additional feature built into the FLAT-BAK vee as well many other Utex vee rings is horizontal bias fabric construction (See Fig. 7.5 This creates a vee ring that has ali fabric reinforcement plies with equal fi Jengths, allowing uniform wear performance. The horizontal bias elimina short and long fiber zones in the vee ring. With the FLAT-BAK vee, a single sea! can be used with greater effectiven than multi-vee ring sets, providing Jower cost sealing and higher pressure seali capabilities.
7.5.10
Knitted Wire Mesh
Knitted Wire Mesh has many uses such as back-up rings, scrapers, filters, a high temperature seals. A patented process ( #4219204) whereby knitted wi mesh is molded in conjunction with homogeneous rubber or other materials act as an anti-extrusion device is available. Knitted Wire Mesh is also available with fillers such as graphite, PTFE, a aramid yarns. Standard materials for the mesh itself include stainless steel, co per, inconel, and phosphor bronze. Other special alloys are available, and no standard densities can be produced from ali materials.
7.5
s ;t;
/ /,¡
1
11 1
1 : : ' ' 1
! '
PACKING
.
223
11 ¡ 11
l 11 111 i 11
¡
_J ¡.
1
k.i-
>c:::x l the rings tumed out to be crowning proof of the existence of Jacoby leakage. ...
7.12
GLOSSARY OF TERMS
Application of a hard facing layer to steel to increase resistance to wear and corrosion. In the spraywelding process, a special type of alloy in extremely fine powdet·
SPRA YWELDING.
7.12
GLOSSARY OF TERMS
235
torro is sprayed through an oxyacetylene flame, impinging on a clean work pi.ece sticking by a mechanical interlocking of the semiplastic metal particles. to point, it is exactly like wire metallizing. In a second step, the sprayed deposit together with another torch-heating operation to form a solid wear-resistant coating that is bonded rrietallurgically to the base material. These special materials have a happy combination of properties. They have wear and corrosion resistance because of the alloys and rnicrostmctures xm~s(;'ll•· They have a matrix of soft nickel containing a variety of very hard par(up to 80 R) including chromium bmides, chromium carbides, anda mixture complex cross-combinations. The result is a very low coefficient of friction and vA\NUVU• corrosion resistance. The soft matrix allows sorne ' for the hard u"'""'v~ to fioat on a microscopic scale. Because of the low temperature about 1900ºF), a variety ofthese base materials can be used. The macro hardness the deposit is uniform throughout. , One of the spraywelding materials contains particles of tungsten carbide in the soft matrix, imparting an effective extreme hardness. This material should be ;'avoided for plunger coating for the reason that the "scrubbing" action of an elas~Jomeric packing will remove sorne of the soft matrix, leaving a sandpaper finish ·:.that is in tum extremely damaging to subsequent packing. While the surface just described may appear smooth, a simple test will reveal such microscopic "sandpaper" surfaces. Just stroke the edge of a copper coin (penny) along the surface; .the "rough" surface will generate a visible streak of bright copper color.
Obtaining higher strength in steel by heating above the transfonnarange (above 1450ºF) and cooling rapidly in a liquid bath. (Exception: ~Quenching an austenitic stainless steel results in annealing or sofiening.)
CQUENCHING.
Heating hardened steel to an íntennediate temperature ( 800 to 1200ºF) to decrease hardness and increase toughness.
c.TEMPERING.
Increasing the strength of a group of special alloys heating at intem1ediate temperatures (800-llOOºF) and allowing a microcon·tuent to precipitate from a metallic solid solution.
PRECIPITATION HARDENING.
FLAME HARDENING. Increasing the hardness and wear resistance of a medium to high carbon steel (with or without alloy) in a localized area by applying flame 'heating to the steel smface and quenching.
Increasing the hardness and wear resistance of a medium carbon steel (with or without alloy) in a locaiized area by generating heat electrical induction in the steel surface and quenching.
INDUCTION HAFIDENING.
Making low-carbon steel more wear-resistant by increasing the surface carbon content through di:lfusion from a carbonaceous medium and subsequenching.
CARBURIZING.
Increasing resistance to wear and coITosion by depositing hard chromium on a surface in an electroplate bath. Hardnesses up to 70 R (750BHN) can be obtained.
· CHROME PLATING.
236
EXPENDABLE PARTS
NORMALIZING. Strengthening steel by heating above the transformation range
(above 1450ºF) and then air cooling. PLASMA COATING. Increasing resistance to wear and corrosion by applying a sur-'
face layer of hard facing materials, utilizíng the plasma are principle. A plasmaforming gas is passed through a de are in a small nozi:le and is superheated, its. molecules breaking down into ionized atoms with a high energy content. Working temperatures of 10,000-40,000ºF are obtained, and gases such as argon, helium, or nitrogen-hydrogen or argon-hydrogen mixtures. Materials to be deposited are< in powder form and are introduced into the are, heated, and blown onto the work piece, where they melt on the surface and form a solid bond. Since the are not contact the work piece, it remains relatively cool.
7 .13
GUIDELINES FOR MATERIAL SELECTION Piston Pump Part
Piston Rods
Material Quenched and tempered 4150 alloy steel, induction hardened. Same, with 0.020-0.030-in hard ehromium plate on surfaee. Carbon steel with spraywelded hard nickel alloy on surface.
Pisto ns Body Snap ring Retainer ring Support rings Rubber
Liners
Valves and Seats Valve
Seat Nut Insert Spring
Forged, quenched and tempered 4140 alloy steel. Shot-peened spring steel. Medium earbon steel. Medium carbon steel. Natural rubber. Chrome-plated. 27 % chrome-iron lining in carbon or low allow steel jacket. Flame-hardened medium carbon or lowalloy 8620 steel. Quenched and tempered 4150 alloy steel forging, flame hardened on wear surfaces. Same as valve. Normalized and shot-peened medium carbon steel forging. Urethane (Buna Nin sorne sizes). Oil-tempered spring steel or titanium.
7.13 GUIDELINES FOR MATERIAL SELECTION
Plunger Pump Parts Plungers
Valves and Seats Disc-type
Externally mounted
Wing-guided
Wing-guided slush type
237
Material Spraywelded nickel-base alloy on lowcarbon steel. (Special-same alloy on 304 stainless steel.) Solid 85 % alumina with 304 stainless steel shank. Sprayed ceramic coating on low carbon or 304 stainless steel, all with 304 stainless steel shank'. Seat-cast 316 stainless steel. Guard-same. Disc-Delrin, titanium, 316 stainless steel. Guide bushing-316 stainless steel, nickel aluminum bronze, 316 stainless steel with delrin sleeves. Spring-Titanium, 17-7 precipitation hardened stainless steel Inconel. Capscrew-K-Monel. Valve-17-4 precipitation hardened · stainless steel wing-guarded. Seat-17-4 precipitation hardened stainless steel. Spring-17-7 precipitation hardened stainless steel. Valve-410 stainless steel, n1ckel-aluminum bronze casting. Seat-410 stainless steel, nickel-aluminum bronze casting. Spring-17-7 precipitation hardened stainless steel. Valve-410 stainless steel, carburized 8620 alloy steel. Seat-410 stainless steel, carburized 8620 alloy steel. Nut-medium carbon steel. Insert-Urethane.
Table 7 .6 gives the chemical analysis of many of the popular metals used in pump construction.
TABLE 7.6 N
Nominal Chemic:al Analyses, percent by welght"
Material
e
Mn
Si
0.20 0.45 0.20 0.40 0.50 0.65
0.45 0.75 0.80 0.88 0.88 LOO 0.60 0.70 0.70 0.70 0.30
0.25 0.25 0.25 0.25 0.25 0.20 0.50 0.60 0.60 0.60 0.50
0.30
0.50 4
Cr
Ni
0.50 0.95 0.95
0.55
c.>
ti>
Low carbon steel Medium carbon steel 8620 alloy steel 4140 aHoy steel 4150 alloy steel Sp1ing steel 27% Cr-iron 410 stainless steel 304 stainless steel 316 stainless steel 17-4 precipitation hardened stainless steel 17-7 precipitation hardened stainless steel Sprayweld
2.30 0.10
0.06 0.05 0.04 0.05 0.65
Mo
----
Cu
Other
0.20 0.20 0.20
27 12.5 19 19.5
10
16
10.5 4
17 15
13
2.5 2.7
7
Al Fe B
1.0
Ni-Al bronze Ni-Al bronze casting Titanium
0.08
Inconel K-Monel
0.15 0.15
1.0 0.60
0.5
16
5
81
5
79
72
65
gD Aluminum Bronze ªOther common materials:
%
4 Urethane-polyurethane elastomer.
0.5 29.5
80
Al Fe Al Fe Ti Fe Fe Fe Al Ti Al Fe
1 4
3.5 10 5 10 5 99 0.25
8 1.0
2.8 0.5 ll
4
'1 7.14 TITANIUM AS A PUMP MATERIAL
7.14
239
TITANIUM AS A PUMP MATERIAL
Titanium possesses the most desirable characteristics for use in pump liquid-ends and parts handling waters of ali sorts, including sea water and oil-field brine. Commercially Pure Titanium (RMI-70) has excellent corrosion resistance and has been used for severa! years giving excellent service. This extreme resistance to corrosion results in reduced liquid-end failures caused by corrosion-fatigue at the highly stressed region at the intersection of bores where a stress-concentration of 2. 75 may be had. In recent years, titanium has become more plentiful and it is well within the acceptable cost-range for pumps in special service. Titanium must not be used in strong reducing acids or chlorine.
8 VALVES
8.1
VALVE TYPE CLASSIFICATION*
Valve and seat configurations can be classified as to type as shown in Figure 8 .1. It is obvious that there can be numerous combinations of most of these features. Probably the main division of greatest difference is between the self-contained ( Q, R) and the in situ (H-P). Configurations of the self-contained type have the advantage of dimensional and assembled accuracy, but they are confined to the smaller pump sizes, about 100 BHP and smaller. Large ph)'.sical size of valves limits the ability to use the self-contained principie. In situ valves require guiding and spring support to be a part of the liquid end. Self-contained valves can be reclassified into center-guided ( Q) versus cageguided ( R). Center-guided valves seem to be preferred because of their simplicity and ease of assembly. Caged valves are not recommended for abrasive liquids. The next logical division would be the metal-to-metal (A) versus the rubber seal or "slush" type (B). As the name implies, the rubber seal valve is mandatory for most liquids containing even small amounts of solid materials and slurry. The matter of valve-guiding methods is very broad in that all five (S, T, U, V, W) and their combinations are widely used. Wing-guided valves (U) are not usually accepted for slurry service because there is rapid wear between the ribs and seat and there is a tendency for solid particles to interfere with the guide motion. The most popular method of mounting the valve in the deck is the taper fit, but the sandwich or ftange method is widely used. The screwed method is no longer used in high-pressure pumps. *Letters in parentheses refer to keyed drawings in Figure 8.1.
240
8.2
Valve Types
A
\
Metal Bevel Rubber seal
B
(
Metal
241
PUMP VALVES
Seat Types
2i ria
H
Slush C 1 METAL
! !PLASTIC 1
Three-rib
Four-rib
Discorflat
J
K
Double-port
Full-flow
Suspended-guida
Bonded Disc Valve for "Dirty" Liquids
' L
1--írr¡-¡ 1 1
Ball
1 I 11 11 l 1
,
1 1
1
1
Bevel-rib
M
' 't:==~:;::;=,.:---1 1 1
1I 1 1 11 11
Spherical
N
_._ Durable disc
1
t
Flat-rib
t----1 : : r--1
/
1 1
Bevel recessed-rib
GW?
1 1 1 1 \ 1 1 1 'l...,) 1
o
p
1
1 1
1 l_J 1 1 I ~ /
1
1
1
Flat recessed-rib
\'¡--------¡} Full-flow
Figure 8.1. Valve classification.
8.2
PUMP VALVES
A liquid valve is a rather simple device in that it is a freely movable plug that is forced open when there is liquid pressure under it and is forced to close and seal when there is pressure on top of it. The simplest valve is the leather ftapper used in the pitcher pump and in air bellows for centuries. But with the advent of highpressure, high-speed pumps and the presence of abrasive solids, even in small amounts, simplicity has given way to extreme sophistication.
242
VALVES
Self-Contained Valves
R
Q
Caged
Center-hole guided Valve Guiding Methods
s
J~L
~ Top stem
t ;
1·. ~
, Ef"FECTIVE THRDUGH ,
....,..,.,;~AR__;;E..... A _--+i,D;:..;;l.;.;;.AM;::.ETc::;ER"-i.~..,·
CPTI CNAL " " ' ..,:
T
T
u
GAUGE-LINE LIMITS SHCULDER
A
Bottom stem
rn Wing-guided
V
B
TAPER
1 1
e : : .
w
1 1 1
STRAIGHT
1 THREADED
1 1 . -
Center-hole
Cage-guided
Figure 8.1. (Continued)
Figure 8.lA. Valve Seat Retention Methods
Two types of high-pressure valve-sealing methods are used (see Fig. 8.1): (A) metal-to-metal seals for clear liquids and (B) elastomeric seals for dirty liquids. (For lack of better terminology, the latter is referred to as the "slush"-type.) The elastomeric seal performs the function of providing a '' dam' ' between the metal parts of the valve and seat even though these parts never come into intimate contact, being held apart by the solid particles in the liquid. The elastomer must be resilient enough to deform over a solid particle so that the valve will not be held open by that particle. However, it must not be so resilient as to allow excessive
8.2
PUMP VALVES
243
extrusion into the gap at the valve and seat contact or to allow "puncturing" by the solid particles. Unfortunately, most elastomers have low strength at maximum resilience and vice versa. Many val ves incorporate the rib-supportéd design ( H, l) for the following obvious reasons. Consider the use in abrasive liquid service of a non-rib-supported slush type (K) seat with a bevel sealing face where both the valve metal and seal contact the seat bevel. Since the guidance of such a valve, either stem or wing ( S, T, U), rnust have sorne clearance, the valve can close on each stroke in a slightly "cocked" position. When the full hydraulic load is imposed on top of the valve, the valve tends to seek its true center, and a small amount of movement on each stroke grinds solids between the metal faces, resulting in rapid wear. If flat ribs are úsed in the valve seat upon which the valve rests, it always lands on a flat surface and cannot shift when the hydraulic load is imposed. A sharp bevel angle ((J) of 55º induces better centering as the valve doses and also reduces ftow turbulence since the flow path is closer to a straight line. All rib-supported valves should use the superior three-rib design (H). Since the entire hydraulic load must be supported by the ribs, the three-rib concept absolutely allows equal loading on eac;h rib. Since the three equally spaced ribs always carry equal shares of the load, regardless of solids trapped on the ribs or dimensional discrepancies due to machining and wear, no one rib is ever overloaded. This also means that the valve body is always uniformly loaded between the 120º segments. Now in the case of four ribs, solids on one or more of the ribs or dimensional discrepancies in the parts could cause support on only two ribs, thereby overloading both the ribs and the val ve body. With a wing-guided valve (U) or with a non-rib-supported stem-guided seat ( K), flow-restricting metal is placed in the through-area path and serves no other purpose than to guide the valve. When the same amount of metal is used in ribs that support the valve, a stronger and longer-lasting valve results without sacrifice of through area. Several types of mud or slurry valves are shown in Fig. 8.2. The failure mode of any elastomeric seal valve follows the pattern of pinch-off of the elastomeric seal at the thin circumferential area between the seal and the metal. Since the elastomer is in effect a liquid, the pressure above is transmitted through the seal to the point where it "wants" to be extruded or squeezed past the gap, if any, between the metal valve and seat. The minute pinching off progresses until a rather large void in the elastomer occurs. Fluid trapped in this void is then subjected to high pressure from above and low pressure from below. The liquid is suddenly squirted out through the relatively close metal-to-metal contact, resulting in "hair-line" or "wonn-eating" washing of metal parts. Corrosive drilling fluid (salt mud, etc.) accelerates the advancement of "worm eating" and reduces valve life due to the more rapid loss of metal. This failure mechanism is regenerating in that rapid failure and complete washout of the val ve and seat soon follow. Therefore, the longer one can delay the above-described pinch-off by replacing the seal, the longer valve life can be expected. Rapid pinch-off results from:
244
VALVES
Figure 8.2. Mud and slurry type valves. (Courtesy Fluid King.)
1. Use of a low tensile strength elastomer. 2. Reduced tensile strength of any elastomer in hot liquids. 3. Presence of large particles or lost circulation material, the material lodging under the elastomer seal, allowing trapped liquid to be squirted out in much the same manner as a pinched-o:ff seaL 4. Use of a new seal on a wom valve, which allows excessive seal overhang and results in the seal bending upward, again allowing trapped fluid to be squirted out. Not only does this cause hairline washing, but it also results in rapid seal wear because the elastomer at the sealing point is placed in extremely high tensile stress even before the full hydraulic load is imposed. 5. Chemical reaction to the seal, which causes it to swell, resulting in excessive overhang anda reduction in tensile strength. These points are discussed in tum below. 1. The inherent high tensile strength of polyurethane (about two times that of Buna N) and its chemcial resistance, particularly in oil, make it the most desirable seal available. 2. High temperature is an enemy of all elastomers, particularly of polyurethanes. The ·effect of temperature on any elastomer is such that it is misleading to apply a fixed limitation to them. For instance, a generally accepted temperature limitation for polyurethane has been placed at 140ºF by the industry, but since elastomers undergo a gradual reduction in physical characteristics, particularly tensile strength, as temperature is increased above room temperature, it is reasonable
8.3
VALVE SEATS
245
to assume that even polyurethane can work ata temperature above 140ºF if other factors such as lower pressure are favorable. There are many cases where polyurethane seals perform satisfactorily above this temperature. Buna N has the desirable characteristic that it retains its physical strength ·over a higher temperature range--to such an extent that Buna N seals may better at high temperatures. Remember that all elastomers are subject to deterioration, and shorter life must be expected at higher temperatures. 3. Solid abrasive particles are a necessary evil in slurry pumping. 4. The obvious remedy is not to try to use a badly worn valve. 5. Chemical reaction becomes a problem. No doubt certain muds and slurries contain chemicals that are detrimental to either polyurethane or Buna N, and these are sometimes difficult or impossible to track down. It behooves one to try one or the other seal when a chemícal reaction is suspected. As previously stated, polyurethane seals will stand up in most slurries," and are particularly suited for oil or oíl-base muds. Buna N, although called "oil resistant," is not completely so. AH seals of Buna N swell and deteriorate in any oil and are not recommended for oils with an analine lower th.:.n 150ºF. (The lower the analine point, the greater the content of aromatics, which are hard on Buna N). Experience and extensive testing have shown that the desirable amount of lift of a valve should be such as to provide a lift area equal to the through area of the valve. Lift in excess of this is not normally harmtul, since the valve stiil will only lift the required amount. However, a stop is desirable at this point since erratic pump operation due to air, gas, or hot mud causes abnormal valve action with pounding and bouncing. It should be stated that in normal operation a valve does not slam shut; it follows a smooth, gradual opening related to the displacement of the piston, which is inherently a slightly distorted sine wave. The velocity of the abrasive liquid through a valve should be limited to avoid erosional effects on the valve parts. For most abrasive materials, including drilling mud, a limit of 12 FPS for uncharged suctions and 16 FPS for charged suctions is generally recommended. Slurry valves should be limited to a maximum of 12 FPS. In investigation of a pump valve lift and liquid velocity, keep in mind that the recommended limits are based on maximum liner or plunger diameter and maximum operating speed. In order to minimize excessive "dash-pot" effect in retarding the valve motion, resulting in delay of closing, the pot area should be at least 1.5 times the valve disc area to provide ample "escape" area.
8.3
VALVE SEATS
Table 8. l shows recommended valve seat taper diameter or straight-bore diameter (gauge-line) for an extended number of valve sizes the present API Range (Table 8.1).
¡ TABLE 8.1 Valve Seat Taper Dimensions (See Chapter 7, API Standards) (Proposed expansion)
Size
Gauge Line Depth, in
Approx. Taper Depth, IN.
GPM/Valve At IO FPS
Approx. Through Area, sq. in.
"Size" Number Proposed
-15 -14 -13 -12
0.45 0.5 0.57 0.64 0.72 0.81 0.92 1.03 1.16 1.3 1.47 1.66 1.87 2.1 2.37 2.75 2.875 3.375 3.875 4.375 5 5.625
0.27 0.29 0.32 0.35 0.38 0.41 0.45 0.49 0.53 0.58 0.63 0.69 0.75 0.81 0.88 0.96 1 1.125 1.25 1.375 1.5 1.625
1.4 1.7 2.2 2.8 3.6 4.4 5.5 6.9 8.6 I0.7 13.4 17 21.2 26.5 33.2 41.6 51 65 81 I03 128 160
0.09 O.JI 0.14 0.18 0.23 0.28 0.35 0.44 0.55 0.69 0.86 1.09 1.36 1.7 2.13 2.67 3.3 4.2 5.2 6.6 8.2 I0.3
1 2 3 4 5 6 7 8 9 10 1 12 13 14 15 16 17 18 19 20 21 22
-11
-IO -9 -8 -7 -6 -5 -4 -3 -2 -1
o API API API API API
1 2 3 4 5
API API API API API API
6 7 8 9 10 11
12 13
14 15 16 17 18 19 20
6.25 7 7.75 8.5 9.5 11 12.5 14.125 15.875 17.875 20.125 22.75 25.5 28.75
1.75 2 2.25 2.5 2.875 3.25 3.75 4.25 4.75 5.25 5.875 6.5 7.25 8.25
202 249 312 389 467 623 779 935 1246 1558 1869 2336 2960 3583
13 16 20 25 30 40 50 60
80 100 120 150 190 230
23 24 25 26 27 28 29 30 31 32 33 34 35 36
~
- - -,-~,·= .
U
a.
"2&$,,L,,~,,.,"iiiii
__
~w-
248
VALVES
Aside from clamping a "ftanged" valve seat into the deck with a washer or gasket under the ftange (for pressure), there have been three other fairly popular methods of securing the seats into the deck: Taper fit (L), ftanged or "sandwich" fit (X), and screwed fit (Y) (Fig. 8. IA). Table 8.1 shows taper dimensions and Figure 8.3 shows the terminology applied the valve and seat dimension. Figure 8.4 gives details of the design of taper fits for valve seats. Tapered valve seats should be provided with a shoulder to help prevent complete pump-through, which would result in damage to the pump valve deck bore if the pump were overpressured by accident. The installation of new valve seats should be preceded by a thorough cleaning of the deck bore with emery cloth and wiping dry and free of oil or grease. The seat should have any protective coating removed with solvent and wiped clean and dry. A preliminary check can be made by dropping the seat into the deck bore with a slight ''thunk. '' If the fit is proper and clean, the seat should be difficult to break loose by hand. With the seat in place, install a valve. Then place a pipe over the stem of the valve and give one or two solid blows with a sledgehammer. With a firmly seated seat, the pipe should ring with the characteristic sound. The widely used taper-fit valve seat seems to be the most practica! for highpressure service. However, such seats are sometimes difficult to pull. A hydraulic valve seat puller using a jack of 150 tons capacity and 2i-in diameter puller bolt is required. In stubbom cases it is sometimes helpful to break a seat loose by sledgehammering the top of the puller bolt (a driving face is provided) or by even sledgehammering the side of the valve pot after the jack has been pressurized. Should it ever become necessary to remove a seat with an acetylene torch, follow this procedure: Cut two or three of the ribs completely free. Heat one spot ofthe seat to a dull red (do not flame cut) while frequently playing the torch around the entire seat to heat it. Then quench the heated seat rapidly with a stream of cold water. This procedure reduces the danger of pump damage from cutting. Heating one spot dull red places the metal in a plastic state. Heating the rest of the metal forces it to expand, and since it is confined in the deck bore the expansion is forced into the plastic region. Upon cooling, the seat diameter becomes smaller than the original, and it can usually be bumped out with a hook or pipe wrench.
8.4
VALVE SPRINGS
A generally accepted rule for approximate valve spring load is: 2 POSIVA for ''poor'' suction conditions such as lift from a dug pit and for low speed. 4 POSIVA for "normal" suction conditions, such as from an elevated tank. 6 POSIVA for ''charged'' suction conditions of 20 to 40 PSI.
'-----Da----Aa----
i.E----¡j v-----.1 i.E----Av-----+i i.E----D.-----.i 1
\ TPF on diameter ~-----Dg
/ Ag _ _ _ ___.
Valve dimensions
Figure 8.3. Valve dimensions. Symbols are as follows: ex = angle of taper, one side, deg (:J = angle of coefficient of friction, deg Aa = disc or valve area, in2
FL = force on valve, maximum lift, lb
P = pressure on valve, PSI L = valve lift, in
Ag = deck-bore area at gauge line, in2
LL = spring space, maximum lift, in
AL = valve lift area, in2
L¡ = spring length, installed, in L¡ = spring, free length, in Na = spring, number of active coils N, = spring, total number of coils
AL = Area of "belt": AL = 1íDv (or D.) X L Av = valve through area, in2 Apo1 = valve pot area at Dpoo in2 Da = disc or valve diameter, in De = seat opening, effective diameter, in Dg = gauge-line diameter at bóre, in D, = spring mean diameter, in Dv. = seat opening diameter, in d = spring wire diameter, in F = force on valve, lb F; = force on valve, installed spring, lb A,,., = 1.5 X Ad
(=Na + 2), closed end Q = force on deck bore due to seat
.drive, lb s¡
= spring, installed stress, PSI
sL = spring, lift stress, PSI TPF = taper per foot on diameter, in/ ft W= Wahl factor x = valve seat depth, in (} = bevel angle, deg
249
Figure 8.4. Taper valve seat bore fit.
f = coefficient of friction TPF = taper per foot, on diameter, in/ft D 8 = gauge-line diameter, in D,, = effective through diameter, in F = force on seat, lb P = pressure on seat, PSI s = allowable stress, PSI Q = force on seat bore, lb Qc = force per circumferential inch, lb
X= seat depth, in a = angle of taper, one side, deg (3 = angle of coefficient of friction, deg
Rule: For seat to be self-locking in bore, a < (3. Sample Calculation: For D 8 = 7 in, P = 2000 PSI, f = 2 in. a=
=
0.1, s
=
75,000 PSI, and TPF
arctan TPF/24 = arctan 2/24 = 4.76º
(8.1)
(3 = arctanf= arctan0.1=5.71º
(8.2)
F = 0.7854D~P = 0.7854 X 72 X 2000 = 77,000 lb
(8.3)
Q = (F/2) tan (a+ (3) = (77,000/2) tan 10.47º = 208,000 lb
(8.4)
Qc = 2Q/ 7r = 2
X
208,000 /3.1416 = 132,600 PSI
X= Qc/Zs = 132,600/2
X
75,000 = 0.9 in
( 8.5) (8.6)
Note: API Standard TPF is 2 in/ft; API Standard for X when Dg = 7 in is 1.25 in. [Formulas do not include requirement for set strength to support the forces to which it is subjected.]
250
8.5 VALVE SPRING DESIGN
251
The greater the pump speed, the heavier the spring required for maximum efficiency and smooth operation. Accordingly, a higher suction pressure is required.
8.5
VALVE SPRING DESIGN
Formulas POSIV A De
= F;/ Av
(8.7)
=
(8.8)
.JAv/0.1854
AL (See valve dimensions, Fig. 8.3)
d
=
;¡8kD;Na/G
(8.9)
f
=
8FD;Na/Gd 4
(8.10)
Kc
=
1
+ (0.615d/D,)
s = (2.55FD,/d 3 )Kc k Na
=
= valve through area, = valve lift area, in2
( 8.13)
= fGd 4 /8FD;
(8.14)
in2
= spring wire diameter, in = =
( 8.12)
Gd 4 /8D;Nª
where Av AL d De D,
(8.11)
effective valve seat diameter, in mean diameter spring, in f = spring deftection, in F = force, lb F; = installed force, lb FL = force at full lift, lb G = spring torsion modulus, lb /in2 k = spring rate, lb/ in Kc = Wahl factor (Figure 8.5) L¡ = free length, in L; = installed length, in LL = spring space length, in Na = number of active coils N 1 = Total coils = Nª + 2 (closed & ground) s = stress, PSI
252
VALVES
2.0
\
1.8
::.:: ... o
\ \
1.6
tí
"'
LL
1.4
1.2
1.0
~ ¡-..,..._ -¡-._
2
8
6
4
-
12
10
Ratio: Mean diameter Wire diameter
Figure 8.5. Total valve spring stress according to Wahl formula. K x S = total stress.
See Figure 8. 6 for required val ve lift to pro vide lift area of 100 % of through area.
Example * (iterative solution) Av Ds
k
= area, through valve = 1.3 in2 = mean spring diameter = 1.9 in
spring rate = Try 30 lb/ in LL = length, spring space = 1.0 in Nª = number of active coils-Try 4 G = torsional modulus, spring wire = 11,500,000 lb/in2 =
POSIV A (pounds per square inch valve area) = 4
l. Determine F;, installed force, lb:
F; = POSIVA
X
Av
=4
X
1.3 = 5.2 lb
(8.18)
2. Determine De, effective diameter from valve through area·(Av):
De= ,JAv/0.7854 *See Figure 8.6.
=
,Jl.3/0.7854
=
1.3 in
(8.8)
8.5
253
VALVE SPRING DESIGN
r-:nd---i I
f-- Dd__,,..,
r------,
\
-~
"....__ - - -
-t11
~Dd----4
\
1
- - r------L
,..-,1
__!:_
~ ILJ
- - L _ _ _ _ _ _J
-'-OIID
,_.,,,
~Dv~
~Dv-1
f--nu-j
@ @ ~
(a)
BEVEL SEAL WING OR STEM
(b)
BALL SPHERICAL
(e)
DISC OR PLATE
8.6. Required valve lift for 100% of valve through area (shaded area). (a) Bevel seal, wing, or stem L, in = A,,/1r cose
(ni + cos f) sin IJ)
15)
(b) Ball or spherical
L, in
=
A,,/0.707 1íDv
(8.16)
(e) Disc or plate
L, in= A,,/1íD,,
(8.17)
where L = lift, in; Dv = seat opening diameter, in; = valve through area, in2 ; e = seat bevel angle, deg.
= seat effective diameter, in; A,,
3. Determine lift
to provide lift area (AL) of 100% of Av:
L=Av/r.De
=
1.3/1.31!' = 0.32in
(8.19)
4. Determine d, spring wire diameter, in: 4
.
d = :;/8kD;Na/G =0.155in *Or D ..
4~---~------~
= :;/g
X
30
X
l.9 3
X
4/11,500,000
(8.9)
254
VALVES
5. Determine L1 , free length of spring, in: L¡
= L¿ + L +
= 1 + 0.32 + (5.2/30) = 1.49 in (8.20)
(F;/k)
6. Check for spring space: 4 active coils
6 x d
=6
0.155
X
+ 2 (closed end)
= 0.93
=
6
[OK, less than LL (1.0 in)]
7. Check stress at F;: S;
= 2.55KJ;D./d 3 = 2.55
X
l*
X
5.2
X
1.9/0.155 3 = 6765 PSI
(8.21)
8. Check stress at FL: F¿
=
S¿
= 2.55
(L¡ - L¿) k X
l*
X
= ( 1.49 - 1.0) 30 = 14.7 lb 14.7
X
1.9/0.1553
= 16,106 PSI
(8.22)
Val ve spring life can be improved by taking advantage of the Goodman effect by designing within the stress ranges shown in Figure 8. 7
8.6 THE EFFECT OF VALVE DESIGN ON SUCTION REQUIREMENTS Section 8.6 reports on an extensive investigation of the valve performance in a six-inch stroke Triplex Plunger Pump. The choice of liquid valves for a plunger pump is dependent upon many factors, the most important of which are Pressure Liquid temperature Suction pressure Liquid corrosion Pump speed The ideal valve would be weightless, springless, corrosion and temperature resistant, andas large as possible (to provide maximum through area). A brief look into these requirements will immediately show the tug-of-war that exists in valve design. One cannot have lightness with strength or large size.
*Shot-peen spring and use Wahl factor of l.
8.6 THE EFFECT OF VALVE DESIGN ON SUCTION REQUIREMENTS
255
1201--~--J.--~--+~~-+-~~-+~..........,,.¡..r::--,r-¡
Anea of additional stress possible dueto shot·peening
"' ro "'::>o
~
soi--.c..~r--~~r--~~r--~.,,._+--~~+-~--1
..;: ~
601---~~+--~~+--~-r-+--~~+-~~+-~--!
~
1ií o; e:
~
40,..._~~i--~-----~~+--~~--~~+--~·--<
ASTM A230 ASTM A232 Wire 0.207 in or smaller
o
40
20
60
80
100
120
lnitial stress, thousands of PSI
Figure 8. 7. Goodman diagram for factor.
stresses. Spring stress range corrected by Wahl
Strength and temperature requirements dictate a metallic valve, which introduces corrosion problems. Heavier springs are required for high suction pressures and higher speed, and this in turn demands a higher TCP requirement.
8.6.1
Determining Valve Efficiency
Before one can begin the search for the "best" valve, a method of determining the "best" valve must be adopted. It is logical to assume that a pump operating at a high volumetric efficiency with a low NPSH has the "best" valve from the point of view of hydraulics as well as endurance. Therefore, since valve design affects the pump's NPSH requirement, it was decided that NPSH tests would be the basis for studying a variety ofvalve designs, through areas, spring loads, valve lifts, and valve weights. The standard for establishing a reciprocating pump' s TCP Figure 3. 7 and a curve Figure 3.8 relating volumetric efficiency wit.h decreasing suction head should be the best way to present the data. By using such a curve, one can select the volumetric efficiency that is satisfactory and then compare all tests at this same figure.
256
VALVES
Throughout this discussion, certain terms will be used: NPSHR. Net positive suction head required at the pump suction flange, in PSI of liquid being pumped Velocity ( V). Average velocity through val ve (based on plunger displacement and val ve through area), FPS Through area (Av). Net area through valve (ribs and wings deducted), in2 Lift ( L). Lift of val ve, such that the circumferential area is a percentage of the through area, in Spring loads. Installed spring load divided by valve through asea, pounds per square in of valve area (POSIVA) Volumetric efficiency (VE)
8.6.2
=
actual oallons e. x 100 theoretical gallons
Valve Tests
Figure 3.8 in Chapter 3 shows a schematic ofthe test setup, along with the formula used to cakulate and construct a family of curves of TCPA versus VE for different pumps.
8.6.3
Valve Combinations
Table 8.2 lists all the valve combinations used in the investigation. Note that for each combination of valve type, through area, weight, and lift, there is a number assigned for easy cross-reference. The first and simplest analysis was to list valve combinations in increasing order of TCP requirement for a selected VE. This is shown in Table 8.3. At 250 and 350 RPM, it is evident that valve combination 28 is the "best" This is a singleport plate valve with maximum through area, maximum lift, minimum weight, and 4 POSIVA load. Valve 18 appears to be the "worst" in this series. This is the same val ve but with a through area of 2 in2 • At 625 RPM, valve types or combinations surprisingly reverse their relative positions in that the ''best'' valve at 350 RPM becomes one of the ''worst'' val ves at 625 RPM. This leads to the conclusion that speed has more effect on valve performance, and consequently on TCP requirements, than was first thought. At one time, it was assumed that if velocity through the valve could be kept down, high e:fficiency could be maintained.
8.6.4
Velocity Through Valve
To continue this analysis, the next step was to compare pump speed with valve velocity, as tabulated in Table 8.4. lt is evident that for equal valve velocity, greater TCP is required for higher speeds.
TABLE 8.2. Valve Combination Numbers
Valve Type Double-port, plate, metal
Comb. No.
Through Area, in2
1 2 3 3-1 4 5
2
6 7 8 9 10
2
Weight, oz
Spring Load, POSIVA
13.5
2 4
6.8
2 4
11 Double-port, plate, Delrin
12
2
3
2
13
14 15 16 17 18 Single-pon, plate, Delrin
Wing-guided
4 7
19 20 21 22 23 25
2
26 27 28 29
3.3
30 31 32 33 34 35
3.3
36 37 38 39 40 41 42 43
3.3
2.75
2 4 6
2.75
2 4
17.3
2 4
8.5
2 4
2
11
2 4
Lift, %
125 100 50 138 100 50 125 100 50 125 100 50 125 100 50 125 100 50 125 125 100 50 125 100 100 125 100 125 100 125 100 50 125 100 50 125 100 50 125 100 50 100 100
TABLE 8.3. Valve Peñormance at Various Speeds with 3-in Plungersª
80% VE
75% VE
N
UI
co
TCP
90% VE
85% VE
95% VE
Valve
Valve
Valve
Valve
Valve
Comb No.
Comb No.
Comb No.
TCP
Comb No.
TCP
Comb No.
12.3 13.8 14.9 15.8 16.9 18.3
28 29 22 15 23 18
14.0 17.1 17.5 19.2 19.7 20.5
28 22 29 15 23 18
TCP
TCP
250RPM
9.8 10.4 10.9 11.5 11.8 13.8
28 22 29 15 23 18
10.5 11.5 11.7 12.4 13.1 15.0
28 29 22 15 23 18
11.3 12.4 13.1 13.8 14.9 16.5
28 29 22 15 23 18
350RPM
15.1 16.1 17.8 18.6 19.0 X
28 29 22 15 18 23
16.2 17.2 19.7 20.0 20.5 21.7
28 29 22 15 18 23
17.7 19.4 22.7 22.7 23.3 24.9
28 29 22 15 18 23
20.5 22.5 28.3 28.1 28.8 X
28 29 22 15 18 23
25.5 28.0
29 15 18 23 22 28
83 89
X X X X
28 29 22 15 18 23
625RPM
35 47 49 ?
54 ?
29 15 22 18 23 28
39 50 55 55 60 ?
29 15 22 18 23 28
45 50 55 60
65 67
29 28 15 18 22 23
58 64
68 80 82 95
X X X X
18 15 23 22 28 29
8.6
259
THE EFFECT OF VALVE DESIGN ON SUCTION REQUIREMENTS
TABLE 8.4. TCP as Function of Velocity, Velocity Obtained by Plunger Size, Speed, and Valve Through Area
Velocity, FPS
Plunger Diameter, in
Valve Through Area, in2
RPM
TCP at 85% VE
7.3 8.3 16.0 14.7 20.6 21.4
1~ 2! 3 3 3 3
3.3 2 3.3 2 2 3.3
625 250 450 250 350 625
21.0 9.1 29.0 13.1 28.3 95.0
TABLE 8.5 Effect of Through Area on TCP with Valves of Same Type. Through Area lncreased 65% (TCP at 350 RPM, 3-in Plungers, 90% VE)
Valve Type Wing-guided Single-port, plate
TCP with Valves of:
Spring Load, lb
Lift, %
2 in2
2 2 4 2 4
100 100 100 125 125
26.0 30.0 31.0 30.8 28.3
3.3 in2 20.2 25.0 22.5 22.8 20.5 Average
Percent lmprovement 22% 17% 27% 26% 28% 24%
Rather than a direct relationship between velocity and speed, it can be seen that speed has a greater effect than valve velocity. It should be noted that these data are based on a 6-in-stroke triplex plunger pump, where various velocities through the valve were obtained by varying either plunger size or valve through area.
8.6.5
Valve Through Area
As previously stated, val ve through area heretofore has been considered one of the most important features of a pump valve. It is a generally held belief among pump users as well as manufacturers that the greater the through area the lower the TCP required. The tabulated data show that this is not necessarily true, because larger valve through areas necessitate larger, heavier, and stronger valves. This, in turn, may increase TCP requirements if carried to the extreme. Table 8.5 Iists the effect of increase in valve through area on TCP requirements. An increase of 65 % in through area results in an improvement of only 24 % in TCP requirement for all types and combinations of valves. It is rather obvious that the increase is beneficia! but that it will have to be weighed with other factors to be discussed later, such as weight.
260
VALVES
TABLE IUi Effect of Lift on TCP with Valves of Same Type (TCP at 350 RPM, 3-in Plungers, 85"/o VE)
Valve Type
Through Area, in2
Spring -Load, lb
3.3 3.3
2 2 2 4
Wing-guided Síngle-port, plate Double-portª Single-port, plateb
2
3.3
TCP at Lift of:
50%
100%
125%
30.0
30.0 19.2
19.0
21.0 45.0
20.8 50.0
29.0
17 .8
ªAt 80% VE (could not obtain 85% VE with 50% lift). bAt625 RPM.
TABLE 8.7. Effect of Valve Weight on TCP with Same Type of Vaive (NPSH at 85"/o VE)
RPM
Weight, oz
350 350
17.3 8.5
19.6
100
350
13.5
100 100 100
6.8
68
350 350 350 625
3.0 12.2
27.8 24.0 29.5 23.6 55.0
125
625
2.8
50.0
Through Area, in2
Spring Load, lb
Lift, %
Wingguided
3.3 3.3
2 2
125
Doubleport
2 2 2 2 3.3
2 2 2 2 5
3.3
4
Valve Type
Wingguided Single-port
125
6.8
TCP 17.8
8.6.6 Required Valve lift The question of required valve lift has been mentioned in the literature, and an old rule of thumb was to provide lift sufficient to equal at least 50% of the through area. A bevel-seal valve (wing-guided) naturally requires a greater lift than a platetype valve in order to provide equal "escape" area. The evidence shown in Table 8.6 indicates that 50% lift is undesirable even at slow speed and cannot be tolerated at high speed. ("Slow speed" in this case is 250 RPM.) The effect of excessive lift on valve life was not evaluated. While the tests indicate that unlimited lift is desirable for best pump performance, it is known that this would result in shorter valve life due to the greater impact on closing. The tests show that for all operating conditions a lift of l 00 % is satisfactory.
8.6. 7
The Effect of Valve Weight
Valve weight, surprisíngly, has little to do with TCP requirements, even at high speed. Table 8.7 shows that at 625 RPM a 12.2-oz valve required 23 PSI TCP
8.6
THE EFFECT OF VALVE DESIGN ON SUCTION REQUIREMENTS
261
while a 2.75-oz valve required 21 PSI TCP, a loss of only 10% in TCP for a gain of 350% in weight ..
Va/ve Lift Formulas
(8.23)
Q for pow_er pumps Q for simplex steam pumps Q for duplex steam pumps
L for bevel-face values
=
total GPM
X ?!" /
nn 1
(8.24)
= total GPM/0.75n
(8.25)
= total GPM / n
(8.26)
=
(F;
+ W - 0.3Fu/k)
{JM[l + (2M/IOO)] + 1 - 1) L for disc-type valves = '(F;
+
(8.27)
W - l.3Fu/k)
· ( v'M[l + (2M/IOO)] + 1 - 1) (8.28). where M for wing valves
= kQ../S/40.5(F; +
W - 0.3Fu) 312
(8.29)
M for disc valves
= kQ..fS/58.5(F; +
W - 1.3Fu) 3 12
(8.30)
.1Pforwingvalves .1Pfordiscvalves
2
= S[Q/72(D - L)L] 2 = S[Q/lOl(D - 2.4L)L]
( 8.31) (8.32)
Nomenclature:
= valve through area, in2 D = diameter of seat opening, in F; = installed spring load, lb L = Iift of valve, in (at maximum flow) .1P = pressure loss through valve, PSI Q = maximum flow rate, U.S. GPM Av
k
= spring rate, lb/in
= specific gravity of Iiquid W = weight of valve, lb n = number of single-acting plungers or total number of working sides of a double-acting piston (for triplex single-acting, n = 3) S
n 1 = number of valves per section (normally 1) Fu = upward force on valve in deflecting flow, lb
262
VALVES
TABLE 8.8 Effect of Spring Load on TCP with Same Type of Valve (TCPA at 90%)
TCP at Spring Load of:
Valve Type
Through Area, in2
2 lb
4 lb
Lift, %
Weight, oz
Wing-guided Double-port
3.3 2
25.5 28.3
29.4 28.1
100 125
17.3 3.0
Conversion of Flow Rates
8.6.8
= 2GPM10131 /
n
(8.33)
GPMmax = ?rGPM1018i/ n
(8.34)
GPMave
Effect of Spring Load
In general, the spring load can be added to the TCP requirement; in other words, the heavier the spring load, the greater the TCP requirement. Previous tests indicated that a general rule for spring load would be 2, 4, a,nd 8 PSI (POSIV A) of valve through area: the 2 POSIVA for low-speed, low-suction heads; the 4 POSIVA for "good" suction conditions and high speed; and the 8 POSIVA for high suction pressure (charged suction) and high speed. See Table 8.8. These tests indicate that the need for a 2 POSIVA spring is doubtful, except on marginal, low-speed applications where an absolute mínimum TCP is required. However, there is something subtle about valve spring selection that is not brought out in these tests. In many cases of "noisy" pumps, particularly those operating in multiple units with a common suction header, a trial of different spring loads will often produce a satisfactory spring that does not necessarily conform to laboratory findings as determined on a single pump.
8.6.9
Summary
To summarize, these tests show that: 1. Pump speed has the greatest effect on valve performance. 2. Velocities through the valve of up to 35 FPS can be used if sufficient TCP is provided.
8.7
DERIVATION OF VALVE VELOCITY
263
3. Improvement in TCP requirement is not proportional to the increase in valve through area; therefore, a compromise through area must be adopted based on operating pressure. 4. Valve lift should be sufficient to provide a circumferential Iift area to the through area of the valve. 5. Valve spring load is still subject to question, but for general operation a load of at least 4 POSIV A is desirable. 6. Valve weight has only a slight effect on valve performance. Generally, it should not be a factor in valve design, except as it affects impact on closing and opening and contributes to rapid wear.
8. 7
DERIVATION OF VAL VE VELOCITY
Valve velocity in a reciprocating pump is liquid velocity through the individual pump valves and is based on the average pump ftow rate during that half-cycle of a revolution for which the valve should be open.
Discharge
Suction
Hall revolution
One revolution
= 2 ( for half rev) *
V
x 231 in 3/gal x GPM 60 s/min X ] 2 in/ft X nAv
~~~~~~~~~~~~~~~~
v or Vv
= 0.642
X
GPM/nAv
(8.35)
where Vv A,, n
= liquid velocity through valve, ft/s = valve area, in2 = number of discharge valves active during a revolution. for triplex single-acting pump, n = 3
For example,
*Beware of formulas that use the entire revolution for the calculation, resulting in an unrealistic velocity of half of the velocity obtained by the formula.
264
VALVES
1~~~~~D2~~~~ 1
1 1
'
1
r----D1----l 1
1
1
(a)
(b) ¡..,;-~~-D2-~~-.,.¡
(d)
Figure 8.8. Unbalanced valve area.
Experience indicates that valve velocity should be limited to about 16 FPS for dean liquid and about 12 FPS for slurries. Note: AH GPM and gallons are in U.S. gallons, where 1 gal = 231 in 3 .
8.8
UNBALANCED VAL VE AREA
For many years a theory has been held that a liquid valve in a reciprocating pump has an "unbalanced area" that results in requiring a much greater pressure in the cylinder to open the valve, which is held closed by the discharge pressure above it, creating a "high" pressure at the start of the stroke. For example, with a practical valve (Fig. 8.8(a)) the area at D 2 could be two times that at D 1 • In a 2000PSI pump, this could amount to a 4000-PSI opening pressure. Magnitudes as high as seven times the discharge pressure have been reported. However, an excess of about 10% overpressure in a pump cylinder that is operating normally has never been seen. In order to investigate the unbalanced val ve area theory, a "visible" valve chamber was constructed to observe and measure valve action. Among other findings it was discovered that a valve made with a large amount of unbalanced area showed little, if any, difference in pressure required to open the valve in excess of the pressure holding the valve shut. The theory of "unbalanced valve area" is convincing, but if practical cases are examined.it will be seen that it does not apply. For instance, considera plate- or disc-type valve (Fig. 8.8(a)). Any material has a modulus of elasticity, which means that it will defiect under load. In this case, the disc defiects so that the seal
8.9
POWER-OPERATED VALVES
265
is a "line contact" at point A (Fig. 8.8(b)). The so-called unbalanced area at Bis actually balanced by hydraulic communication to the discharge pressure, even though the communication path is extremely small. The same deflection takes place a bevel wing-guided and with any type of valve, as shown in Figure the same explanation applies. A val ve with an elastomeric seal is sometimes accused of having a large ''unbalanced area'' because the outside diameter of the seal is used to calculate the "topside" area versus the diameter of the seat, usually resulting in a excessively large difference. Figure 8.8(d) shows that here too there is line contact. The elastomer itself is a high-viscosity fluid, and it transmlts the pressure to the usual point of seal at B. If point A did seal (if there were rí.o solids in the liquid), the entire unbalanced area to point A would become balanced and the trapped liquid from B to A would become
8.9
POWERmOPERATED VALVES
It is possible that the use of reciprocating pumps for handling "coarse" coal or other soft materials will require the use of positively driven or power-operated liquid-end valves in order to actually crnsh the that become trapped between the valve and seat upon closure. There are three basic methods of driving the valves: (1) mechanical, pneumatic, and hydraulic.
Mechanical. The intemal combustion engine type of cam-dliven valves could be considered, allowing cam opening and spring closure. This would limit the closing force to the spring load. But would the fixed spring load always be sufficient to crush the particle? "Heavy" springs would tend to increase cam and tappet wear and would affect mechanical Positive mechanical closure would be ruled out because of possible damage from metal or hard objects caught in the valve. Cam operation also dictates the type of valve motion available. Hydraulic. Hydraulically operated valves (power cylinder) would possess a computer-controlled advantage of any desirable and closely controlled valve motionº The crushing force required for for example (and limited by supply pressure), would build upas necessary. Pneumatic. Pneumatically operated valves might be considered because of their "softness." They have the same force as the hydraulic but have the desirable feature of opening and closing more rapidly. Both pneumatic and hydraulic valves are less complicated and less costly than mechanically operated valves. However, the complexity and delay of valve action associated with any of these methods of operation may introduce insum1ountable problems.
266
VALVES
8.10
VALVES IN SERIES
Sorne reciprocating pumps employ multiple suction and discharge valves in series (one or more above the other), and sometimes hydraulic systems are designed with two or more spring-loaded check valves in series, always in an attempt to obtaín maximum assurance of preventing back-flow. Statistically, the degree of assurance is in direct proportion to the number of valves. However, in both applications the magnitude of the pressure required to open all the valves is equal to the sum of the POSIV As (spring pounds per square inch of valve area) of each of the valves. This should be realized in any discussion of TCP, since the total valve opening pressure (POS IVA) is directly related to TCP.
8.11
VALVES IN PARAllEl
Sorne years ago several pumps appeared on the market whose design took the desire for low valve liquid velocity to the extreme by using double, side-by-side (in parallel) suction and discharge valves in the liquid end on the theory that flow velocity is a val ve' s worst enemy. Elsewhere in this book it is explained that the worst moment in a valve's life is that at the instant of closure. High velocity does result in a greater pressure drop through the valve, adding slightly to the TCP requirement but not nearly as much •as the relatively heavy valve spring POSIVA required for efficient pump operation. Experience has shown that valves in parallel do not perform as one would expect-they do not open simultaneously and equally as required. Manufacturing tolerances, particularly in valve springs, do not offer the precision necessary to obtain exactly equal installed loads. The valve with the least POSIVA will open first, and once it is opened a pressure equilibrium will be established which destroys any opening differential for the second valve (until by possible opening at maximum flow rate later in the stroke). Single-valve opening is especially apparent in such pumps being operated, as is usual, ata slower speed or with smaller pistan diameter than the design maximum. Therefore, it is generally noted in such pumps that one valve of the pair always shows more wear. It has been found that largecapacity pumps perform well with seemingly large single valves scaled up in size to suit the pump.
8.12
VAL VE FLUTTER
Free-falling valves (usually with the absence of springs or little or no installed spring load), both ball and disc types, have a tendency to flutter at the moment of closure, which contributes to lower volumetric efficiency and noise. Such flutter is a sort of planetary oscillation best described as similar to the motion resulting from dropping a coin flat on a hard surface: usually it will roll in an oscillatory motion until it comes to rest, whereas at other times it will "plunk" to rest im-
8.13
STEADY-STATE FLOW THROUGH VALVES
2o7
mediately. This motion in a val ve is set in operation when the free-falli.ng ball strikes an edge of its seat in a slightly off-center position or when the disc strikes the flat seat in a slightly camed position. Many times when ball valves are used without springs, the reason is to allow the ball to seat in an infinite number of positions in order to distribute wear over the entire surface of the balL Even though in sorne cases it may appear advantageous to have a val ve ''rotate'' in order to distribute wear, experience has shown that normal spring loads will not allow the ball or disc to rotate, in spite of attempts to force them to do so by means of skewed ribs or roller-bearing spring seats. Subsurface or bottom-hole pumps used in pumping crude oil wells employ freefalling ball valves, and it is quite common to hear the noíse of flutter at the of the well. Sorne proponents of light installed-valve-spring load on disc valves often go so far as to provide zero load, which would not only invite valve fl.utter but, more important, would also fail to provide the high spring load on closing required to reduce the delay as much as possible. Conventional vertical pumps with a horizontal valve axis cannot accept springless val ves because of lack of any closing force from gravity. Such pumps must be equipped with 90º suction and discharge elbows, with the springless verticalaxis valves at the manifold ends of the elbows. This design greatly increases the volumetric clearance and consequently contributes to lower volumetric e:fficiency and possibly greater noise. There is no known method of preventing such valve flutter, and if pumps must be run without valve springs, they should be operated at reduced speeds.
8.13
STEADY-STATE FLOW THROUGH VALVES
Steady-state flow of liquid through a valve does not duplicate the dynamics of the varying nature of fiow in a reciprocating pump. However, an experiment with steady-state fiow in a test setup, whereby a "free" disc-type valve was installed in a chamber with pressure taps above and below the valve, led to sorne interesting results. Figure 8.9 shows that without the disc, the pressure drop through the openings (1-, 2-, and 3-in2 seats) followed the expected orifice laws of flow with low pressure drops. However, with a "free" disc placed on top ofthe seat, sorne surprising results were noted. First, the Bemoulli effect that restricts the free lift of valves (where the high velocity of flow under the disc generates a low pressure that tends to force the disc against the valve) was well demonstrated. It is obvious that the Bemoulli efl:ect is greatly exaggerated when the area of the disc is large compared to the seat opening area. A critica! point was discovered with the two square inch area seat; at a particular fl.ow rate, a change of equilibrium took place and a constant-pressure flow condition was established. One should find this chart of extreme interest.
268
VALVES
Loose !itting pin to keep 0
disc in place over seat. No
1 in 2 with disc
Delrin disc
3"Dia.
contact with pin during te.st.
~
~ 301-.~~-l-~--iJ-1..~~~+-~4---f-~~-¡
2 3 in with disc encouraged to hug seat by temporarily _._ _......¡_ _ _ lorcing against seat
~
¡;¡
~ 201--~~-l----,!~-l-~~-!-~--'\.-l\---~---; ~
'
o
10
20
30
40 50 Flow rate, GPM
3 in 2 seat only
\
60
and with disc 2 in 2 only
70
80
Figure 8.9. Steady-state flow through valve.
8.14
VALVE DELAY
The term valve delay specifically refers to the finite time delay encountered from that instant of the mechanical end of the delivery stroke until the actual full closure of the discharge valve. Just prior to full closure, the liquid trapped between the val ve and the seat must have work done on it to displace part of it into the discharge manifold space and part back into the cylinder. This will involve an infinitely small time period but the ratio of that time to the stroke time becomes significant at higher pump speed. Viscous liquids and the presence of solid or semi-solid particles hinder rapid valve closure. An addition to this delay is another contributed by the high pressure liquid remaining in the space between the discharge and suction valve (Clearance Volume) that requires sorne "useless" movement of the piston in order to reduce the pressure of the trapped liquid to a value somewhat below the suction pressure before the suction valve can open. Delay as discussed exists in all reciprocating pumps and it is impossible to predict the degree. Delay does contribute to lower volumetric efficiency and noise and it can be determined after the fact from pressure waveforms as described in Chapter 12, Instrumentation. A signal picked up from any moving part ofthe pump by the use of a proximity switch can serve as a marker for the absolute end-of-
8.14
VALVE DELAY
269
stroke on a dual-trace A simultaneous trace of the cylinder pressure will enable one to determine the degree of delay. Valve delay can be minimized by the use of valve springs with a greater on the shape of the pressure POSIVA. See figure 8. IO for the effect of valve waveform. For further discussion of Valve Delay, see Chapter 3, SUCTION REQUIREMENTS. NOTE
In the preceeding Chapter 8 the !erms NPSH or NPIP have heen changcd to the new terminology, "TCP."
9 SLURRY PUMPING
9.1
SLURRY PROPERTIES
A slurry is a mixture of solid particles in water or other liquid, the mixture being of such a consistency that it can be pumped like a liquid. The most ancient slurry pumping system in existence is the animal blood-circulating system, where a positive displacement pump (the heart) circulates a slurry of particles (blood corpuscles) in a liquid (the serum) through a complex pipeline (the viens). The rules for fiow of slurries differ from the Darcy notion of "clean" liquids because the rheology differs. In all fiow problems the viscosity of the liquid has a greater effect than any other property. However, while most liquids behave like water or oil, with the viscosity-fiow relation being Newtonian, slurries represent a new phase, Bingham plastic, where the relation of shear stress to shear rate takes on new meaning due to the Fanning friction factor f, the ratio of frictional forces to inertial forces:
f =
144Dg i1.P /2pLV2
(9.1)
Figure 9. 1 shows the various types of fiow behavior (shear rate vs. shear stress) encountered in slurry service. Each type has its own friction factors. lt is beyond the scope of this book to describe the technology involved in slurry pumping. For those interested in the subject a good reference is Solid-Liquid Flow, by Wasp, Kenny, and Gandhi. *
*E. J. Wasp, J. P. Kenny, and R. L. Gandhi, "Solid-Liquid Flow, Slurry Pipeline Transportation," Trans Tech Publications, Clausthal, Germany, 1977. 270
9.2
PUMPS FOR SLURRY SERVICE
271
Rate ol shear
Figure 9.L Viscosity, shear rate vs. shear stress. A, Bingham plastic; B, yield pseudoplastic; C, dilatant; D, Newtonian; E, pseudoplastic.
9.2 9.2.1
PUMPS FOR SLURRV SERVICE lntroduction
The abrasivity of a slurry is mainly a function of the hardness and shape (sharpness) of the particles. However, there are several modes of abrasivity, one of which is the action on metal or elastomer caused by erosion resulting from velocity of fl.ow and another the reaction of the metal or elastomer caused by mechanical abrasion. In the first instance, particle size and density are additional characteristics that must be considered. In the second case, density probability has no effect on wear rate. Mechanical abrasion as opposed to erosion is unpredictable, and few data have been heretofore available. It stands to reason that there is sorne general relation between the wear generated by both modes and others. Considerable work has been done in this area, and as a result a standard method of measurement of abrasivity of slurries has been developed; this is ASTM Standard G75.82, known as the Miller number (see Section 9.7). The movement of liquids in pipelines requires the use of pumps. Those who have had experience with the petroleum industry, where the movement of slurries is an everyday matter, are familiar with the transport of solids with mud pumps and cementing and fracturing pumps. Over the years, mud pumps have been improved so that rather long life can be obtained from liquid-end parts subject to the effects of abrasive liquids. Reciprocating-type slurry pumps are one result.
272
SLURRY PUMPING
Centrifugal pumps have also been used to transport solids, but they have been used where low heads are required, typically up to 100 PSI or so, for short pipelines. R~aders may recall that a centrifugal pump is a hydrokinetic device where the velocity of a liquid stream is converted to pressure, and to achieve high pressures a large change in velocity is necessary. Abrasive liquids have a deteriorating effect on the impellers and casings through which they flow, as a result of the erosion caused by the liquid and the suspended particles. Therefore, these pumps can be used only where the intemal velociry of flow i.s relatively low. · Traditionally, the advantage of centrifuga! pumps is that they have a high capacity for a relatively low capital cost and usually require relatively little space. One of their disadvantages when they are used in sluny pipelining can be seen in the typical pressure-volume performance relationship, which tends to work against the application (Fig. 9.2). If an increase in pressure (head) is occasioned by flow restriction in the pipeline, say by the dropping out of solids, a desirable characteristic of a sluny pump would be an ability to develop increased pressure to overcome the restriction. The centrifugal pump provides the increased pressure only at the expense of considerably reduced volume, which then results in a lower flow velocity. With the reduced flow rate, the velocity might not be adequate to hold the material in suspension and keep it fiowing in the line. On the other hand, reciprocating pumps maintain a constant flow rate regardless of pressure, thereby tending to "purge" any plugging effect. Electrical power must be transmitted to each pumping station of a long sluny pipeline systern, such stations at most times being many miles from the main transmission lines, and this adds to the already rather high cost of power. Any savings resulting from the more efficient conversion of energy during the life of the project
Performance limit íor abrasive service
AH
Capacity, U.S. GPM
Figure 9.2. Centrifugal pump characteristics.
9.2
PUMPS FOR SLURRY SERVICE
273
is desirable, and the greater mechanical efficiency of reciprocating pumps, on the order of 85 to 90%, should certainly be considered in the design of such projects. Reciprocating pumps have the desirable characteristic of maintaining a high volumetric efficiency at any desired flow rate. This allows greater flexibility in system design. Becuase of the positive displacement and high-efficiency features, these pumps can be used for metering station throughput. Reciprocating slurry pumps are so designed that liquid-end parts that are subject to the deteriorating effects of slurries can be easily and quickly replaced. Other pump designs usually require complete dismantling and overhaul. Figures 1.1 and 1. 7 in Chapter 1 show a typical duplex double-acting piston pump and single-acting plunger pump, respectively. Because of their inherently larger capacity at lower speeds, duplex double-acting piston pumps may appear to be a "natural" for ali abrasive pumping applications. When high pressures are considered (above 2000-3000 PSI), sorne are quick to point out that such pumps have been used for years in the oil-well drilling industry for pressures up to 4000 PSI or more, so why not apply them in abrasive slurry service?
A. Practically all pumps in the higher horsepower range sold to the drilling industry in recent years have been of the triplex single-acting type, regardless of anticipated pressure. B. Triplex (plunger) pumps were considered for drilling service because: 1. They have an inherently a high pressure pump. 2. They are light in weight per horsepower (important in a transportable rig of any type). 3. A flushed stuffing box can prolong parts life. C. When single-acting pumps were introduced to the drilling industry, they were of the plunger type. Sorne attempts were made to flush the stuffing box, but it was found impractical because (1) dilution of drilling mud is usually undesirable, and (2) there is no source of clean flushing water on a drilling rig. (So point 3 above is no longer valid, and all pumps now use pistons.) D. Drilling mud per se is not an abrasive liquid in the sense of present-day slurry concepts. Typical drilling mud has an abrasivity of about Miller number 10. (The reputation of drilling mud for being "abrasive" comes from the fact that it picks up sand from the drilled formation.) It is ironic that the drilling industry goes to great pains to reduce the sand content of the drilling mud to less than 2 % in order to obtain greater pump parts life while in the slurry pipeline industry the battle to increase the percentage of solids to the ideal 99.9% goes on. E. It is improper to directly compare drilling mud pumping to the pumping of most slurries. Many muds contain oil and special chemicals that are corrosive and detrimental to elastomers. Muds run at relatively high temperature, 130ºF being common. Chemistry, corrosion, high temperature, and high pressure combine to overshadow abrasivity.
274
9.2.2
SLURRY PUMPING
Packing
A discussion of plunger pump packing must be preceded by an explanation of why plunger purnps are sometimes used for abrasive slurry service and how they differ from piston-type pumps, particularly in the matter of stuffing boxes and packing. With the common duplex double-acting piston pump, typical design requires an increase in piston rod strength, in both tension and compression, in sorne proportion to the increase in pump discharge pressure. Therefore, a point is reached where the piston rod diameter theoretically becomes so large that the pump, in effect, approaches a single-acting duplex, the discharge characteristics of which are extremely "rough." Accordingly, single-acting pump design dictates three, five, or more cylinders, and multiplex single-acting pumps inherently have smoother discharge characteristics, even over a small-piston-rod duplex doubleacting pump. Of extreme importance is the often overlooked fact that the packing action of an outside packed plunger pump is completely opposite to that of any piston type, including a multiplex single-acting pistan pump. In a plunger pump (Fig. 9.3), the plunger, during the pressure stroke, is traveling to the right out of the pressure-loaded packing into the liquid, and during the suction stroke the plunger is traveling to the left out of the dirty liquid into the relaxed packing. Conversely, in a piston-type pump (Fig. 9 .4) (with both the piston and the piston rod packing), on the pressure stroke the piston is traveling to the left into the pressure, and on the suction stroke it is traveling to the light away from the liquid. With the piston rod packing, the same action is seen: on the pressure stroke the rod is traveling into the packing, which is loaded by hydraulic pressure.
;t
Lubrication
~
"' " "' s pressure
Plunger travel
Figure 9.3. Single-acting plunger pump on pressure stroke-packing action. Note that travel-of-plunger drag is counteracting tendency for pressure to extrude packing into clearance (clearance exaggerated).
9.2
Lubrication
PUMPS FOR SLURRY SERVlCE
~:Frj
275
Piston~
Hyd-ra-u,.,-lic----, pressure ~
\
1
1
Heei (extruded)
/
Heei (extruded)
Figure 9.4. Double-acting piston type pump on pressure stroke-packing action. Note travel of piston and rod drag are reinforcing tendency for pressure to extrude packing into clearance.
The purpose of packing is simmply to close up the clearance gap between the moving plunger and its associated parts, particularly the gland bushing, in the stuffing box or the piston and its cylinder, and the piston rod and its stuffing box parts. With ordinary packing this is accomplished by the use of material with considerable resiliency. The mechanics of all packing are such that regardless of the general shape of the sealing member, the hydraulic pressure tends to force the member through the clearance gap. Accordingly, practically all of the sealing and subsequent wear or extrusion take place at the "heel" (Figs. 9. 3 and 9 .4). It can be seen that the action in a plunger pump (Fig. 9.3) is such that on the pressure stroke the heel is being "dragged" away from the clearance gap, thereby greatly overcoming the force produced by the hydraulic pressure that causes extrusion through the clearance gap, a benefit in high-pressure service. With the piston-rod packing (Fig. 9.4), the heel is being dragged into the clearance gap by both the motion and the hydraulic pressure, accelerating wear of the packing. Lubrication of pacldng is extremely important in high-pressure service. It can be seen that only with the plunger pump can a lubricant be applied to the plunger as it is entering the hydraulically loaded packing, when it is most needed. This is another benefit in high-pressure service. Any attempt to lubricate a piston or piston rod is not as effective, since the lubricated moving parts enter the packing only on the unloaded or suction stroke when lubrication is not required. Of extreme importance, because of the opposite packing mechanics, a plunger pump in itself is not as satisfactory as a piston-type pump for pumping abrasive material. Because the packing is relaxed on the suction stroke of a plunger pump, the "dirty" plunger can readily load up the packing with abrasive particles and subsequently act as an efficient lapping tool. But this objection can be overcome by fiushing the packing internally with clean liquid-even to the extent that a
276
SLURRY PUMPING
plunger pump is more desirable for pumping abrasives if the dilution from ftushing can be tolerated.
9.2.3
Plunger Flushing Methods
There are two fundamentally different methods of ftushing packing for slurry service: synchronized and nonsynchronized ftushing. Synchronized flushing is the positive injection of an exact volume of clean ftush Iiquid, preferably during the suction stroke of the main pump plunger. This is accomplished by directly coupling a reciprocating pump with individual cylinders to the main pump crankshaft (Fig. 9.5). Nonsynchronized flushing is the continuous injection of a certain amount of clean ftushing liquid by an independently driven reciprocating pump (Fig. 9.6).
Main pump
Flush pump directly driven by main pump
Figure 9.5. Synchronlzed flushing, typical hookup.
Main pump
-Btt
~-~11
11
Manifold
Flush pump separately driven
Gas-bladder dampener (Accumulator)
Figure 9.6. Nonsynchronized flushing, typical hookup.
9.2
PUMPS FOR SLURRY SERVICE
2n
TABLE 9.1 Flushing Methods for Slurry Pumps Method
Synchronizedª Nonsynchronized High-pressureª Low-pressureb Orifice used Check valve used Flush on suction stroke Flush on discharge stroke
A
B
e
D
E
X
X
X
X
X
X
X
X
F
G
H
X X
X
X
X
X
X X
X
X
X
X X
X
X
X X
X
X X X
X X
X X
X X
X
ªVariations in timing-Usually timed to ful! suction or discharge stroke of main pump.
There are several versions of both of these methods as shown in Table 9. 1. Of these, the most popular are A and H. Method A has been most popular in the past, but experience has shown that it has many shortcomings. Inadequate flushing fluid is injected at the end of each plunger stroke due to the sinusoidal shape of the ftow pattem of a reciprocating pump. See Figure 9.7. At the present state of the art, it is evident that method high-pressure nonsynchronized, is the most practical and efficient if properly designed flushing bushings are used and if a sufficient supply pressure is available to produce the presently acceptable mínimum of 3 % of main pump displacement. In any method, the cleanliness of the fl.ushing liquid is paramount. A pressure of about 500 PSI is required to provide a ftow of 3 % through the ftush system of a triplex pump. Accordingly, in H, a pressure of 500 PSI above the main pump operating pressure would be required. The advantages of method H are: 1. With continuous flushing the chance of any lack of fl.ushing due to phasing is minimized. There is assurance that positive flushing is always achieved well befare the start and well after the end of the main pump plunger suction stroke.
2. Sorne flushing during the pressure stroke is desirable to compensate for any slight packing leakage which, if not flushed, would allow slurry to enter the packing space. 3. It allows prestart and post-stop flushing for sorne time before and after the main pump is started and stopped. This provides added assurance that abrasives are well fl.ushed out of the packing space before the plunger makes a stroke. 4. A single standard flush pump can be used to flush one or several main pumps. 5. A change in flushing rate can be more readily implemented by a simple change of flush pump speed.
278
SLURRY PUMPING
Main pump suction
--
Flush flow rate
----.1..... ----~
Flush pump discharge stroke
r----
¡----------- -t / 1
Flush pressure 2500 PSI
' 1
Main pump valve lag
3GPM
l'tttt'b'~wt--1'\l~"""'H+
1
Figure 9. 7. Flushing analysis. (a) Synchronized flushing on suction stroke of main pump. Flush pressure is not important, as flow is positive as shown. Note that at beginning and end of main-pump suction stroke, flush flow rate has diminished to zero. Dueto variations such as valve lag, there could be periods of zero flush during sorne part of the main-pump plunger stroke. (b) Nonsynchronized high-pressure flushing. Admits a constant flow-maximum during the main-pump suction stroke-with overlap at each end and even slight flushing during the discharge stroke. There can be no period of starved flushing.
9.2.4
Flushing Details
A rate of about 3 % of the total main pump displacement is required to guarantee sufficient flushing. The actual requirement should be determined by test, and the rule that ''the more the better'' applies up to a reasonable limit. lt bears repeating that the flushing liquid should be as "clean" as possible.
9.2
PUMPS FOR SLURRY SERVICE
279
The following features are desirable in a fl.ushed slurry stuffing box: l. Spring-loaded main and auxiliary packing.
2. Water-cooled stuffing box. 3. Dimensions such that "wetted" portian af plunger never enters main packing. 4. Clase-fitting stuffing box trim (cast iran or ductile iron preferred). Figure 9. 8 shows the appraximate dimensions and general design af a caal conversion type stuffing box. See Figure 7 .6, Chapter 7, for recommended stuffing box trim clearance for ali applications. Flushing liquid velocity should depend upon the flushing rate and the plungerflush bushing díametric clearance. The following formula can be used to approximate the carrect velacity:
V= 0.4085
X
GPM
percent flush
D2
X
b
_
D2
X
number af cylinders
(9.2)
p
where
Db DP
= stuffing box diameter, in = plunger diameter, in
The "flush" bushing should be of the design shown in Figure 9.9. This design provides uniform fiush by directing the fl.ush liquid to the bottom of the plunger.
--------2.5S------
Tell· tale
Coo!
Flush
-----r-1
.5S
- - - - - + - - - _ .n_I_
.._________,______. . __ _____ l_J 1
,,,, JI
~s
:1
¡.o---------------4.5S-------------____,.,
Figure 9.8. Generalized coa! conversion stuffing box.
280
SLURRY PUMPING
¡ji Y."-;;.j¡11¡...__ 11
11 See Fig, 7 ,26 lor recommended diameters,
,..._____ ,¡, stroke----Figure 9.9. Typical flush bushing for horizontal pumps. R 1 and R 2 offset as shown so as to result in feathering out of grooves at the 90º limits, as indicated at A = A.
9.2.5
Pistons
The piston is so constructed as to have three basic elements, as shown in Chapter
7. Under hydraulic loading, the ''rubber'' is pushed back against the fabric section and out against the liner to form a seal. The fabric section provides extrusion clearance control, and the metal back-up plate or piston body provides the structural capacity to hold the piston load.
9.2.6
liners
The liners are made of abrasion- and corrosion-resistant metals that have been found in extensive service to resist wear for specific slurries. Piston rods and plungers are usually coated with similarly suited materials for the same objectives while retaining base-metal characteristics for the required mechanical loads.
9.2.7
Piston Membrane Pumps
There is increasing interest in pis ton membrane pumps (described in Chapter 1) for the pumping of abrasive slurries, particularly with slurries of abrasivity above Miller number 50. There have been many improvement in engineering concepts, metals, and elastomers, and perhaps sorne of the old ideas may flourish. The membrane pumps deseribed in Chapter 1 are in service in many applications with extreme success. While membrane pumps will protect the pistons, liners, or plungers against
9.2
PUMPS FOR SLURRY SERVICE
281
Leg 1 filling
Clean liquid
Main pump
Leg 2 displacing
Figure 9.10. Switch-loop pumping.
abrasive slurry, no design has ever offered protection for the liquid-end valves of a pump.
9.2.8
Switch-Loop Pumping
Switch-loop pumping is a method of isolating pipeline pumps from the destruction of abrasion, allowing "standard" reciprocating pumps to operate at ali times in an environment of "clean" liquid, thus prolonging the life of parts, including valves. One version of the system is shown in Figure 9 .10. Legs 1 and 2 are reasonable lengths of pipe, either "legs" or "loops," of sufficient volumetric capacity between the directional valves A and C or B and D to allow a decent slurry pumping period of several minutes before switching to the other leg. In operation, Figure 9.10 shows that the slurry previously introduced into leg 2 is being forced into the pipeline with "clean" high-pressure liquid through directional valves B and D. While this event is occurring, leg 1 is being filled with low-pressure slurry, displacing the clean liquid remaining from the last high-pressure cycle through valves A and C. Timing devices can cause the directional valves to operate on a predetermined cycle, and such timing can allow the liquid to continue through the valve for a short interval of time after the slurry passes, permitting the valve to close in clean liquid. The slight amount of slurry dilution caused by this operation could probably be compensated by an original higher concentration of solids. The cost of maintaining at least four large high-pressure, high-cost directional valves must be weighed against the saving in pump parts life.
9.2.9
Other Methods
Aside from the present 50% by weight coal/water slurry pumping with reciprocating pumps directly into the pipeline, other versions are mentioned;
282
SLURRY PUMPING
l. Lock-Hopper. A system similar to the Switch Loop method, alternate hoppers are arranged at the inlet of the pump whereby one hopper is being filled with slurry while the other is being pumped. 2. Capsules. Is a method of sealing water or liquid sensitive materials, (grain for instance) in a plastic capsule and pumping through the pipeline with a water vehicle. 3. For pipelining, there has been a proposal that grain be coated with and protected by sorne material stable in water until time for removal. 4. Sewage of course, can usually be handed by one of the lock-hopper methods. 5. Pneumatic air or gas as the carrying medium has been considered. 6. Liquid C0 2 has been successfully used to transport coal in a pipeline. 7. Proposals have been made to withdraw sorne of the pipeline coal and water to generate steam for station pumping power. 8. Sulphur-oil slurries have been considered. 9. Slack-flow energy recovery methods have been considered. Slack-flow is typical in hilly country where there are substantial down-hill runs to the station or destination. 10. In areas of scarce water supply, double pipelines have been consideredOne to pump slurry and the Qther to return the separated water. l l. Coal "logs"-coal molded into logs and pumped through the pipeline like a pig. High concentration coal (80% by weight) systems are being considered, even to the extent of burning the slurry as received without water separation. There is extreme interest in pumping course coal (run of the mine) but little success has been had. Present high pressure reciprocating pumps will not tolerate large particles. Pumps with power driven valves may be developed for such service.
9.3 HORIZONTAL VS. VERTICAL PUMPS FOR SLURRY SERVICE Any claim that a vertical plunger pump requires less plunger flushing than a horizontal pump is based on the conjecture that gravity aids in keeping solid particles away from the packing. However, only large particles can be kept from the packing by gravity. It is an axiom that large particles do not affect packing and plunger wear as muchas small particles; it is much easier for the packing to exclude large particles than small ones. The smaller particles can be readily carried into the packing, become embedded, and actas a lap on the plunger. The turbulence that exists inside a fluid cylinder of a high-speed plunger pump is so severe that it is impossible to rely on the force of gravity to keep particles from the packing of any typical pump. Unsuccessful attempts have been made to create "permanent" bar-
9.4
SUCTION PRESSURE FOR SLURRY PUMPS
283
riers by the use of grease, oil, etc. Sorne highly specialized pumps successfully maintain an oil barrier between the fluid and the plunger but run at very low speed. It has been stated that plungers or pistons in horizontal units in such service tend to undergo greater wear than in vertical untis. There is no evidence that wear is concentrated on the bottom of any plunger or piston in a propedy designed horizontal pump. (Remember Henry Ford's critics who said the pistons of a Vtype engine would wear out rapidly because they were lying down?) The wear pattem of all plungers is the expected hourglass shape, with uniform wear around pumps the center portion of the plunger, and the typical liner and rod in exhibit the familiar wear at each end of the stroke. The mechanics of packing are such that the effect of piunger weight is trivial. As the hydraulic pressure works on the packing, it forces the resilient members against the plunger for its entire circumference, thereby centering the plunger in the stuffing box with a greater force by far than the opposing force of gravity. It is during that part of the stroke that the plunger is experiencing its greatest rate of wear due to abrasion. The horizontal design has the distinct advantage of having a lower fluid end with a gain of several feet of actual suction head. Sorne think the horizontal design is more accessible for servicing. Because valves should operate in a vertical motion, vertical pumps must be equipped with surge legs or elbows of considerable length to which the valve pots can be attached, thus adding extensively to the volumetric clearance of the pump. Horizontal pumps allow vertical motion of the valves, a mandatory requirement.
9.4
SUCTION PRESSURE FOR SlURRY PUMPS
It is an axiom that slurry pumps must have a "charged" suction, usually provided by the use of a centrifugal pump or by the controlled pipeline pressure at the
downstream stations. Other methods of fumishing high suction pressure can be used. For instance, where conditions will permit, elevated conical-bottom supply tanks have been used with success. One objection to this system is the drastic drop in suction head as the tank liquid leve! is lowered with vv ithdrawaL Slurry-pump suction pressure requirements are affected by the viscosity of the liquid, greater viscosity resulting in greater pressure drop between the source and the pump inlet. The greater density of rnost slurries also affects the losses due to liquid acceleration. These losses, exacerbated by unusually long and tortuous suction systems associated with slurry-pumping installations, demand that such pumps have their suctions charged, usually with centrifugal pumps. (With very high viscosity slurries, such as sorne coal-oil mixtures, it may be necessary to consider limiting the maximum pump speed.) Slurry pumps require heavier than normal (greater POSIV A) valve springs for severa! reasons. A closing val ve cannot take advantage of the applied (discharge) pressure to effect a seal until the valve is almost completely closed against its seat. If the apparent high viscosity of the slurry and the presence of rather large solid particles delay the final valve closure, poor volumetric efficiency and a roughrunning pump are the result. The use of heavier springs helps to overcome these
284
SLURRY PUMPING
deficiencies. Installed valve spring loads as high as 8 POSIVA are used. Of course, the penalty of heavy valve springs is the required higher suction pressure or NPSHR. Single-acting piston-type pumps usually require high suction pressure to allow proper filling of the cylinders on each suction stroke because the piston design is such that a "suction" cannot be created with the "one-way" piston. Efforts to supply a piston seal on the suction stroke by the use of a "double-acting" piston have not been successful because of the early failure of the back-seal owing to lack of lubrication in a partiaily dry liner. (It should be realized that with a doubleacting piston, the seal generated by the pressurized rubber also provides the "suction" required on the back side.) · Rather than the need for calculating or testing for the NPSHR for each slurrypumping application, experience has shown that a suction pressure of at least 50 PSI should be provided, either with an appropriate centrifugal pump or by regulating the upstream pressure on in-line station pumps to that value.
9.5
COAL SLURRIES
Currently, the most widely used liquid phases for coal slunies are water, oil, toluene (or other solvents), and liquid carbon dioxide.
9.5.1
Concentration of Solids
Frequently, the question is asked, ''What is the maximum concentration of coal solids that can be pumped?" Confining the answer to the pump only, a general statement can be made: The rheology of the slurry is dictated by the pipeline requirements, and the pump can usually handle anything that can be transported through a pipeline. In the case of a coal-water slurry, Figure 9 .11, the chart of a typical coal slurry, indicates that the apparent viscosity increases with concentration. In a reciprocating pump, no unusual operating conditions are encountered with viscosities up to 8000 SSU for true Newtonian liquids. It will be seen that in this "coal B" slurry the equivalent value of 8000 SSU was reached at about 70% by weight solids. Note also that at 73% the mixture had no fluidity (was pasty). So again, as far as the pump is concemed and with that particular coal, there is good reason to believe that a concentration of 60% by weight could be readily pumped. Coal-oil slurries are more critical in that they increase in viscosity at a more rapid rate and are highly affected by temperature and the viscosity of the mixing oiL Figure 9.12 shows that for the particular case illustrated, concentrations above 55 % result in very high viscosity. This phenomenon must be taken into account in arriving at a concentration for such slurries. From this, it is evident that the limiting concentration could be determined only by actual test. Coal-toluene mixtures would probably follow coal-water characteristics, but little information is available on this.
8 ::¡ IJ'l IJ'l
§.....
¡;:
6
·¡¡;
o
u
vi ·;;;
.,_,
4
e:
...
Q)
~ c.
<
2
O_!.-~-,,!~~~~~-,,,~~~i,,,.........,,,,~
30
40
50
60
70
-So
Concentration, percent by weight
Figure 9.11. Coal-water slurry viscosity. A, fine coa! ( 80% pass 200 mesh); curve B, coarse coal ( 80 % pass 100 mesh).
8 :::::>
IJ'l VJ
§.....
6
¡5.
·¡¡;
ou
(/)
·:;;
e: 4
f:'.
"'c.a.
<
2
Concentration, percent by weight
Figure 9.12. Coal-oil slurr)1 viscosity. Oil is No. 6 fuel oil. A, 200ºF, B, 160ºF.
285
286
9.5.2
SLURRY PUMPING
Particle Size
Again, there is sorne relation to particle size vs. pipeline requirements, and it can be generally stated from experience to date in actual slurry projects that the pump has not been the limiting factor on particle size. In a reciprocating pump, the particle size only affects the operation ofthe valves. In pumps of larger capacity (larger valves), no trouble is encountered with particles up to 8 mesh. (Fortunately, crushed coal has a good distribution of smaller particles below this maximum size.) Statements appear in the literature that l-in diameter particles of coal have been pumped. These were cases where the percentage of l-in particles was very small, and there is no doubt that the pump will tolerate a few large particles. Types of valves vary in their ability to handle large particles. The elastomeric seal slurry-type valve is far superior for normal coal-water slurries at low temperature. But dueto the wide metal-to-metal and elastomer-to-metal contact surfaces, large particles have more of a tendency to hold the valve open. Such valves have no difficulty in handling coal with 8 mesh maximum particle size. Tests show that particles of coal up to !-in in diameter can be handled with properly designed spherical valves. The high loading of a line bearing contact easily crushes those particles caught between the edges when the valve closes. Particles on each side of the sealing line are readily displaced away from the sealing line by the rapidly diverging shape of the spherical portion of the valve, which minimizes the tendency of large particles to hold the valve open. Spherical valves are also valuable for hot or chemically active liquids and slurries that are detrimental to elastomeric seals. Spherical valves should be considered only in the applications listed above. They lack the advantage of a renewable elastomeric seal. This, combined with the inherently high metal-to-metal bearing loads, results in shorter life than a slurrytype valve. Spherical valves will not tolerate highly abrasive slurries, of a Miller number of above 50. A slight reduction in volumetric efficiency may be expected dueto lack of the more efficient elastomeric seal.
9.5.3
Concentration and Particle Size
In the milling process, coal and other minerals appear to follow a rather consistent pattem of particle size distribution. In other words, a coal reduced to the extent that the largest particles have a dimension smaller than another milled coal will have a larger percentage of "fines." These fines tend to control the apparent viscosity of a water mixture, and a slurry with a large percentage of fines will have a higher viscosity than another slurry of equal concentration of solids by weight but with a smaller percentage of fines. In view of this, it is difficult to predict the pumpability of coal slurries of a given concentration without knowing the approximate apparent viscosity at that concentration.
'V SLURRY EROSION
9.6
287
VALVE SERVICE FOR SLURRY PUMPING
Valve service for slurry pumping is covered in Chapter 8, but this statement serves as a waming that limited valve lift caused by reduced fiow through the valve opening when a lower than rated pump speed (RPM) is maintained may create a restriction to the passage of solid particles. Extended pump operation at signí:ficantly reduced speed may result in an accumulation of solids in the pump cylinder with drastic results.
9.7
9.7.1
SLURRY EROSION
lntroduction
For the purpose of this discussion, a "slurry" is described as a mixture of solid particles in a liquíd (usually water), of such a consistency that it can be pumped like a true liquid. The term "slurry erosion" is strictly defined as that type of wear or loss of mass of material when exposed to a high velocity stream of slurry, whether the material is moving at a certain velocity through the slurry or whether the slurry is moving past the material at a certain velocity. However, one should include other forms of wear encountered in handling slurries-a process seeing increasing interest in industry, especially with the rather new method of transporting minerals, principally coa!, and other solids (even with the possible indusion of grain), for long distances through pipelines at pressure in the order of 2,000 PSI (13,790 kPa). Dry Abrasive Wear, another mode of wear, is mentioned in this discussion but it is a type of wear seldom if ever encountered in slurry handling. The combination of Abrasion-Corrosion of a typical slurry system is responsible for the most severe form of wear and it leads the list of severa! other important modes.
9. 7 .2
Slurry Wear Modes
Sorne of the most common wear modes are listed below and described in Figure 9. IA. Note that a few of these basic modes can be extended into sub-modes, according to whether they are responding to the following motions; reciprocating, oscillating, circular or continuous; oi! or liquids other than water; and ratio of areas of mating parts as shown in Figure 9. lA. Mode A. Abrasion-Corrosion wear is the result of any metal-to-metal rubbing in the presence of abrasive solids in a liquid. Aside from high-velocity erosion, this is the most destructive and most misunderstood mode encountered in handling slurry. Typical parts of reciprocating pumps involved are; metal-to-metal valves and seats (upon each closure), metal piston parts rubbing on metal liners and plungers, or piston-rods rubbing against metal stuffing box parts or trim. In the case of parts of different metals exposed to the slurry, it is obvious that electro-chemical {electrolysis) effects are included in this mode.
288
SLURRY
PUMPING
--
A
llEAR AREAS ECUAL
e
' 'f
GRIND
'Jb : , ~,'.;D, q> ,...
~
7-~""""'º~ LARGE TUMBLING ROCKS
HIGH VELOCITY ERDSIDN
SALTATIDN ERDSIDN
B2
B3
SCDURING llEAR llEAR AREAS UNECUAL
SCOURING llEAR llEAR AREAS UNEQUAL
G
PIPE \IALL ~
V
"~~'
1
E
CRUSHING
PIPE 11~
t. --
ABRASIDN-CORRDSIDN
Bl
F
D
LO\/ VELOCITY ERDSIDN
~ ':"o "::.-/o:c:_;é)_":_. / -c:aLLArsrn'u VAPOR
BUBBLES. CAVITATION
Figure 9.lA. Slurry Erosion Wear Modes
Mode B. Scouring Wear is encountered with elastomer-to-metal rubbing with abrasive so lid particles becoming embedded in the softer elastomer or rubber, Le. pistons, packing and valve inserts. Mode C. Crushing and Grinding in abrasive metal-to-metal contact. For example, a valve repeatedly closing with great force against solid particles trapped between the valve and seat at closure. Mode D. High-velocity Erosion, while not a usual mode of wear in reciprocating pumps handling slurry, it can become a very destructive one. For example, when a valve seat or piston wears to the extent that a slight leak develops, the extremely high velocity of slurry leakage through that small gap can result in catostrophic and rapid failure of the parts and even the costly liquid-end of the pump. See Figures 2 and 3. Also slurry-throttling valves and parts downstream experience this type of rapid wear. The impellers and cut-water of centrifuga! pumps are subject to this type of wear. "High" velocity is usually considered as that greater than 20-30 ft/s (65100 mis). Mode E, Low-Velocity Erosion is usualiy a low rate wear mode that takes place where there is flow of slurry at regular low velocities. In a pipeline with laminar flow, the velocity profile (in the shape of a parabola) is such that the velocity near the wall of the pipe is nearly zero, and minimum wear takes place. Also the impellers and cut-water of centrifuga! pumps are sometimes subjected to this mode.
9.7
SLURRY EROSION
289
Mode F. Saltation Wear comes about in pipelines handling a great number of larger than usual particle size-actually "chunks"-which tend to tumble along the bottom of the pipe, resulting in rapid wear. An example is the transportation of phosphate rock from slurry-pit to the processing plant. The pipe requires frequent turning to distribute the wear. Mode G. Cavitation can result in damage to the metal in the liquid-end of the pump or to the parts of a reciprocating pump through the microscopic but intense liquid pressure blasts against the metal near the cavitation area following the repeated collapse of the vapor bubbles.
9. 7.3
Effects of Wear
The effect of solids concentration on abrasivity should be recognized. Figure 10.6 shows how the abrasivity increases very rapidly from zero to about 10 percent concentration, then begins to ftatten. lt is an interesting fact that in the oil well drilling industry the well known slurry called "drilling mud" in itself is not abrasive-the abrasivity comes from the solid particles of crushed and broken rock or "cuttings" generated in the drilling process. Contaminated mud is usually "cleaned" by; settling, screening or centrifuging. Curve 10.6 is supported by the fact that the sand content of drilling mud must be reduced to less than 2 percent before effective improvement in pump parts life can be realized.
9. 7.4
Dry Abrasivity
As a result of further work it was decided that ali Miller or SAR Number Tests
would be run in duplication, one with the "as received" material and another with an inhibited slurry obtained by adding a -89-511, William S. Morrison, Richard A Corbett: Corrosion Testing Laboratories, lnc. Wilmingron, DE 19804. Charles F. Jenkind: Westinghouse Savannah River Laboratory, Aiken, SC 29802.
9.10 A METHOD FOR LOCATING A 'PLUG' IN A SLURRY PIPELINE
303
TABLE 9.2A.
SO UDS J. Tale S. Tale CaCo3 Gun Cleaner
MOHS SCALE
¡ 3
Fine coa! Fine coa! Fine coa! Fly ash Pum ice
7
··---RATIO G/M*
U QUID
MILLER NUMBER
GOLD NUMBER
water water water water
I .4 !.6 2.2 4.l
19 i 14 116 394
96
oi! water condensate
5 17 2.6
479 751
44
926
356
water water
28 34
1328 2806
47
!4 71 53
96
83
*Note wide difference in Ratio.
9.10 A METHOD FOR lOCATING A 'PlUG' IN A SLURRY PIPELINE It is almost inevitable that an accumulation of solids wil! sometime occur at a certain point on a long slurry pipeline, such an accumulation turning into a "plug" of such an extent as to cause permanent stoppage of ftow with further pressuring in an attempt to move the plug, resulting in an increase of the tenacity of the plug due to fürther pressure "wringing-out", through the plug's inherent permeability, what little liquid was left in the plug. The following method for precicely locating such a plug is offered; Experience with operation of the pipeline will have revealed the fact that a pressure wave generated at the station by a rather sudden build-up of pressure following a sudden shut-down, will generate a pressure surge or wave that will be reflected back to the station from any change in pipeline impedence resulting from such parameters as an abrupt change in pipe diameter, open end or restriction at the end of the pipeline, sharp-bend elbows, valve c!osure or a solids plug, From observation of this recorded pressure wave on a time basis, the speed of wave travel in that particular slurry would have been established. See Section 4.13, Surge Control in Water Systems. By the use of such wave velocity study, the approximate location of the plug can be determined from the relation L
t/2a
18)
Where; L
ft (m) time, s a - speed of pressure wave, ft/s (mis) Once the approximate location is determined, the exact location of the plug can be determined in the following manner: Select a location in the region of the
304
SLURRY PUMPING
Figure 9.15. Black Mesa pipeline pumps.
plug and, rather than making severa! time-consuming hot-taps for a pressuresensing device, simply apply a quick-cement strain gauge to the pipe or, better still, clamp a special extensiometer (a clamp-band with a strain gauge attached) and cabled up to a battery-operated bridge amplifier and strip-chart recorder. A radio message to the station operator would ask him to generate a pressure buildup by starting a pump. If the strain gauge is located beyond the plug, no pressure rise will be detected-if on the pump side, the pressure rise will naturally be detected. By repeating that procedure the exact location of the plug can be bracketed. A suit-case sized kit, containing the strain gauge equipment or extensiometer, a bridge amplifier and recorder and necessary cables can be assembled or purchased.
9.11
BLACK MESA PIPELINE
The Black Mesa pipeline (Fig. 9 .15), one of the world' s longest and largest coal pipelines, has been in operation for over 12 years. The capacity is about 4.5 million tons per year of solids. Four pump stations on the lineare used to pump the coal-water slurry through an 18-in line from a mine located at Black Mesa in northeastem Arizona for a distance of 275 mi to a power-generating station on the Colorado River west of Kingman. All main pumps are 18-in stroke, double-acting piston-type rated at 1700 BHP. A total of 13 pumps are used. The pumps are assigned to four stations, with three pumps at each of three stations and four at the other. Each pump is driven by an ac induction motor through a variable-speed fluid
9.13 SLURRY TABLES
305
Figure 9.16. Savage River Mines pipeline pumps.
drive anda reduction gear directly coupled to the pinion shaft ofthe pump. Normal operation is 65 RPM, with one pump at each station on standby. Complete automation of the line through microwave radio is used.
9.12
SAVAGE RIVER MINES
The long-distance pumping of heavier materials such as iron ore concentrates is admittedly more difficult than that of coal and similar light materials. However, a 54-mi pipeline was placed in service in Tasmania, Australia, in October 1967, pumping iron ore concentrate, and it has proveo highly successful. This line has a capacity of 2.5 million tons per year. The actual installation is a single pumping station comprising four triplex plunger pumps (Fig. 9.16), pumping iron ore sluny of 1.92 specific gravity through a 9-in pipeline 54 mi long. The sluny is 60% magnetite by weight with 85% minus 200 mesh particle size. The four pumps are electrically driven, two at 175 RPM fixed speed and two with variable-speed liquid coupling drive at 173 RPM maximum speed. All pumps have 5!-in diameter boron-alloy-coated sleeve-type plungers and are rated 560 BHP input.
9.13
SLURRY TABLES
Tables 9 .4 through 9 .12 list the important properties of solids and slurries and how to calculate the specific gravity of slurries. A set of precalculated data is also included.
TABLE 9.4. Specific Gravity and Hardness of Minerals
Albite Anhydrite Apatite Aragonite Asbestos Azurite Barite Bauxite Becyl Calcite Chalcopyrite Coal Corundum Cyanite Dolomite Feldspar Fluorite Galena Gamet Gypsum Hematite Ilmenite Kaolin Lignite Limes tone Limonite Magnetite Olivine Phosphate Potash Pyrite Quartz Rutile Sulfur
Spec. Gr.
Hardness
2.6 2.9 3.2
6-6.5 3-3.5 2-3 3.5-4 1-2.5 3.5-4 2.5-3 1-3 7.5-8 3 3.5-4 2-2.5 7-9 5-7.3 3.5-4 6-6.5 4 2.5 6.5-7.5 1.5-2 5.5-6.5 5-6 1-2.5 2-2.5 3 5-5.5 5.5-6.5 6.5-7 2-3 3.5-4 6-6.5 7 6-7 1.5-2.5
2.9 2.5 3.8 4.5 2.5 2.7 2.7 4.2 1.3 4.0 3.6 2.9 2.7 3.1 7.5 4.0 2.3 5.1 4.7 2.6 1.3 2.7 3.8 5.2 3.3 3.2 2.7 5.0 2.7 4.2 2.0
TABLE 9.5. Screen Size
U.S. No.
Mesh
Opening, in
Opening, 1-tm
4 5 6 7 8 10 12 14 16 18 20 25 30 35 40 45 50 60 70 80 100 120 140 170 200 230 270 325 400
4 5 6 7 8 9 10 12 14 16 20 24 28 32 35 42 48 60 65 80 100 115 150 170 200 250 270 325 400
.187 .157 .132 .111 .0937 .0787 .0661 .0555 .0469 .0394 .0331 .0278 .0234 .0197 .0165 .0139 .0117 .0098 .0083 .0070 .0059 .0049 .0041 .0035 .0029 .0025 .0021 .0017 .0015
4760 4000 3360 2830 2380 2000 1680 1410 1190 1000 841 707 595 500 420 354 297 250 210 177 149 125 105 88 74 63 53 44
38
TABLE 9.6. Relatlve Size of Mlcronic Particles
Relative Sizes
Lower limit of visibility (naked eye) White blood cells Red blood cells Bacteria (cocci)
40 microns 25 microns 8 microns 2 microns
Linear Equivalents
1 micron = 1 micrometer (1-tm) 1 inch (in.) = 25.4 mm = 25,400 1-tm 1 millimeter (mm) = 0.0394 in = 1000 1-tm 1 micrometer (1-tm) = 1 /25,400 in = 0.001 mm 1 micrometer (1-tm) = 3.94 X 10- 5 in = 0.000039 in. 307
Rhombohedron stacking of spherical particles
Figure 9.17 Bulk properties of Mineral solids. A-Principie solid particle material. (i.e. Coal) B-Porosity, as percent of volume of particle (may be occluded air, gas or connate water). C-Voids, between particles as percent of bulk volume as function of size, shape, size distribution and stacking mode. O-Water-soluble material. E-"Tramp" material such as ash in coal and silica in limestone. BULK VOLUME-Volume of container, ft3. BULK DENSITY-Weight (mass) of Bulk Volume, lb/ft3. BULK SPECIFIC GRAVITY-Bulk Density/62.3. APPARENT SPECIFIC GRAVITY-Density of solids, including A, B, D and E, compared to Water. TRUE SPECIFIC GRAVITY-Density of Solids A compared to Water. Void percentage is independent of particle diameter. One cubic foot of baseballs or marbles has the same void percentage; 47.6% for cubic stacking and 25.9% for rhombohedrol stacking. Random particle size solids result in much lower void percentage simply because the smaller particles tend to fill the voids between larger particles.
308
TABLE 9.8. Calculation of Specifü: Gravity of a Slurry of one Solid
l. Water-Mixed
Sm
=
ll. Other Liquids
C = CvSs
( 9 .9 )
sm
w
S = _ _ _ _S_1- - m l - Cw(l - S¡/Ss)
( 9 .S)
1 - Cw(: - 1/Ss)
C = Sm - l " SS - 1
(9.11) (9.12)
C
( 9 .10)
=
Sm - S1
"
S,, - S1
(9.13)
where Cv = volume fraction of solids Cw = weight fraction of solids sm = specific gravity of mixture (sluny) Ss = specific gravity of solids S1 = specific gravity of Hquid
TABLE 9.9. Calculafü:m of Specifü: Gravity of a Slurry of a Mixture of Solids
lf Given in
l.
sm
Weight Fraction
= -----------
wt. frac. A SA
+
wt. frac. B SB
(9.15)
+
EXAMPLE 0.4 wt. frac. A 0.3 wt. frac. B 0.3 wt. frac. C
sm ll.
=
SA = 5.0 SB = 3.0
Se = 4.0
0.4
0.3
0.3
5.0
3.0
4.0
-+-+-
lf Given in
Sm = vol. frac. A
X SA
=
(9.16)
3.92
Volume Fraction
+ vol. frac. B
X SB
+
17)
EXAMPLE 0.4 vol. frac. A 0.3 vol. frac. B 0.3 vol. frac. e
Sm
= 0.4
X
5.0
+ 0.3
X
SA = 5.0
SB = 3.0
= 4.0 3.0
+ 0.3
X
4.0
= 4.1 309
w .... o
TABLE 9.10. Pipeline GPM per Mllllon Short Tons per Year of Sollds
Solids Sp. Gr.
1.1
1.2 1.3
1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5
Solids Percent Concentration by Weight with Water
30
35
40
45
50
55
60
65
70
75
1,482 1,447 1,418 1,393 1,371 1,352 1,335 1,320 1,307 1,295 1,284 1,274 1,265 1,257 1,249 1,242 1,236 1,230 1,224 1,219 1,214 1,209 1,205 1,201 1,197
1,264 1,230 1,200 1,175 1,153 1,134 1, 118 1,103 1,089 1,077 1,066 1,056 1,047 1,039 1,032 1,024 1,018 1,012 1,006 1,001 996 992 987 983 979
1,101 1,066 1,037 1,012 990 971 954 939 926 914 903 893 884 876 868 861 855 849 843 838 833 828 824 820 816
974 939 910 885 863 844 827 812 799 787 776 766 757 749 741 734 728 722 716 711 706 701 697 693 689
872 838 809 783 762 743 726 711 698 686 675 665 656 647 640 633 626 620 615 609 604 600 595 591 588
789 755 725 700 679 660 643 628 614 602 592 582 573 564 557 550 543 537 531 526 521 517 512 508 504
720 686 656 631 609 590 573 559 545 533 522 512 503 495 487 480 474 468 462 457 452 447 443 439 435
662 627 598 573 551 532 515 500 487 475 464 454 445 436 429 422 415 409 404 398 393 389 385 380 377
611 577 547 522 501 481 465 450 436 424 413 404 395 386 379 372 365 359 353 348 343 339 334 330 326
568 533 504 479 457 438 421 406 393 381 370 360 351 343 335 328 322 316 310 305 300 295 291 287 283
3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 507 5.8 5.9 6.0
1,193 1,190 1,187 1,184 l, 181 1,178 1,175 l,173 1,170 1,168 1,166 1,164 1,162 1,160 1,158 1,156 1,154 l, 153 1, 151 1,149 1,148 l ,147 l,145 1,144
-
1,143
976 972 969 966 963 960 958 955 953 950 948 946 944 942 940 938 937 935 933 932 930 929 928 926 925
812 809 806 803 800 797 794 792 789 787 785 783 781 779 777 775 773 772 770 769 767 766 764 763
686 682 679 676 673 670 667 665 662 660 658 656 654 652 650 648 646 645 643 642 640 639 637
762
635
636
584 581 577 574 571 568 566 563 561 559 556 554 552 550 548 547 545 543 542 540 539 537 536 534 533
501 497 494 491 488 485 483 480 478 475 473 471 469 467 465 464 462 460 459 457 456 454 453 451 450
432 428 425 422 419 416 413 411 409 406 404 402 400 398 396 394 393 391 389 388 386 385 383 382 381
For water-mixed slurries only: 457 GPM* = - - , = U .S. GPM of slun-y for each million short tons per year of solidsº
CwSm
...... w
Use pump volumetric efficiency to calculate pump size.
373 370 366 363 360 358 355 352 350 348 345 343 341 339 337 336 334 332 331 329 328 326 325 324 322
323 319 316 313 310 307 305 302 300 297 295 293 291 289 287 285 284 282 280 279 277 276 275 273 272
279 276 273 270 267 264 261 259 256 254 252 250 248 246 244
242 240 239 237 235 234 233 231 230 229
w .... NI
TABLE 9.11. Fraction Volume of Solids in Slurry Mixture,
c.
Solids Percent Concentration by Weight with Water
Solids Sp. Gr.
30
35
40
45
50
55
60
65
70
75
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3
0.280 0.263 0.248 0.234 0.222 0.211 0.201 0.192 0.184 0.176 0.169 0.163 0.157 0.152 0.146 0.142 0.137 0.133 0.129 0.125 0.121 0.118 0.115
0.329 0.310 0.293 0.278 0.264 0.252 0.241 0.230 0.221 0.212 0.204 0.197 0.190 0.183 0.177 0.172 0.166 0.161 0.157 0.152 0.148 0.144 0.140
0.377 0.357 0.339 0.323 0.308 0.294 0.282 0.270 0.260 0.250 0.241 0.233 0.225 0.217 0.211 0.204 0.198 0.192 0.187 0.182 0.177 0.172 0.168
0.427 0.405 0.386 0.369 0.353 0.338 0.325 0.313 0.301 0.290 0.280 0.271 0.262 0.254 0.247 0.239 0.233 0.226 0.220 0.214 0.209 0.204 0.199
0.476 0.455 0.435 0.417 0.400 0.385 0.370 0.357 0.345 0.333 0.323 0.313 0.303 0.294 0.286 0.278 0.270 0.263 0.256 0.250 0.244 0.238 0.233
0.526 0.505 0.485 0.466 0.449 0.433 0.418 0.404 0.391 0.379 0.368 0.357 0.347 0.337 0.328 0.320 0.312 0.304 0.296 0.289 0.283 0.276 0.270
0.577 0.556 0.536 0.517 0.500 0.484 0.469 0.455 0.441 0.429 0.411 0.405 0.395 0.385 0.375 0.366 0.357 0.349 0.341 0.333 0.326 0.319 0.313
0.628 0.607 0.588 0.570 0.553 0.537 0.522 0.508 0.494 0.481 0.469 0.458 0.447 0.436 0.426 0.417 0.408 0.399 0.390 0.382 0.375 0.367 0.360
0.680 0.660 0.642 0.625 0.609 0.593 0.579 0.565 0.55J 0.538 0.526 0.515 0.504 0.493 0.483 0.473 0.464 0.455 0.446 0.438 0.429 0.422 0.414
0.732 0.714 0.698 0.682 0.667 0.652 0.638 0.625 0.612 0.600 0.588 0.577 0.566 0.556 0.545 0.536 0.526 0.517 0.508 0.50Ó 0.492 0.484 0.476
3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0
w .... w
0.112 0.109 0.106 0.104 0.101 0.099 0.097 0.095 0.093 0.091 0.089 0.087 0.085 0.084 0.082 0.080 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.070 0.069 0.068 0.067
0.137 0.133 0.130 0.127 0.124 0.121 0.119 0.116 0.114 0.111 0.109 0.107 0.105 0.103 . 0.101 0.099 0.097 0.095 0.094 0.092 0.091 0.089 0.088 0.08(í 0.085 0.084 0.082
0.164 0.160 0.156 0.153 0.149 0.146 0.143 0.140 0.137 0.134 0.132 0.129 0.127 0.124 0.122 0.120 0.118 0.116 0.114 0.112 0.110 0.108 0.106 0.105 0.103 0.102 0.100
0.194 0.189 0.185 0.181 0.177 0.173 0.170 0.166 0.163 0.160 0.157 0.154 0.151 0.148 0.146 0.143 0.141 0.138 0.136 0.134 0.132 0.129 0.127 0.126 0.124 0.122 0.120
0.227 0.222 0.217 0.213 0.208 0.204 0.200 0.196 0.192 0.189 0.185 0.182 0.179 0.175 0.172 0.169 0.167 0.164 0.161 0.159 0.156 0.154 0.152 0.149 0.147 0.145 0.143
0.264 0.259 0.253 0.248 0.243 0.239 0.234 0.230 0.225 0.221 0.217 0.214 0.210 0.206 0.203 0.200 0.196 0.193 0.190 0.187 0.185 0.182 0.179 0.177 0.174 0.172 0.169
0.306 0.300 0.294 0.288 0.283 0.278 0.273 0.268 0.263 0.259 0.254 0.250 0.246 0.242 0.238 0.234 0.231 0.227 0.224 0.221 0.217 0.214 0.211 0.208 0.205 0.203 0.200
0.353 0.347 0.340 0.334 0.328 0.323 0.317 0.312 0.307 0.302 0.297 0.292 0.288 0.283 0.279 0.275 0.271 0.267 0.263 0.259 0.256 0.252 0.249 0.246 0.243 0.239 0.236
0.407 0.400 0.393 0.387 0.380 0.374 0.368 0.363 0.357 0.352 0.347 0.341 0.337 0.332 0.327 0.323 0.318 0.314 0.310 0.306 0.302 0.298 0.294 0.290 0.287 0.283 0.280
0.469 0.462 0.455 0.448 0.441 0.435 0.429 0.423 0.417 0.411 0.405 0.400 0.395 0.390 0.385 0.380 0.375 0.370 0.366 0.361 0.357 0.353 0.349 0.345 0.341 0.337 0.333
w .... .... TABLE 9.12. Specific Gravity of Slurry Mixture, Sm
Solids Percent Concentration by Weight with Water
Solids Sp. Gr.
30
35
40
45
50
55
60
65
70
75
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3
1.028 1.053 1.074 1.094 1.111 1.127 1.141 1.154 1.166 1.176 1.186 1.196 1.204 1.212 1.220 1.226 1.233 1.239 1.245 1.250 1.255 1.260 1.264
1.033 1.062 1.088 1.111 1.132 1.151 1.168 1.184 1.199 1.212 1.224 1.236 1.247 1.257 1.266 1.275 1.283 1.290 1.298 1.304 1.311 1.317 1.323
1.038 1.071 1.102 1.129 1.154 1.176 1.197 1.216 1.234 1.250 1.265 1.279 1.292 1.304 1.316 1.327 1.337 1.346 1.355 1.364 1.372 1.379 1.387
1.043 1.081 1.116 1.148 1.176 1.203 1.227 1.250 1.271 1.290 1.308 1.325 1.341 1.356 1.370 1.383 1.395 1.407 1.418 1.429 1.439 1.448 1.457
1.048 1.091 1.130 1.167 1.200 1.231 1.259 1.286 1.310 1.333 1.355 1.375 1.394 1.412 1.429 1.444 1.459 1.474 1.487 1.500 1.512 1.524 1.535
1.053 1.101 1.145 1.186 1.224 1.260 1.293 1.324 1.352 1.379 1.405 1.429 1.451 1.472 1.493 1.512 1.530 1.547 1.563 1.579 1.594 1.608 1.622
1.058 1.111 1.161 1.207 1.250 1.290 1.328 1.364 1.397 1.429 1.458 1.486 1.513 1.538 1.563 1.585 1.607 1.628 1.648 1.667 1.685 1.702 1.719
1.063 1.121 1.176 1.228 1.277 1.322 1.365 1.406 1.445 1.481 1.516 1.549 1.581 1.611 1.639 1.667 1.693 1.718 1.742 1.765 1.787 1.808 1.828
1.068 1.132 1.193 1.250 1.304 1.356 1.405 1.452 1.496 1.538 1.579 1.618 1.655 1.690 1.724 1.757 1.788 1.818 1.847 1.875 1.902 1.928 1.953
1.073 1.143 1.209 1.273 1.333 1.391 1.447 1.500 1.551 1.600 1.647 1.692 1.736 1.778 1.818 1.857 1.895 1.931 1.966 2.000 2.033 2.065 2.095
3.4 3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0
...w UI
1.269 1.273 1.277 1.280 1.284 1.287 1.290 1.293 1.296 1.299 1.302 1.304 1.307 1.309 1.311 1.314 1.316 1.318 1.320 1.322 1.324 1.325 1.327 1.329 1.330 1.332 1.333
1.328 1.333 1.338 1.343 1.348 1.352 1.356 1.360 1.364 1.367 1.371 1.374 1.377 1.380 1.383 1.386 1.389 1.392 1.394 1.397 1.399 1.401 1.404 1.406 1.408 1.410 1.412
1.393 1.400 1.406 1.412 1.418 1.423 1.429 1.434 1.438 1.443 1.447 1.452 1.456 1.460 1·.463 1.467 1.471 1.474 1.477 1.480 1.484 1.486 1.489 1.492 1.495 1.497 1.500
1.466 1.474 1.481 1.489 1.496 1.503 1.509 1.516 1.522 1.528 1.533 1.538 1.544 1.549 1.553 1.558 1.563 1.567 1.571 1.575 1.579 1.583 1.586 1.590 1.593 1.597 1.600
1.545 1.556 1.565 1.574 1.583 1.592 1.600 1.608 1.615 1.623 1.630 1.636 1.643 1.649 1.655 1.661 1.667 1.672 1.677 1.683 1.688 1.692 1.697 1.701 1.706 1.710 1.714
1.635 1.647 1.659 1.670 1.681 1.692 1.702 1.712 1.721 1.730 1.739 1.748 1.756 1.764 1.771 1.779 1.786 1.793 1.799 1.806 1.812 1.818 1.824 1.830 1.835 1.841 1.846
1.735 1.750 1.765 1.779 1.792 1.806 1.818 1.830 1.842 1.853 1.864 1.875 1.885 1.895 1.905 1.914 1.923 1.932 1.940 1.949 1.957 1.964 1.972 1.979 1.986 1.993 2.000
1.848 1.867 1.885 1.902 1.919 1.935 1.951 1.966 1.981 1.995 2.009 2.022 2.035 2.048 2.060 2.072 2.083 2.094 2.105 2.116 2.126 2.136 2.146 2.155 2.164 2.173 2.182
1.977 2.000 2.022 2.044 2.065 2.086 2.105 2.124 2.143 2.161 2.178 2.195 2.212 2.227 2.243 2.258 2.273 2.287 2.301 2.314 2.328 2.340 2.353 2.365 2.377 2.389 2.400
2.125 2.154 2.182 2.209 2.235 2.261 2.286 2.310 2.333 2.356 2.378 2.400 2.421 2.442 2.462 2.481 2.500 2.519 2.537 2.554 2.571 2.588 2.605 2.621 2.636 2.652 2.667
1 PARTS WEAR ANO LIFE
10.1
10.1.1
THE MECHANICS OF WEAR IN PUMPS
lntroducUon
The word wear has many connotations, but in the pumping industry it means the gradual deterioration of any part in the system to the point of danger or uselessness. The word has no quantitative meaning, and a value must be applied before it can be included in any discussion. The obvious approach is to apply a mass loss rate. Then the related term life can be derived from the time function. There are times when the point of uselessness or failure is reached without mass loss, as in the case of fatigue failure. Nevertheless, for the work at hand, the point of uselessness, reached by whatever means, determines the life of that part.
10.1.2
Wear Modes
An extraordinary number of wear modes may be encountered in the pumping of liquids, and a list and description of them would be of great interest. Twelve of the most common are listed below and shown in Figure 10. l. Note that most of these basic modes can be classified into submodes, according to whether they are affected by the following factors: reciprocating, oscillating, circular, or continuous motion; dry, oil-wet, or water-wet; and ratio of areas of mating parts. Mode A. Adhesiva Wear. Usually metal-to-metal rubbing in any of the stated motions and with oil lubrication. For example, plain joumal bearings, crosshead pin bushings, crosshead shoes and guides. 316
10.1
Al
Applied load
THE MECHANICS OF WEAR IN PUMPS
A2
317
A3
- ~~1-~~
1
"""'~~~~~~LL.¿LL.; - - - -
Adhesive wear Wear areas unequal Material posilion elected
Adhesive wear Wear areas equal
82
- .J.=
Abrasive wear Wear areas equal
Abrasive wear Wear areas unequal Material position elected
1
1
Adhesive wear Wear areas unequal Material position reversed
83 Motion: Reciprocating -oscillating -continuous
'77TT7:'7/"' /'""/.'.'.~'' 7 7 ? 7 )
///,:;,
//'.
Abrasive wear Wear areas unequal Material position reversed
Cl
~ rr~~"""~-'-k'f-4~~
~
Polyrner
Seo u ri ng wea r Wear areas equal
with embedded
abrasive particles
Seo u ri ng wea r Wear areas unequal Material position elected
Scouring wear Wear areas unequal Material position reversed
Figure 10.1. Wear modes.
Mode B. Abrasiva Wear. Same as mode A except in the presence of abrasive solids or particles. Figure 10.2 shows abrasive particles of various sizes and shapes. Mode C. Scouring Wear. Elastomer-to-metal rubbing with abrasive particles embedded in the elastomer. For example, rubber pistons, packing, and valve inserts. Mode D. Abrasion-Corrosion Wear. Any metal-to-metal in the presence of water-mixed slurries. Aside from high-velocity erosion, this is the most severe and -destructive mode encountered in slurry pumping. Parts involved are metal-to-metal valves and seats (upon each closure), metal piston parts rubbing on metal liners and plungers, or pistan rods rubbing against metal stuffing box parts or trim. Wear in this mode also accelerates scouring wear. Normal flow in pipelines also causes this type of wear. Mode E. Crushing and Grindíng. In abmsive metal-to-metal contact. For example, a valve repeatedly ciosing with great force against solid partides trapped between the valve and seat at closure.
318
PARTS WEAR ANO LIFE
F
E
D
Abrasion-corrosion
Crushing and grinding
G
High-velocity eros ion
H
..- -·-_,_.. -
.
~~~~~~ Pipewall
--
~~~~~ Pipewall ~
-·;:::;·~·
- • --.• -.::;;• !-
;~·~-
~~~
Low-velocity erosion
· Sa ltation eros ion
J
L~lor
K
~ _. _- , ;o0
_ ' _
1,
, O _' ·
Cavitation
-
Corros ion
roller beari
Collapsing vapor bubbles
Fatigue and corrosion fatigue
Fretting wear
Figure 10.1. (Continued)
Mode F. High-Velocity Erosion. Forexample, when a valve seal orpiston rubber is worn to the extent that there is a slight leak, the extremely high velocity of the leaking slurry results in catastrophic failure of both mating parts. Such a condition existing for a matter of minutes and not attended to will result in washout of the liquid end of the pump, as shown in the photographs of Figures 10.3 and 10.4. Mode G. Low-Ve/ocity Erosion. This is a slow rate of erosion that takes place in the pipeline or in any passage where near-normal velocities are maintained. Mode H. Saltation Wear. Comes about in pipelines handling unstable slurries with larger than usual particles, which tumble along the bottom of the pipe. An example is in the transportation of phosphate rock from pit to processing plant, where the pipe wears rapidly on the bottom and requires frequent tuming to distribute wear.
(a)
(e)
(b)
(d)
Figure 10.2. Abrasive particles. Note 1 mm division. (a) Bunker Hill sand, Miller number 218. (b) Saskatchewan sand, Miller number 149. (e) Los Angeles sewage, Miller number 77. (d) 50-70 "standard" test sand, Miller number 136.
F - HIGH VELOCITY EROS ION B - ABRASIVE WEAR E - CRUSHING WEAR
I - CORROSION WEAR
Figure 10.3. Typical wom and washed out sluny valve. 319
320
PARTS WEAR AND LIFE
G - HIGH VELOCITY EROS ION C - SCOURING WEAR
E - CRUSHING WEAR B - ABRASIVE WEAR
Figure 10.4. Typical wom and washed-out sluny valve seat. (*Note washed-out liquid end.)
Listed as a mode of wear since it can still contribute to metal loss in the absence of abrasive materials.
Mode /. Corrosion.
Mode J. Cavitation. Can result in damage to the metal in the liquid end or other parts of a reciprocating pump through the microscopic but intense liquid blasts against the metal near the cavitation area following the collapse of the vapor bubbles.
While not a true ''wear'' mode, fatigue does result in early failure of pump parts, particularly the liquid end.
Mode K. Fatigue.
A minor cause of failure, particularly in roller and ball bearings and other loose-fitting parts that tend to generate a form of chafing, as between the rollers and the mating cup or cone when the bearing is loaded but not rotating.
Mode L. Fretting Wear.
10.1.3
Effects of Wear
Sorne of the aspects of wear of pump parts have been briefly covered. Most important, the regular replacement of these wom parts over the life of a pipeline can often amount to a much greater cost than the first cost of the pumps and becomes a significant consideration in the economics of any project. See Figure 10.5. Of the modes of wear just listed, mode D, abrasion-corrosion, is most destructive. This type of wear can be encountered with many "clean" liquids. For example, most clean and even potable waters originating from rivers, lakes, canals,
10.1
c::::J
THE MECHANICS OF WEAR IN PUMPS
321
Incremental power cost
~ Partscost ~ Dampener cost
P:::'''''''''::':''i':J Pump cost
2.0
1.0
4
5
6
Number of pumps per station
Figure 10.5. Number of pumps far a given station. Costs based on 20-yr life of project. (Courtesy Worthington Pump Division-Dresser Industries)
aqueducts, and wells often accumulate and carry dissolved air, airbome dust, and minute amounts of particles of sedim~nt, usually silica sand, which have a tendency to become concentrated in the close clearances of parts and in the elastomeric (rubber, leather, etc.) parts of the pump. In this respect, the effect of solids concentration on abrasivity should be recognized. Figure 10.6 shows that abrasivity increases very rapidly from zero to about 10% with an increase in the concentration of abrasive particles. It is interesting to note that in the oil-well drilling industry, drilling mud is in itself not abrasive-it actually inherits its bad abrasivity reputation from the particles picked up from the geologic formation and recirculated through the mud pump. Various "desanding" methods are employed, such as screens, cyclones, centrifuges, and settling, and it is significant that the percentage of sand must be reduced to below 2 % befare effective life-of-parts improvement can be realized. Of course, in slurry pumping it is obvious that one is dealing with the insidious contribution of high concentration and corrosion. It is evident that the combination of abrasion and corrosion results in greater destruction than the sum of the individual effects. This phenomenon is shown in Figure 10. 7 where the introduction of agitation that continually removes the protective products of corrosion results in a fantastic increase in metal loss rate and reverses the effects of pH for sorne unexplained reason.
120 110 100 -;::-
l./"
90
/
CI)
..Q
E
:::J
e:
80
....
70
!
60
~
·f ·¡¡;
50
-----
~ ~
/
I I 1
E 40 ..Q
<
30 20 10
o
12.5
25
-
50
Solids concentration, percent by mass
Figure 10.6. Solids concentration vs. abrasivity for 70 mesh um sand. Showing the abrupt change in the relationship of solids concentration to abrasivity in the region below about 10 to 12% solids.
400
> D.
::¡;
~
300
e: o ·¡¡;
e.... o
200
(.)
7 pH of distilled water
Figure 10.7. Effect of pH of distilled water on erosion-corrosion of carbon steel at SOºC (velocity, 39 FPS). A, erosion-corrosion disc. B, specimens immersed in tank, (From M. G. Fontana and N. D. Greene, "Corrosion Engineering," McGraw-Hill, New York 1967. Copyright© 1967 McGraw-Hill.)
322
10. 1 THE MECHANICS OF WEAR IN PUMPS
323
. Sr1aded area-Liner wear _)Metal (piston body)
\
~Piston
! Piston rod
6"
Figure 10.8. Wom liner profile (opposite sides) showing "end-of-stroke scmbbing wear." This typical liner wear pattern in a single-acting pump is explained: The stored energy of high-pressure compression of the elastomer parts of the piston rubber is suddenly reduced to near-zero pressure at the end of the pressure stroke. With abrasive material trnpped between the rubber and the liner wall, this sudden (explosive) change of shape of the to its natural shape generates a greater rate of wear for that instant than at any other position of the piston in the liner. Note that even at the midstroke of the piston, where maximum velocity is seen, there is no tendency for greater wear as one would expect. This bears out the contention that number of reversals is the greatest cause of wear.
10.1.4
EFFECT OF PUMP STROKE REVERSAl RATE
A reciprocating pump and piston rod follows a more or less distorted sine wave shape of instantaneous velocity by the crank mechanism, the maximum velocity occurring about mid-stroke but with zero velocity at each end-of-stroke. One would expect maximum liner and rod wear to take place at such mid-stroke. However, many years of observation shows that maximum wear takes place at each end of a pressure stroke. This can be explained from an analysis of the action of any sealing element, such as resilient pistons and rod packing or even metallic ring-type sea.Is. Sealing must rely on a pressure-generated distortion of the sealing elements in order to seal the gap between the moving parts and this distortion occurs in a rather short period of time (high energy) at each end of the stroke, with the sudden application of discharge pressure. The violent generation of such distortion at one end-of-stroke and return from such distortion at the other end-of-stroke, results in a concentrated wearing condition between the mating parts, being exacerbated the presence of abrasive material as in the case of drilling-mud and slurries. In an interna! combustion engine the effects are also shown in the "shoulder" on the cylinder wall of a worn engine at the top of the piston stroke where there is zero piston velocity but with explosive forces acting on the rings in an extremely short instant. See Figure 10.8 for a typical mud-pump liner wear profile.
324
PARTS WEAR AND LIFE
Figure 10.9. Wom slurry pistori.
"Relaxed" piston installation
High
at
pressure Piston motion _ .
Zero
· pressure -+-- Piston
motion Liner
t::::=::===========~::::::::~::j wear
Figure 10.10. Liner wear at reversa!. (a) Liner. (b) Deformed piston, caused by pressure and friction. (e) Scouring of liner by violent retum to natural shape of piston.
Also a critical examination of the pump sequence of operation will revea! that the worst moment in the life of a valve in a pump cycle is that instant when the valve doses, again at the end-of-stroke of the piston or at the moment of reversa!. The valve at these moments is subject to every wear mode known: Abrasion, Crushing, Veiocity erosion, Scouring, etc. Once the valve is closed and sealed there is no effective wear for the entire remaining time of a stroke when the valve opens at end-of-stroke. An exception is the case of a rapid (a matter of
10,1
High pressure
,l.
THE MECHANICS OF WEAR IN PUMPS
c. ol
325
Zero pressure
Jlilll
11------'j
J
Rod wear
Jlllll (b)
(a)
Figure 10.11. Piston rod wear at reversal. (a) Sealing ring deformed by pressure and friction. (b) The sudden retum to original shape tends to scour the metal rod.
minutes) complete deterioration of a valve and seat with the high velocity of a smaH leak rapidly cutting away nearby metal. Valve guiding requires considerable clearance for proper action and such clearance allows a valve to seat in a slightly 'cocked' or canted position in its seat. Then when the high discharge pressure applies a high load to the top of a beveled valve, it forces the closed valve to slide a short distance as it seeks its natural mating position with its seat-all a severe wearing mechanism at each closure and ali at the end-of-stroke instant. So again, valve wear occurs at the end-of-stroke, or at reversa!, exacerbated by the presence of abrasive materiel such as drilling mud and slurry. In view of these facts it is obvious that most rapid wear of expendable parts occurs at each end of the stroke, or at each stroke reversa!. Then the life of parts becomes a function not of speed, per se, but of the reversa[ rate, again a matter of stroke-length and RPM. 10.1.4.1
PUMP SPEED REPORTING
Because pump RPM is design-related to pump stroke length, the term Feet Per Minute (FPM) becomes a factor that includes stroke-length and speed, the use of FPM must be involved in the relation to pump reversal-rate and parts life: FPM RPM R'PM
Where s
s x RPM/6 6 X FPM/s 2 X RPM
(lO.I) (10.2) (10.3)
pump stroke, inches
R'PM
=
Reversals per minute
Now ali punips can be limited to a constant maximum speed by the term FPM. For example, Table lO. l will show;
326
PARTS WEAR ANO LIFE
TABLE 10.1
Relafü:m of RPM, FPM and Reversa! Rate
(R'PM)
Stroke
6" 8" 10" 1211
14 16
11 11
IO"
20 22" 24
11
11
100 FPM R'PM RPM 100 75 60 59
43 38 33 30 27 25
200 150 120 IOO 86 76 66
200 FPM 300 FPM RPM R'PM RPM R'PM 200 150 120
400 300 240 200
300
86 76 66 60
172
225 180 150 129
152 132
113 99
120
90
54
54
50
50
108 100
82 75
60
100
600 450 360 300 258 226 190 180 164
150
Thus it can be seen that the Rate of Reversa! is a function of both RPM and stroke length. Experience has shown that piston speeds below 200 FPM should provide trouble-free hydraulic performance. See Chapter 3. Apparently many drilling mud pump manufacturers failed to recognize this 'reversa!' mode of wear because recently introduced Triplex SA mud pumps appeared with short stroke (sorne 1700 BHP pumps with a 12 inch stroke compared to the 18 inch stroke in a Duplex DA pump of the same power). Note that 1211 falls in the worst part of the scheme in Figure 10.4A. Also over the years, smaller pumps saw an arbitrary increase in speed rating, resulting in increased power per pound and power per dollar. There are appropriate needs for such design where portability or space is at a premium, but for the greater number of stationary installations, long stroke and low speed should be the requisite. The argument that 'long stroke pumps cost money' is not conclusive as shown in Figure 10. lA where even a double capital cost would still remain well below the long-term expendable parts cost. Accordingly, the wearing process on pump 'expendabie parts' is responsive mainly to the 'reversal rate'. Simply stated, the following Cases will result in exponentially extended expendable parts life by putting these facts to work. CASE 1, Figure l0.2A. By slowing the main pump(s) down below rated speed and complimenting with the other or 'standby' pump(s) at the required reduced speed. Multiple pumps in such applications as pipelines, particularly abrasive slurry pipelines, tend to garner the most from the 'ali pumps rmming' application. Table 2 compares such multiple pump usage. This scheme should perform well on oil well drilling rigs that invariably make use of two pumps, one main pump and one stand-by, alternating the position to distribute the wear between both pumps over the long time period.
PARTS LIFE VS PISTON SPEED AS FUNCTION OF STROKE LENOTH
40000
•••••••••••• ····-·· •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••
•• ,..t:. ••••••••
.
' 30000
······ :::;::• .~:::::........
....... ....... ....... ;-;"'·
••••••••••••• ····-·· •••••••
1 ,
,,,,~'
~
1 20000
•••••• ••••••
111······· ....... ······· ........
/
/
,,
... .. .. ::::: ::::· ·····- ···-· ....... ;;; :::::: :::::., ,,..11'"
.•...
J. . .
J.······· 1(··": 1 • ' 1 1 ,...::. ~~---·· '·······1······· ·······l:;:;:::.' ••:::.' 1
10000000 !0000000
!,....·¡
1
······· ......... ........... ······· ······· ······· ······•······ --:::.:::::: .......................................... ::::::: ::::::: ,.,. ...! .:::::: ::::::: :;:::::
,,,,,·,
10000 -··-/- •••••• ····-·· ··::: ,.,,..:. •••••••
/
······~¡;.,
A~(J
•••••••
..........
................ ..
o'P"-~+---t,.....-+~-+~-+~-+-~+-~-t-~t---t,.....-+~-t-~-+~-+-~+-~-t-~t---t~-t~-t-~-t
10
8
3
11
12
13
14
16
18
17
18
19
20
21
22
23
24
STROKE LENGTH - INCHES . . 100 fpm ·•· 200 fpm 300 fpn ... 400 lpm
+
Figure 10.lA
PUMP SPEED VS PARTS LIFE:: INCREASE
6.00
·········r········r·······T········r········¡··········· ··········· ........... ··········r········· ........... ··········· ..........
5.00
····················l···················-r········l·········1·································································
4.00
.......... ¡...........•........•...........•.......... 1 1 i ¡ ¡
1
~
1
~
.,w :;\ IC
u
111"'··············--············t·····································I···················-··············· ·····················•·••••••••••••
~I
f'AESSURE, 1000 PSI
Figure 10.3A Mud pump pressure vs. parts cost
10.1.4.4 INCREASING PUMP HORSEPOWER AVAILABLE
On applications where multiple pumps are used, the demand for extra power allows one to run both pumps for a demand for more power than allowed with one pump. Even if this is carried to the extreme of using the ful! power of both pumps, the improved parts life would still be had over single pump of the required BHP. but when maintenance of one pump is required the "standby" is nil and the system would have to operate at half through-put, if permissible. For normal two-pump operation in a drilling rig see the following Section. 10.1.4.5 STANDBY PUMPS
The following discussion should dispel any idea that one is trying to operate without a standby pump and the idea is not as careless as it may seem. With two pumps (one running and one standby) the standby capital cost is two times that for a single pump to perform a certain function but with two pumps running, as described in CASE l, the capital investment pays a greater dividend in the form of greater parts life. With two pumps running, the need for standby is greatly reduced because of the ability to extend the operating life of both pumps. But there may be understandable objection to the apparent loss of 'standby'. However, it is not a complete loss for one of the two pumps can be speeded up to the rated RPM while the second one is being maintained. If the described method of obtaining more total power by combining two pumps, and
c.!
(,) Q
TABLE 10.2 Operating Data
COMB
l 2 3
4 5 6 7 8 9
TYPE PUMP
NUMBER PUMPS
STROKE INCHES
DUPDA DUPDA TRIPSA TRIPSA DUPDA TRIPSA TRIPSA DUPDA DUPDA
l 2 l 2 2 2 2 4 4
18 18 12 12 18 12 18 18 18
SPEED FPM RPM 195 98 240 120 144 176
98 195 98
65 33 120 60 48 88 33 65 49
COMBINATIONS OF ABOYE DATA
BHP PUMP
GPM PUMP
TOT BHP
PARTS COST COST POWER
COST TOT
1706 855 1612 806 1009 1009 806 1706 1280
682 342 682 341 403 428 342 682 512
1706 1706 1612 1612 20!9 2018 1706 5118 5118
$2020 1129 1692 1065 2034 1819 499 23924 18371
$6529 5872 6172 5545 7645 7092 4979 38133 32580
PARTS COST
$4743 4743 4480 4480 5611 5273 4480 14209 14209
> REDUCTION %
A One DUPDA full speed vs two DUPDA at half Speed; l 1700 BHP DUPDA, One, ful! speed 2 1700 BHP DUPDA, Two, half speed B One TRIPSA full speed vs two TRIPSA at half speed; 3 1700 BHP TRIPSA, One, full speed 4 1700 NHP TRIPSA, Two, half speed C One DUPDA ful! speed vs one TRIPSA at ful! speed; l 1700 BHP DUPDA, one at ful! speed 3 1700 BHP TRIPSA, one at full speed
2020 1129
44%
1692 !065
37%
2020 1692
16%
D Greater than normal one-pump power output 5 1700 BHP DUPDA, (two) running above half speed 6 1700 BHP TRIPSA, (two) running, above half speedE 12" TRIPSA (NORMAL) vs 18" Theoretical long-stroke TRIPSA 3 1700 BHP TRIPSA, 12" stroke, two running 7 1700 BHP TRIPSa, 18" stroke, two mnning F Four-pump slurry station, slurry abrasivity Miller Number 80. 8 l 700 BHP DUPDA, Three running full speed 9 1700 BHP DUPDA, Four running, reduced speed
2034 1819
11%
1692 499
71%
23924 18371
23%
Ali COSTS are in $1000 for 20 years pump life. PUMP PARAMETERS EXCEPTAS NOTED; DUPDA-1700 BHP Duplex Doubie Actíng Pump-18 inch Stroke. TRIPSA-1700 BHP Triplex Single Acting Pump-12 inch Stroke. Normal System Through-put-683 GPM, 3640 PSI, 1450 HHP. 2049 GPM for Slurry Station. ~~~~--~~~.~~~~~~~~
TABLE 2 reveals that; 1-Running both pumps 011 a drilling rigor al! pumps in a pipeline station, at reduced in a great saving in pump expendable parts. 2-A long-stroke pump offers superior parts saving over a short-slroke pump. 3-A TRIPSA pump is more Mechanically Efficient than a DUPDA purnp.
c.>
w ....
for equal throughput, results
332
PARTS WEAR ANO LIFE
98 ························-·· •••••••••.••..•...•••••••••
••••....••••.•....•••••••••
~
~
~
i
·····························t····························· .........................•.. 1 1
97 ························-···
1
i
····························f·············································· ...•.... ···························· ········•••··•·•••····•·····
98 ························-·· ••••••.•••••••••.••...•••••• •••••••·•·••·••••·•·••••••••·•••••••••••••••••·••••••••••••••••••
•••••••••••••••••••••••••••••••••••••••••••••
96 ························-··· ••••••••••••••••••••.••••••• •••••••••••••••••••••••••••• •••••••••••••••••·••••••••••• •••••••••••••••••••••••••• ••••••••••••••••••••••••••••
94.l..-~~~-l-~~~~+-~~~-+~~~~-+-~~~-+-+~~~ 200 260 300 160 100 400 PISTON SPEEO • FEET PEA MINUTE
Figure 10.4A Pump speed (test data) vs. volumetric efficiency
if the power difference is great (up to the full power of both pumps) then one would have to consider a period of time of half power if the system would allow it. For example, with two 1700 BHP 120 RPM rated TRIPSA pumps running at 75 RPM each, the total BHP would be 1700. With both pumps running at, say, 90 RPM the output would then be 2040 BHP at which the system could probably be operated for a short period of time at 1700 BHP. This Standby reasoning discussion also applies to multi-pump systems such as long slurry pipelines where as many as seven or more large pumps are used, but with less advantage in parts life extension. However, if the slurry in question is highly abrasive, such as sorne iron ores, the extension of parts life takes on more importance. Table 2 shows such reasoning on a slurry application, for example, pumping 80 Miller Number phosphate slurry. 10.1.4.6 VOLUMETRIC EFFICIENCY
Any speed reduction below the pump's rated speed will usually result in improved Volumetric Efficiency as a result of improved hydraulic performance. See Figure l0.4A that shows actual test data for a Triplex Single Acting pump, typical of all pumps. With such manipulation of speed as above, piston diameter need not be considered.
10.2 PLUNGERS
1003 • 903 :!:: 803 .~ 703 Q)
~
--~ ~ :::..:~'~·~ '''"""'""'
'· ~
o
~
1¡ 2
~ .,..
'(A
a> "'603 .tl
333
3000 Ps1'Xí} ·~·
503
........ ,,,,~ ..... ~~~ '
'
•,.
"'
"'i¡¡;':•~
"'~:;!!!I .~.....
1500 PSI
°'U\ ':'
·\.\. ' 2000 PSI
~:~=~-t---+----t~+--t--+~+--t---+----t~+--+---+-~--1 203~-t---+----t~+--t--+~+--t---+----t~+--+---+-~--I 103~-t---+----t~+--t--+~+--t---+----t~+--+---+-~--I
.010
.020
.030 .040 .050 .060 .070 Piston-liner diametrical clearance - inches
.080
Figure 10.12. Importance of piston-liner clearance. (© TRW Inc. 1957. Reprinted by permission of TRW Inc.)
10.1.5
PISTON-LINER CLEARANCE
Figure 10.12 shows the effect of piston-liner diametrical clearance, as the result of wear of the liner and piston body, on the life of piston rubbers. For example, if the service life of a piston operating at 2000 PSI is 300 hours when the initial clearance is 0.01 in, then the expected service life of the next rubber, when the clearance is 0.04 in, would be 80% ór 240 hours.
10.2
PLUNGERS
Liner and piston rod wear modes and the fact that they wear more rapidly at the end of each pressure or delivery stroke have been discussed. However, because of the distinct difference in the mechanics of packing in a single-acting pump, at reversal ofthe pressure stroke the packing has already been ''dragged'' by friction forces away from the severe extrusiOn-gap seal to its "relaxed" condition, thereby minimizing the scrubbing wear at that point. Plungers invariably contradict the end-of-stroke type of wear and exhibit a typical ''hourglass'' or necking-down at midstroke where the velocity is greatest. As to the fear of greater wear on the plunger bottom due to its own weight in horizontal pumps, that fear can be dispelled, as no wom plunger has ever been observed without more or less uniform wear around its circumference. This can
334
PARTS WEAR AND LIFE
be explained by the fact that the forces of pressure on the packing circumference tend to force the plunger toward the center of the stuffing box and generate unifonn wear. A phenomenon exhibited by solid ceramic plungers is that under the ideal conditions of almost surgically clean liquids, with no abrasive materials or particles, they exhibit no reduction in diameter from wear as such. They take on a discolored, polished appearance and would probably run ''forever'' but for other factors. These factors are: (1) Abrasive material in the liquid, (2) drastic temperature changes that produce thermal shock and fracture (a typical case is where a pump runs without prime for sorne time and is suddenly subjected to a dose of cold water), (3) misalignment in the pump causing breakage of the rather fragile ceramic, pitting due to cavitation as described earlier, and (5) rough handling and striking with tools. Certain sprayweld coatings that consist of a rather soft matrix with the addition of extremely hard particles, such as tungsten carbide, should be avoided for plunger service. Scrubbing wear or selective chemical attack will remove sorne of the soft matrix, leaving a sandpaper surface that is extremely damaging to packing. This process is almost microscopic, and a used plunger may appear to be in excellent condition but a magnification will show the effect described. A simple test to determine if such a condition exists is to rub a copper coin (penny) along the plunger surface. A bright copper-colored streak will indicate a damaged surface. Sprayed ceramic coatings for plungers have performed satisfactorily in many applications, but certain corrosive liquids may tend to penetrate the porous coating and attack the base metal, resulting in spalling of the coating. It is reported that such plungers have been improved by the application of pressure-applied sealant. Because the bond between the ceramic particles and the sealant may be doubtful, the repeated application of high to low pressure (discharge to suction) could have a detrimental e:ffect by early fatigue of the bond with subsequent loss of seal.
10.3 CERAMIC PLUNGER PITTING Ceramic (alumina) plungers have a propensity to pit and there are three distinct types of pitting: ring, local, and end. Type I or ring-type pitting occurs in a circumferential pattem usually completely around the plunger diameter in a single row of pits at a uniform distance back from the end of the plunger. Measurements show that this type of pitting usually occurs at the last ring of lip-type packing at the end of the forward or pressure stroke as shown in Figure 10 .13. Type II or local pitting occurs in a single patch or area from ~ in to as large as 1 in in diameter, always on top ofthe plunger and always in the regionjust forward of the stuffing box throat bushing on the end of the forward or pressure stroke. Type m or end-type pitting occurs on the very end of the plunger, usually at th.e top, and is an "eating out" of a large portion of the plunger, resulting in holes as Iarge as a walnut.
10.3
Type 1 - Ring Pitting
/
CERAMIC PLUNGER PITT!NG
335
Type 11 Local Pitting
/
Type 11! End Pitting
I
Area of Local Pitting
Plunger at end oí pressure stroke.
Longer throat bushing.
moved to non-contributing location by use o! longer throat busr1ing.
Figure 10.13. Ceramic plunger pitting.
Types I and II, ring and local pitting, IJTE 4
,,,.-g~\
\~
~
f'RESSIJiE GAUGE
AIDID STRAINER5
m
FTIJl'ERS IN T!lE
su::noo
LINE
FLEXIBLE HJSE - t 175% 165% 160%
7-112 10 15 20
25 30 40 50
60 75 100 125
150"A. 150".4 1500/o 140'!/ó 140"/o i40"/o 140"/o
12.SOA 110".4
150
110"/o
200 250
100%
300 350 400 450 500
80";(, 80"/o 80"/o 80"/o 80".4. 80".4
1200RPM Moton;
170"/o 165% 160"/o 155% 150"/o 150"/o 150\'lo 1500/o 135% 135%
135%
135'%
135% 135"/o 135% 125"/Ó 125"/o 1200/o 120% lOO"Ai 100"/o HJOO/o
Note: In the range from 1 through 75 horsepower, the 1800 RPM motors show higher locked-rotor torque ratings than do the 1200 RPM motors. However, from 125 through 350 horsepower, the 1200 RPM motors have larger NEMA ratings. Locked rotor torques ol large motors must be carefully evaluated befon.! final selection.
low the liquid to discharge back to the tank thereby expelling the air. When running smoothly, close by-pass valve and thus load the pump.
Electric Motor Locked~Rotor Torques Table 11.1 summarizes minimum locked rotor torque ratings for standard NEMA Design "B" 60 Hertz squirrel-cage induction motors expressed as percent of fuUload torque. lnlet System for Power Pumps An inlet system for a reciprocating power pump must provide a flow of liquid, at a relatively constant pressure, to the pump at a pressure sufficiently above vapor pressure to prevent flashing as the liquid enters the pump chambers. If gas bubbles are entrained in the liquid, or if flashing occurs in the pump, damaging vibrations may occur in both inlet and outlet lines, volumetric efficiency will drop, and various pump and system components may foil. Small amounts of gas or cavitation can reduce Hfe of packing, valve springs, valves, seats and gaskets. Larger quan-
354
APPLICATIONS
tities of gas, or more severe cavitation, can cause pitting of liquid end components and catastrophic failure ofthe liquid cylinder, crankshaft, bealings, and drive train components. It is recommended that the design of the inlet system for a power pump follow these guidelines:
1. The liquid source shown as a tank in Fig. 11.4, should be designed with the following features: a. Sufficient size to allow entrained gas bubbles to rise to the surface. b. Lines which feed liquid into tank below minimum liquid level. c. Completely submerged baffle plate separating incoming from outgoing liquid. d. Vortex breaker at outlet connection (to pump). 2. Each pump should be provided with a separate inlet line from liquid source to pump, rather than connecting two or more pumps to a common manifold. Mutually reinforcing pulsations are thus avoided. 3. Inlet pipe diameter should be at least equal to, and preferably larger than, pump inlet connection. 4. Inlet pipe should be as short and direct as possible with a minimum of tums, bends, and restrictions. All turns should be made with long-radius elbows or laterals. Pulsations resulting from a long inlet line {:an sometimes be partially reduced by a pulsation dampener and sometimes by raising the liquid level at the source, but these changes seldom provide results as satisfactory as a short, direct, large-diameter line. 5. The inlet system must provide NPSH that exceeds the sum of the NPSHR of the pump, all friction losses, and acceleration head. Additional head must be
BAO OES!GN
GOOD DESIGN
Figure 11.4, Suction tanks.
11.2 HYDRAULIC INSTITUTE STANDARDS OF APPLICATION
355
provided if the liquid contains dissolved gases. It is recommended that a margin of at least 7 feet be provided. 6. The inlet system should contain no high points that would conect gas. An "horizontal" runs should slope up toward the pump. The pipe reducer at the pump inlet should be of the eccentric type, instaned with the flat side up. 7. A strainer, if used, should have a free flow area at least three times the flow area of the inlet line. If there is doubt about its regular maintenance, a strainer should not be used. (A plugged strainer may cause more damage to a pump than solids.) 8. The inlet line valve should have a flow area equal to that of the inlet line. 9. If a foot val ve is used (for a source liquid level below the pump inlet opening), the net flow area should at least equal the flow area of the inlet line. 10. An inlet pressure gauge should be located adjacent to the pump. If a system will not provide sufficient NPSH, and cannot be redesigned, it shan be necessary to do one or more of the fonowing:
1. Install pulsation dampener in inlet line adjacent to power pump liquid cylinder. A dampener, properly instaned and charged, may significantly reduce the length of pipe used in the acceleration head equation (see Pulsation Dampener, fonowing). 2. Reduce the power pump NPSHR by selecting a larger, lower-speed unit. The lower speed will also reduce acceleration head. 3. Instan a booster (charge) pump. A booster pump for a power pump is normany a centrifuga! pump, but may be a positive displacement pump under special conditions. Care must be exercised in the selection and installation of a booster pump, because improper selection and/ or instanation can result in increased pulsations and attendant problems. In addition to the recommendations contained in the appropriate section of these Standards, the fonowing are recommended: 1. Instan booster pump as close to inlet source as practica!. 2. The booster pump must add enough pressure to the system to provide sufficient NPSH to the power pump allowing for the acceleration head and friction losses. 3. Install pulsation dampener in inlet line adjacent to power pump liquid cylinder (or if of proper construction, on the opposite side of cylinder). The dampener is often omitted, though, between a centrifuga! booster pump and a low-speedpower pump under the fonowing conditions: a. Diameters of inlet and outlet connections of booster pump are equal to, or larger than, inlet connection on power pump.
356
APPLICATIONS
b. Diameters of all piping between liquid source and power pump are equal to, or larger than, inlet connection of power pump. c. The booster pump is sized for ffi-51--1---+-+-+--+--+"""~-+-+-.¡._j~I--+--+---~ 41--t---f-+-+--+--+--'~~~'+-'--+-+-+- - + - - - + - - - - - - t 31--+--1--1-~---+---t-~--''"""
"....
2 l--+--1--1--1--+---+--~
o
tí
~
(;'
:¡¡
"'
~
l 1--t---t---+--+---t---t--·-+--+.81--+--+--+--+---t--t---+-+---11~~..--'k---+-t----~
u..
.41--t--t--t---+---t---+---+-+--+-+--flr\ct-T---. Out-of-plane vibration .31--+--+--+--+---t---t----+-+--+-+-+-' ·.;:;;
"'
-.;;
o::
1
1 1 1 1
1.1
Relative first cost of pumps oniy
1
1.0
1(Minimum at 4 pumps) 1
0.6
1 1
Relative cost of expenda ble parts only (Present value of 20 yr requirements at 103 interest)
0.5 0.4 0.3
o
2
3
4
5
6
Number ol pumps in a station (including one spare)
Figure 11.12. Optimization ofpumps per station. (Courtesy Worthington Pump DivisionDresser Industries)
would consist of a certain number of pumps that would supply the total displacement requirements, with the addition of one pump of the same size for standby. Figure 11.12 shows the optimum number of total pumps per station as four, on the basis of the previously mentioned exponent of O. 75 for pump cost alone. The effect of parts cost tends to shift the optimum cost toward a smaller number of pumps, in this case three. But due to "windows of nonutilization," size of pumps available, and the diversity of station requirements, this ideal can seldom be realized.
11.5.5
Procedure for Pump Selecfüm *
l. List available pumps with specifications: Type, piston range, RPM, BHP,
pump cost, number of parts per pump, and parts cost. 2. List number of stations and requirements: Station number, GPM, pressure, pumping BHP. *AH costs in thousands of dollars. Parts include val ves and seats; liners and rubbers; piston rods and packing.
11.5 SIZING PUMPS FOR PIPELINES
381
For each station and for each pump type: 3. Determine total number of pumps per station, Ns
= (. station pumping BHP ') * + 1 ( standby)
N s
pump BHP
,
,
(11.15)
4. Calculate excess BHP, E percent:
E=
N, x pump BHP - station pumping BHP . X 100 station pumping BHP
(11.16)
5. Calculate station pump cost, CP:
CP = N,
X
cost of 1 pump
(11.17)
6. Cakulate station expendable pump parts cost, CP 1 :
CP 1
= (Ns -
l ) X parts cost per pump t
(11.18)
For entire pipeline system: 7. Calculate and combine totals and arrange in ascending order of total cost (see Table 11 Pump, total number of pumps, percent excess, pump cost, parts cost, total cost, parts per changeout, power cost
11.5.6
Stations
In order to show the fundamental relationship between horsepower and number of pumps, a hypothetical station of 3290 GPM at 1500 PSI (2880 BHP) is selected. The pumps listed in Table 11.5, Group l (single-acting) and Group 2 (doubleacting) are specially designed pumps with HHP ratings exactly divisible into the station HHP, resulting in maximum utilization of the pump's capability. From the practical standpoint and to show the effects from available and randomly selected pumps, Groups 3 and 4 indude a probable family of geometrically sized pumps. *With this fraction increased to next whole number. tFor any period of time, 20 years in the example.
TABLE 11.5 Costs for all Permutations
w
Oll N
Pump BHP
Number of Pumpsª
Pump Cost
Dampener Cost
Total
Parts Cost
Total
Power Cost
Total
Piston Diam, in
8892 8892 8892 8892 8892
10150 10069 10084 10116 10154
16.4 11.6 9.5 8.2 7.3
9415 9415 9415 9415 9415
10866 10845 10909 10987 11065
12.0 8.5 6.9 6.0 5.4
8892 8892 8892 8892 8892
10208 10380 10149 10171 10238
16.9 13.0 12.1 8.5 6.9
9415 9415 9415 9415 9415
10870 11131 10878 10990 11390
12.0 9.7 8.6 6.0 4.9
Group l. Single-Acting Triplex, Divisibleb
3200 1600 1067 800 640
2 3 4 5 6
905 807 794 800 812
199 177 174 176 178
3387 1694 1129 847 678
2 3 4 5 6
944 843 829 835 848
209 187 184 185 188
1104 985 969 976 990
154 192 223 248 271
1258 1177 1191 1224 1261
Group 2. Double-Acting Triplex, Divisible
1154 1029 1012 1020 1036
297 400 482 552 614
1450 1430 1494 1571 1650
Group 3. Single-Acting Triplex, Randomc
3400 2200 1750 850 560
2 3 3 5 7
947 1025 863 837 857
208 225 190 184 188
1155 1250 1053 1021 1045
161 238 204 258 300
1316 1488 1257 1279 1346
Group 4. Double-Acting Duplo:, Random
3400 2200 1750 850 560
2 3 3 5 8
947 1025 863 837 980
210 227 191 185 217
1157 1252 1055 1023 1196
297 463 408 553 779
1454 1715 1462 1575 1975
Station: 3290 GPM, 1500 PSI, 2880 HHP Ali values in thousands of 1983 dollars. "Number of pumps includes one standby. b¡}ivi.sible: station. HHP divisible by whole number of p~mps from 2 to 6 (Pumps designed to exact station requirements)
1i .5
11.5. 7
SIZING PUMPS FOR PIPELINES
383
Calculations
With the above data on hand, the calculations are carried out in the order shown in Section 11.5.5. In order to dramatize these results, Figure 11.13 is provided. There is only a slight difference in total pump cost vs. the number of groups, but the diíferences in parts cost and power cost (incremental) between the single-acting and the double-acting pumps are pronounced. Once the combining mechanics have been completed, selection logic can be applied using the data at hand. First, let's assume that five pumps per station will be desirable. As shown in Table 11.5, Group l and 2, the least costly would be the 800-BHP, special divisible, single-acting triplex. On the other hand, if available or random pumps are considered, Group 2 and 3, then the 850-BHP single-acting triplex would be the next choice. The absolutely least-cost random pump would be the Group 3, three-per-station 1750-BHP pump. There are other subtle factors that could temper t.he choice. A parameter that is difficult to evaluate is the sanctity of the proven unit, particularly physical size scale-up. For example, the lowest-cost triplex single-acting pump might require the use of uncommonly large diameter pistons and a high piston rod load.
C::::J Incremental power cost ~Partscost
~ Dampener cost
c::::::J Pump cost 2.0
1.0
2
3
4
5
6
Number of pumps per station
Figure 11.13. Number of pumps per station. Based on 20-year life of project. Shows the long-term cost in constant dollars of pump operation, stressing cost of parts. Note differences in cost for pump type and number of pumps per station. (Courtesy Worthington Pump Division-Dresser Industries)
384
APPLICATIONS
Another factor difficult to evaluate is the requirement for a wide variety of different piston sizes (and associated liners and valves) for each pipeline. To obtain the advantage of a lower inventory of parts and possible cost reduction on a quantity basis, one could choose the option of more pumps with one fixed piston diameter. A redeeming feature of this choice is the fact that the parts cost, even with more pumps, would remain about the same as with fewer pumps because of the direct relationship of parts life to actual horsepower. A compromise of, say, only two different piston diameters could be considered.
11.5.8
Study Results
Perhaps the most startling revelation of this study is the fact that the pump cost alone for a diverse pipeline system may have little relation to any particular pump type or size (see Table 11.5). Long-term operating costs are greatly affected by the type of pump because of the variation in liquid-end parts requirements and incremental power costs. lt is impossible to design an individual pump of a size that would provide absolute optimization for all pipelines. In general, the optimum pump size or horsepower can be directly related to the station horsepower on the basis of four, five, or six pumps per station (including standby). Reiterating, maximum optimization could be gained by designing a specially sized pump to best fit the proposed system. This approach is not necessarily out of the question for long pipelines because of the long lead time from system conception to completion. The magnitude of sorne projects would certainly warrant this approach.
11.6
BOLT TIGHTENING SPECIFICATIONS
All bolted assemblies require proper torqueing in order to obtain maximum efficiency and to prevent eventual failure dueto uneven tightening. Table 11.6 gives the torque specifications for most bolt sizes and materials. TABLE 11.6 Bolt Torque Specificatlons•
Tensile Stress Area
Size* !(20)
-fu (18) iC16) ~(14)
!(13)
i(l l)
Area, in2
Size*
Area, in2
.0318 .0524 .0775 .1063 .1419 .2260
iCIO)
.3340 .4620 .6060 .7630 .9690 1.1550
~ (9)
1 (8) 1!(7) 1!(7) Ii(6)
*Bolt diameter, in; threads per inch given in parentheses.
TABLE 11.6 (Continued)
Tightening Torquefor ASTM A-307 OR SAE Grade l; low-carbon bolts, heads not marked Bolt Diam. in 1
4
5
T6 3
8 7
T6 1
2 5
8 3
4 7
8
1
lk
Dry Threads
Lubricated Threads
Torque, lb-ft
Force, lb
Arm, ft
Torque, lb-ft.
Force, lb
Arm, ft
Bolt Clamp Load, lb
2.6 5.4 9.6 15.3 23.5 46.5 82.7 133 200 282
5.2 10.8 9.6 15.3 23.5 31.0 41.3 53 67 71
2
1
1.95 4.05 7.2 11.5 17.6 34.9 62.0 100 150 211
3.8 8.1 7.2 11.5 17.6 23.3 31.0 40 50 53
2
1
630 1,040 1,535 2,100 2,810 4,470 6,620 9,410 12,000 15,100
ªBased on tensile stress
= 60%
1
2
1 1 1! 2 2! 3 4
1
2
1 1 1! 2 2! 3 4
yield strength. T
= 0.2DL/12
L
where T = torque, ft-lb; D = nominal diameter, in; L and A = stress area of bolt, in 2
= EYA
= clamp load,
lb; E
= 0.6;
Y
= yield,
PSI;
Tightening Torquefor ASTM B-7 or SAE Grade 7 Alloy steel studs, head marked letter H Bolt Diam. in 1
4
5
T6 3 ¡¡ 7
T6 1
2 5
8
i7 ¡¡
1
lk 1!
li
Dry Threads
Lubricated Threads
Torque, lb-ft
Force, lb
Arm, ft
Torque, lb-ft.
Force, lb
Arm, ft
Bolt Clamp Load, lb
8.3 17.2 30.5 48.8 74.5 148 262 425 635 900 1270 1660
16.6 17.2 30.5 48.8 37.2 48 87 106 159 180 254 276
2
1
6.2 12.9 23.9 36.6 55.8 111 196 318 477 675 955 1245
12.4 12.9 23.9 36.6 28 37 66 79 119 135 191 207
2
1
2000 3,300 4,880 6,700 8,930 14,200 21,000 29,100 38,200 48,000 61,000 72,500
1
2 3 3 4 4 5 5 6
1 1 1 2 3 3 4 4 5 5 6
385
386
APPLICATIONS
TABLE 11.6 (Continued)
QoRe
Tightening Torque for ASTM A-325 OR SAE Grade 5 or A325 Heat-treated bolts; capscrews, head marked with ticks at each of si.x points and!sometimes ''A325 ''.
Bolt Diam. in l
4
~ 3
8 7
ITí l 'i: 5
8 3
4 7
8
1
lk 1!
li
Dry Threads
Lubricated Threads
Torque, lb-ft
Force, lb
Arm, ft
Torque, lb-ft.
Force, lb
Arm, ft
Bolt Clamp Load, lb
6.7 13.9 24.7 39.4 60.3 120 212 315 472 633 900 1170
13.5 13.9 24.7 26.3 30.2 60 71 79 118 127 180 195
2
l
5.06 10.4 16.5 29.6 45.2 90 159 236 354 475 675 877
10.1 10.4 16.5 19.7 24.6 45 53 59 88 95 135 146
2
l
1,620 2,670 3,950 5,400 7,240 11,500 17,000 21,600 28,400 33,800 43,000 51,000
1 1! 2 2 3 4 4 5 5 6
1 1! 2 2 3 4 4 5 5 6
12 INSTRUMENTATION
12.1
PRESSURE MEASUREMENTS METHODS
1. To obtain uniformity of data collections, standard transducer locations and identification (A, B, C, D, E) have been adopted as shown in Figure 12.1, which also illustrates the use of the terms "upstream" and "downstream." 2. The pressure taps should be on the horizontal centerline of the pipe so as to eliminate air entrapment if on the top and sediment entrapment if on the bottom, and to provide a zero datum point. 3. The transducers should be located as close to the pump inlet and outlet as possible (within 1 or 2 in). 4. All taps should be !-in NPT. In preference to using a welded-in coupling or other fitting, it is best to drill and tap the pipe, when possible, so as to make a ''close-to-the-liquid'' connection. 5. Whenever possible, a cylinder pressure waveform (location C) should be taken simultaneously (through a tapped cylinder head) to obtain a "marker" that will help in the analysis as shown in most of the oscillographs included in this text. 6. A strain-gauge type of transducer (of 'flush" construction that places the sensing element or diaphragm directly into the liquid stream) is recommended, since there would be no cavity to introduce resonance and frequency response problems. It is recommended that the transducers be left installed for the duration of the test only because most transducers have a finite life when subjected to pulsating pressure. 7. No nipples, valves, or other fittings should be interposed to create resonant cavities. 387
388
INSTRUMENTATION
Transduc:er locations
E
Upstream - . - Downstream
Figure 12.1. Pressure-measuring points.
READ IN THIS DIRECTJON---
SCOPE VERTICAL GAIN FROM WHICH PRESSURE IS CALCULATED
GAUGE PRESSURE AT LlMITS MARKED CALCULATED FROM TRANSDUCER SPECS. AND f1EASURED (Z) •
TRANSDUCER LOCATION
MINIMUM TO MAXIMUM PRESSURE (Af') O, 2
E
0.2
C3
20082 HIGH
2,oos LOW
PRESSURE IN
ONE CYLINDER
2.r270
AS "MARKER" 44 SUCT ION
ONE
REVOLUT!ON BETWEEN MARKSMEASURE (Y) SCOPE SWEEP
o.oso
235 RPM
% THEORET!CAL DISCHARGE CYC.
80016-S
TEST NUMBER
RECIP.
PUMP PP-49,
PUMP DESCR l PTI ON
:
~
CALCULATED FROM SCOPE SWEEF FOR ONE REVOLUTION (Y)
99.3~IME
READINGS
SPECIAL
~T
PUMP
TATEMENTS
~
1 RATIO OF DISCHARGE LENGTH ()() TO
LENGTH OF STROKE (Y) (RELATED TO V. E. l
Figure 12.2. How toread oscillographs.
8. In making a survey it is wise to always use the same transducer before and after any changes are made to the system. 9. The use of an oscilloscope for pressure waveform readout is considered the rnost reliable method, since it removes the problems of frequency response, inertia, resonance, and other mechanical doubts associated with recording chart devices. Figure 12.2 shows the method of interpreting a typical oscillograph.
12.3 TYPICAL WAVEFORMS
Pump No. 4 Natural frequency of suction pipe
9-8-79 11:28 AM Pump shut down
389
Calculation of frequency 20 cycles/125 mm Chart speed - 100 mm/s 20/(125/100) = 16 Hz Amplitude - 50 mV /div
Figure 12.3. Oscillograph-pipe vibration.
12.2.
VIBRATION MEASUREMENT
Complete instrumentation of a pump for the purpose of analyzing problems should include (in addition to pressure transducers) vibration transducers (accelerometers) placed on the piping system in order to determine the degree and frequency of vibration of the particular section of piping that may be subject to excessive vibration. The frequency can be related to the pump-generated pulse or rotational frequency to determine if a critica! resonance is present. In all of these measurements it is assumed that the recording device (oscilloscope or oscillograph) has an accurate time-base trace. One can determine the natural frequency of a section of pipe by striking the pipe with a wooden ball bat, for example, while the accelerometer is mounted in the proper location and with the pump stopped but with the piping filled with liquid. (See Figure 12.3.) Figure 12.4 offers a good example of how the vibration of pipe spans can be measured and related to the pump rotation by the second simultaneous trace of the pump cylinder pressure. lt will be seen that the pipe vibration is related to the second harmonic of the pump pulsations. Figure 12.5 is handy to convert acceleration to velocity or displacement.
12.3
TVPICAL WAVEFORMS
The series of 35 oscillographs shown in Figures 12.6 and 12.7, obtained during NPSH tests, show the typical shapes generated under a myriad of conditions. (An apology for the poor quality of this series of oscillographs is in order. They are part of a series of hundreds of oscillographs taken during an extensive test that would be most difficult and expensive to rerun and record. They all show the important shape of the suction waveform.) Note the variation of the suction pressure waveform shapes, particularly the "rounded-bottom, sharp upward spikes" at 360 RPM (and others) indicating cavitation.
390
INSTRUMENTATION
Discharge pipe vibration
=Ft=J~~r=icF'cF'c ~ ~ st~oke 1 Cylinder pressure /
100 mm
1
One
Figure 12.4. Pipe vibration vs. pump pulsations. Chart data: Chart speed, 100 mm/s; upper trace, discharge pipe vibration; lower trace, center cylinder pressure, PSI. This cha1t is an actual trace taken on a 7 X 10 in triplex single-acting pump pumpíng water at 1000 PSI. The lower trace is the cylinder pressure obtained from a transducer located in the center cylinder head. The upper trace is the output of an accelerometer attached to the discharge pipe at the point of maximum vibration. From this chart it was determined that the basic speed of the pump was 133 RPM, generating the following numerical and pressure frequencies: Basic pump speed, 133 RPM (2.2 Hz). Discharge pipe víbration frequency, 25 Hz. Pulse frequency of triplex single-acting pump, 13.3 Hz (Almost second harmonic of pump pulsation frequency. Slight difference provides phasing as shown in the periodic nature of the pipe vibration frequency.)
The test involved a 3 X 6 in triplex single-acting pump with a valve spring POSIVA of 4 anda discharge pressure of 1400 PSI. The controlled suction pressure was measured by a damped Bourdon tube pressure gauge, and the suction pressure was controlled by a throttling valve. In order for these oscillographs to be presented in a form that will allow direct comparison, they have been rather congested, and sorne further explanation may be needed. The graphs are arranged vertically by decreasing suction pressure and horizontally by increasing speed as shown at the top of each column. Each graph is labeled with its associated volumetric efficiency. Figure 12.6 is for a 90-ft long suction pipe and Figure 12.7 is for a 10-ft suction.
12.4
MISCEllANEOUS WAVEFORMS (OSCILLOGRAPHS)
The typical self-described oscillographs included here as Figures 12. 8-12 .17 show the variations of pressure waveform shapes generated by different operating conditions. It should be noted that in many of these waveforms the suction and dis-
12.4 MISCELLANEOUS WAVEFORMS (OSCILLOGRAPHS)
391
Frequency, Hz
Figure 12.5. Vibration nomograph. Arrows indicate direction of lines.
charge traces are aligned with the cylinder trace, which is usually shown. In other words, any disturbance in the suction or discharge can be related to a particular position of the crank rotation by reference to the cylinder trace. For example, in Figure 12.8 the marked disturbances (pressure spikes) in the suction can be related either to a flow or acceleration peak as shown. Without a suction stabilizer and with a "good" suction head (upper left), an acceleration spike is identified as such because it occurs immediately at the start of a suction stroke in the cylinder trace immediately above. To show how the disturbances can change when the suction head is reduced to 2 ft (lower left), the acceleration spike has disappeared and a flow variation spike has replaced it as a major disturbance occurring at a point of maximum flow.
100 RPM
1 1 1 1
98% VE
1 ,. ! . i
, , .
1 1 1 1 ; 1 1 1
1 ¡
200 RPM
;
'·i
1 1
1
¡j,. .
.f1tv-I;
1>. •
:S7I ~.. !J f
I~
¡
1
.
1
1 1 '
¡¡
1 ,
: 1 ; 1 ·t 1 .
i 1 ;. 1 i ' il..1 1ll: i 1~ 1-
1
frr
!- :
1 1 ,1
1
vE.
• .. I· ~ 1 ¡ 1 1
1 ! :
1 1
1 1 1 1 11.~ ~ .1f., 1
1
ni:
---1. . 1. 1.....1_.... 1· ....·--·i..... · 1J_1.
·O PSI
99.6%
F ·-t--=:d :
v __ : ~...:....'
,~.. .r. "T ~-' 1: • • ((..¡_ ·-'- · .-. ,_._ -· - . -~ - -
~: 96% VE
\: _..,. n
•
:
,, ; ' ' '! . lllt. . ·-,- i ··~-~
t·ttff.~
: ~·97.5% VE1-,1~~;:::t.' 97.5%
! I'
;1.
i. ¡ ! /.i 1 ºiJ i.J7!'H'l
•
360 RPM
91.2%V - - ·-"--. 97% VE,
1
~ ~ .. '
r u
1 l , L.1. 1 1 1 ¡ YI
,
300 RPM
' . ,_j
i ;
¡ lJ.,,J
¡·¡ f"tl_Jfi- _f¡ iJi·tn
:·-~ 97.5% ! ' ! I~ . ¡., . , ! : 1" ¡, 1: 1 1 ¡ 1 1 1 h 1'"' l.
vr..·
' ;
1 ,;
1
1 .
• .;
1 1 11 1 1 i . ! 1 ..1 1111!
1 1 '
. . ¡
. i
1:
l:. ¡
93.BXV, 1 ; :
¡
1
.
i
1
~
l L..:..J
WlJ trrr ~r-r.1 rJti
98.1% VE _·_:"'......!. 97 '. 4% vt ~~' 80% VE
-r--· '
-
·1- - -~ . ! . - .___j_ =-·
-
.;
\
----==11
l==~,·=·=-;~:~·-:......,.._r:::::.::=: l=d!~-.t.J.L·-~i....:.._,_...:...::=I==-;_.;__.· _;..._~:;;_¡:~;"-·-,___/\,.___./._;_ :-·t 1 -~-.:...·~t--""11'! 1 i 1 ¡-,- ~¡ ¡ 1 ~ ,,,.._1¡__,
;-1:
N
-5 PSI
- - -L9f.5X VE -·- - :.. 95% VE;-:,.--;-· ;
-_
_c1 ·:
T
~-
--- ·- '.- ......:.
.--~~-· - L--··
COMPLETE CAVITATION
Figure 12.6 Long Suction Pipe. Oscillographs at various RPMs and suction pressures. Typical cylinder and inlet (suction) pressure waveforms for 3 x 6 in triplex single-acting plunger pump. 4 POSIVA valve spring load. Vertical scale (suction): JO PSI per division. Suction system: 90 ft of 4-in pipe. RPM, suction pressure, and volumetric efficiency noted.
392
100 RPM
200 RPM
300 RPM
SPACE COMPLETE CAVITATION
N - NOISE
1
1
TOP TRACE CYLINDER PRESSURE
- - 7 • 5 PSI·
:f 11 ¡ tf)l
N : ·: /
Figure 12. 7 Short Suction Pipe. Oscillographs at various RPMs and suction pressures. Typical cylinder and inlet (suction) pressure waveforms for 3 X 6 in triplex single-acting plunger pump. 4 POSIVA valve spring load. Vertical scale: IO PSI per division. Suction system: 8 ft of 4-in pipe. RPM, suction pressure, and vo!umetric efficiency noted.
393
Figure 12.8. Oscillographs of pressure waveforms. Left: No suctioh stabilization. Right: with 30-gal suction stabilizer. Top: Suction head, 14 ft. Bottom: Suction head, 2 ft. This series of oscillographs show how maximum disturbance (arrow A) is caused by "acceleration" at start of suction stroke as marked by cy linder trace above that trace and at "valley" in the theoretical fiow pattem plotted below each card. After lowering the suction head to 2 ft, lower left, the arrow B shows the predorninant spike is now a "flow" -induced disturbance because it occurs at a peak in the plotted ftow. Upper-right card (arrow C) shows how the "acceleration" spike has been drastically reduced by the use of a suction stabilizer. The "flow" spike at lower right (arrow D) showed that the stabilizer reduces the "flow" disturbances somewhat also.
394
(a)
(b)
Figure 12.9. Oscillographs of pressure waveforms. (a) Unrealistic "butterfty" type of trace produced by natural frequency of vibration or cavity resonance of the particular transducer, havihg a small cavity between the connection and the sensing element. lt can be recognized by the symmetrical shape above and below the average and the fuzziness produced by the extremely high frequency (in this case about 3000 Hz). (b) Actual suction pressure waveform in the same pump, operating under the same conditons, but obtained with another (nonresonant) transducer with the sensing element flush with the liquid.
395
(a)
(b)
Figure 12.10. Oscillographs of pressure wavefonns. Suction pressure trace of 5 X 8-in quintuplex plunger pump. (a) Pump not equipped with suction stabilizer. Note typical "cavitation" wavefonn with sharp upward spikes and rounded bottoms. Also note extreme pressure excursion in an upward or positive direction while the bottom of the trace is prevented from extending into the negative region by the fonnation of vapor. 63 PSI peak-topeak. (b) Same pump with suction stabilizer, same operating conditions. Note the "clean" sine wave and high frequency typical of "good" suction. The low-frequency cycles, over which the high frequency is imposed, is the remnant of pump rotation-generated cycles. While this flow-induced pulsation is not serious, it could have been reduced by the use of a properly gas-charged bladder in the stabilizer. 13 PSI peak-to-peak.
396
AT PLW INLET WITl-OUT STABlllZER
"BEFORE"
(GA!N ·• 57 PSI/IN)
UPSTREN1 OF STABIL!ZER
11AFTER" AT PLW INLET WITH STABIL!ZER
(GAJN - 126 PSI/IN) 1
Figure 12.11. Oscillographs of pressure waveforms. "Before" and "after" test results ali flow and acceleration showing the effects of a suction stabilizer that is almost disturbances in the suction system of a reciprocating pump. This particular test was made with a 60-gallon stabilizer of the type shown in Fig. 4.9, Chapter 4 on a 6 X 8-in triplex pump at 3000 PSI discharge and 30 PSI suction.
3"
:X
6"
28% PULSATION
TRIPLEX
800 PSI
NOTE SIX FLOW
DISTURBAN~ES
PER REVOLUTION
ONE PUMP REVOLUTION
3n X 5t~ QUINTUPLEX
10% PULSATION
NOTE 15 FLOW DISTURBANCES PER REVOLIJTION
Figure 12.12. Oscillographs of pressure waveforms. Nondampened discharge pressure waveforms. Not shown is the duplex double-acting pump with four flow-disturbances per revolution.
397
PSI
---,,..,..,..?-psr 2828 PSI
DISCHARGE PRESSURE,PSI
264 PSI
PSI 2828 PSI
CYLINDER PRESSURE,PSI
SUCTION PRESSURE, PSI. (a)
t.P = 38 PSI) 94 PSI ~ SUCTION PRESSURE AT INLET, PSI
80 PSI 66 PSI (b)
Figure 12.13. Oscillographs of pressure waveforms, showing the presence of high-frequency pressure waves in the suction, cylinder, and discharge of a quintuplex plunger pump. (a) Cylinder and discharge pressure waveforms. Only remnants of flow-induced, low-frequency pulsations appear in the discharge. Major pressure excursions in both suction and discharge are high-frequency, acceleration-induced. ( b) Cylinder and suction pressure waveforms. He re the predominant pulsations are of the high-frequency, acceleration-induced type.
398
PUMP DATA:
FREQUENCIES PRESENT:
4! x 9-in quintuplex 184 RPM 2800 PSI discharge 80 PSI suction
Rotational, 3.1 Hz Cylinder, 15.3 Hz Flow pulse, 31 Hz Acceleration, discharge, 138 Hz Acceleration, suction, 77 Hz
!~ _, r.6"
Figure 12.14. Oscillographs of pressure wavefonns. Typical pressure wavefonn of highvapor-pressure liquid (ethylene). Pressure wavefonn of cylinder and suction pressure. Of extreme interest is the shape of the cylinder wavefonn. The effect of vaporization of the liquid in the cylinder due to heat transmitted through uninsulated cylinder drain fittings, being manifested by the low volumetric efficiency indicated by the length of the delivery portion of the wavefonn being considerably shorter than the suction portion. Note the plateau at the critica! pressure of 700 PSI, which prevails until the cylinder pressure builds up to the discharge pressure of 1000 PSI. This demonstrates how a pressure wavefonn can be used to estimate the volumetric efficiency of a pump. Determine the full-stroke length by scaling from one obvious point on the wavefonn to another, in this case, 2 in. Accordingly, a full delivery stroke would theoretically be 1 in, but the actual delivery is measured as 0.6 in. Therefore, the volumetric efficiency is about 60 percent.
399
DISCHARGE PRESSURE
PULSATION PERCENT
llP
114 PSI
68 PSI
46 PSI
3.8
2.3 %
1.5 %
Figure 12.15. Oscillographs of pressure waveforms. Oscillographs taken at intervals to show the "phasing" or in-and-out of step of multiple pump pulsations, whereby the pulses tend to "add" for a short period of time and then tend to "subtract" for another period of time. It is impossible to prevent pumps from such phasing. Regardless of the pump drive ratios, there will be repeated periods of phasing.
400
294 PSI
94 PSI or 47% Overshoot ,----0
Rise time; .0052 sec, .109 sec/rev (a)
PSI PSI 106 PSI or 4,5% Overshoot
_ _ _ _ __._..3~4...,3 sec/rev (b)
Figure 12.16. Oscillographs ofpressure waveforms. (a) Triplex single-acting pump, .708 X .945 in, 550 RPM. (b) Triplex single acting pump, 6 X 8 in, 175 RPM. These show actual typical cylinder pressure "overshoot" amplitude and rise time of two triplex pumps differing greatly in size and speed. The overshoot is related to time rise (pump speed) but can also be present at slow speed with low NPSHA.
401
402
INSTRUMENTATION
t •I!!!~ -~~ 1111••1•••••1111 :1111•·-···· r l
1/2
STROKE
ONE STROKEJ
:1
~~il6~R~ALF
STROKE
92% VE
-·--CYLINDER
.llJl'•••r•••llli---22_so_p_sr_A_vE_. (a)
DELIVERY 81% OF
ONE STROKE
HALF STROKE_. . .
~~
1111.iM.• •
HALF STROKE
••
·--·--CY-LI-ND_ER_
-~··•L••··~
1000 PSI AVE.
~-·•llliiiiiiilll--.-
-
(b)
Figure 12.17. Oscillographs of pressure waveforms. (a) Typical cylinder pressure waveform of liquid containing little dissolved gas. Note approximate square wave with abrupt rise in pressure at beginning of delivery stroke. Single-acting quintuplex pump pumping water (boronated with hydrogen blanket), 105 ºF, 226 RPM. ( b) Typical cylinder pressure containing a large amount of "free" gas. Note compression type of pressure rise at beginning of delivery stroke. Free gas in cylinder must be compressed to. discharge pressure befare liquid can be delivered. Note low VE caused by dissolved gas. 2ft X 10-in doubleacting duplex pumping crude oil with gas. Ambient temperature; 82 RPM. Suction-charged with centrifuga! pump, 30 PSI.
12.5
OPTICAL PHASER
A useful device to be used in conjunction with oscillograph displays of waveforms generated by a reciprocating pump is a simple light-sensitive pickup or phaser positioned to view a white sticker placed on any visible reciprocating part of the pump. The end-of-stroke blip can be related to any secondary trace recorded on a dual-trace oscilloscope as shown in Figure 12. IA.
403
12.6 POSITIONING STRAIN GAGES TO MONITOR TORSIONAL LOADS
: One pump revolution 1
1
....... ¡. P~~·~· ;t~~k!e-: -s-
1 CC·E-)
...
Pump
1 1 1
1- 1
1
Harker blip, end-o'-st;oke 1 l . ¡ ¡ 1; : 1 · De ay, suct1on ' Delay, discharge -1,..._,,.valve closing 1 valvs closing
~
kt-
1
1
1
Delay,
co~pressior.
; 1
JI
__ ~
••
...L l
¡.
1
ir
1
1
1
1
. . . . '••.• 1
1
1
1
:
1
1
1
~
1
1 1 1 1
¡
¡
1
• Dela y ,1 decompress1on
.....
·r---·- -.. ·-¡- --. -
•
,. _. r
-
1 ·¡·
-
1
• - ......... I
1
-
1
1 1
_J _________,l ... .:......
l
~ 1
f
Figure 12.IA. Use of Optical Phaser to Mark End of Mechanical Stroke.
12.6 POSITIONING STRAIN GAGES TO MONITOR TORSIONAL LOADS To measure minute strains one must be capable of measuring minute resistance changes. The Wheatstone Bridge configuration as shown in Figure 12.2A is capable of measuring these small resistance changes. Note the signs associated with each gage numbered 1 through 4. The total strain is always the algebraic sum of the four strains. The total strain is represented by a change in "V" out. If each gage had the same positive strain, the total would be zero and "V" out would remain unchanged. Bending, Axial, and Shear strain make up the most common types of
404
INSTRUMENTATION
V In
Reguloted
DC
V out
+
Figure 12.2A. Wheatstone bridge
strain measurements. The actual arrangement of the strain gages will determine the type of strain measured and the output voltage change. TORSIONAL STRAIN (y) equals torsional stress (T) divided by torsional modulus of elasticity (G). See Figure i 2.3A and Equations (12.1) and (12.3). Where torsional stress (r) equals the torque (M,) multiplied by the distance from the center of section to outer fiber (d/2) divided by (J) the polar moment of inertia. The polar moment of inertia is a function of the cross sectional area. For solid circular shafts only see Equation (12.7). The modulus of shear strain (G) has been defined in the preceding discussion on shear stress. Strain gages can be used to determine torsional moment (M,), from which can be calculated in Equation (l 2.6). T
"'=2Xe = '
'
Where e, = e 1 1'
MT
=
MT
=
r(J)
) =
(12.3)
'}'G(J)
L
G(J)
2nNMT/33,000
J = 7T(d) 4 /64
(~)
yG( 1TD 3 / ! 6)
(12.4)
(12.5) (12.6)
( 12.7)
12.8 MEASURING PRESSURE DROP BY OSCILLOSCOPE
405
180 DEGREE ROSETTE STRA!N GAGES
11 4
y
.---~4--~li\_-. ~Jb-~=-~)=-~--- z
3
(
7
2 MT
L
1
\~
L
y Figure 12.3A. Torsional strain
y-Torsional strain, uinch/inch E-Normal strain, uinch/inch r-Torsiona! Stress, lbf/inch 2 G-Modulus of Elasticity, Shear, lb/inch 2 M-Moment, Torque, lb.ft D-Diameter shaft, inches J-Polar Moment of Inertia, inches 4 -Angle, radians L-Length of shaft 1.mder stress, inches BHP-Brake Horsepower N-RPM
12.7
DAMPED PRESSURE GAUGE
The series of oscillographs in Figure l2.4A serve to show that a properly "damped" pressure gauge of the bourdon tube type wil! show the approximate "average" pressure of a complex pressure wave. This aspect is important in the measurement of suction pressures with the presence of standing waves generated by acceleration, where the "average" only of that pressure, is indicated.
12.8
MEASURING PRESSURE DROP BY OSCILLOSCOPE
The ability of sorne dual-trace oscilloscopes to invert one of the pressure traces allows one to display the pressure drop of two complex pressure waves as shown in Figure 12º5Aº
------.-----MAXIMUM
-----·-;
--------
M!:Al<
M'.NIMIJM
STATIC OR: INLE'T GAUGE :
_JER!J.......
. PS_IG
- - - - - - ; - - - - - - - - - - - - : - O. 7 PS ¡-;.- O. 75 PS IG L,__ _ _ __;__ _ _ _ _ _ _
SCOPE - 5 PSI P':':F
l SUCTI!JN
, ~
-'--------'--------
J:.:s:mi
0.7 PSi-:- O PS!G
- - - - - - ·-------.:..- - - - - - - - - - · - 2 SUCTION
200 PSIG
O PSI
SCOPE -
3 DISCHARGE
16~
"'S: PER
::~ISIDN
' 1
-
5.6 PSI
'3.0 "'SIG 1
-·--------'-· - - - - - - - ·-----~ - - -----;! 4 SUCTHJN
SCCPE • 7.7 PSI
.4 PSi PER ClVISIDN
1 1
SEE 7 3.0 PSIG
BELD~'
O PSI --'---
5 :SUCTIIJN
SCDPE - 1.4 PSI PER DIV!S!DN
1
---'--------'
! 1 1 1
1
2.0 PSI
6 :SUCTIDN
2..0 PSIG
~~---=J
SCDPE l .4 PSI PER DIV!SIDN
!NTEGRAT
_r_N~-. A_MP~l F!ER ... ¡
3. 4 P S I - - - - - - - - - - - - -
'7 SUCTHJN
SCDPE - 1.4 PSI PER DIV!SION
Figure l2.4A. Accuracy of Damped Pressure Gauge Readings
406
i
3.0 PSIG
----------....---B
.....
LDV
e 6 4 2
1------'····A ....+.... 8 ............~~~~1
o DUAL TRACE SCOPE
···················¡:,-Rfs.SúRE .. riR.i:if=>················· 3
.. ·········
......................... A..................................... .
8 6
-e .........
4
·························~--·················
t------C. ......
-----t
7" ...
+
B
!
A - Bl
._._._._._.__ ._._._._·_·_·_-_._._._._._._._._._._E:::::::::.: ..:"""""""-"""".·"""""""""".
2
o -2 -4 -6
RECORD A AND B AS POSITIVE
ADD A
-8 PRESSURE
t----- 4000), the friction factor depends not only upon the Reynolds number but also upon the relative roughness, e/ D, the roughness of the pipe walls (e), as compared to the diameter of the pipe ( D). For very smooth pipes such as drawn brass tubing and glass, the friction factor decreases more rapidly with increasing Reynolds number than for pipe with comparatively rough walls. Since the character of the interna! surface of commercial pipe is practically independent of the diameter, the roughness of the walls has a greater effect on the friction factor in the small sizes. Consequently, pipe of small diameter will approach the very rough condition and, in general, will have higher friction factors than large pipe of the same material. The most useful and widely accepted data of friction factors for use with the Darcy formula have been presented by L. F. Moody* and are reproduced in Figures 13.11-13.13. Professor Moody improved upon the well-established Pigott and Kemlert friction factor diagram, incorporating more recent investigations and developments of many outstanding scientists. The friction factor ,J, is plotted in Figure 13 .12 on the basis of relative roughness obtained from the chartjn Figure 13.13 and the Reynolds number. The value off is determined by horizontal projection from the intersection of the e/ D curve under consideration with the calculated Reynolds number to the left hand vertical scale of the chart in Figure 13 .13. Since most calculations involve commercial steel or wrought iron pipe, the chart in Figure 13.12 is furnished for a more direction solution. It should be kept in mind that these figures apply to clean new pipe.
Effect of Age and Use on Pipe Friction Friction loss in pipe is sensitive to changes in diameter and roughness of pipe. For a given rate of flow anda fixed friction factor, the pressure drop per foot of pipe varíes inversely witli the fifth power of the diameter. Therefore, a 2 % reduction of diameter causes a 10% increase in pressure drop; a 5% reduction of diameter increases pressure drop 23 %. In many services, the interior of pipe becomes en*L. F. Moody, ''Friction Factors for Pipe Flow,'' Transactions of the American Society of Mechanical Engineers, Volume 66, pages 671-678, November 1944. tR. J. S. Pigott, "The Flow of Fluids in Closed Conduits," Mechanical Engineering, Volume 55, No. 8, page 497, August 1933; E. Kemler, "A Study of Data on the Flow of Fluids in Pipes," Transactions ofthe American Society of Mechanical Engineers,.Volume 55, page HYD-55-2, 1933.
13.7
FLOW THROUGH NOZZLES AND ORIFICES
419
crusted with scale, dirt, tubercules or other matter; thus, it is often prudent to make allowance for expected diameter changes. Authorities point out that roughness may be expected to increase with use (due the pipe material and nature to corrosion or incrustation) at a rate determined of the fluid.
13. 7
FLOW THROUGH NOZZLES AND ORIFICES
The discharge of fluids through nozzles and orifices has been subject to continued investigation and, as a result, well-established data are still being supplemented. A portion of the subject is covered on these facing pages but more complete references will be found from the data supplied by meter manufacturers. The rate of flow of any fluid through an orifice or nozzle, neglecting the velocity of approach, may be expressed by: ( 13.6) Velocity of approach may have considerable effect on the quantity discharged through a nozzle or orifice. The factor correcting for velocity of approach,
may be incorporated in Equation (13.6) as follows:
(13.7)
The quantity
is defined as the flow coefficient C. Values of C for nozzles and orifices are shown in Figure 13 .14 and 13 .15. U se of the ftow coefficient C eliminates the necessity for calculating the velocity of approach, and Equation (13.7) may now be written:
q
=
r;;:-;-
CA v2ghL
=
[2;( 144) L:i. p
CA~ -"'-·~P~-
(13.8)
420
THEORY OF FLOW IN PIPE
Orífices and nozzles are normally used in piping systems as metering devices and are installed wíth fiange taps or pipe_ taps in accordance with ASME specifications. The values of h¿ and ll.P in Equation (13.8) are the measured differential static head or pressure across flange taps when values of C. The fl.ow coefficient C is plotted for Reynolds numbers based on the intemal diameter of the upstream pipe.
Flow of liquids For nozzles and orifices discharging incompressible fl.uids to atmosphere, C values may be taken from Figure 13.14 if hL or !lP in Equation (13.8) is taken as the upstream head or gauge pressure. For most conditions of flow of fl.uids having a low viscosity, i.e., water, gasoline, etc., the Reynolds number need not be calculated since it will fall in the range of the values in Figure 13 .14, where the flow coefficient C is a constant.
13.8
PRESSURE DROP ANO VELOCITY IN PIPING SYSTEM
Example 13.1 Bemoulll's Theorem-Water Given: Water at 60 F is fl.owing through the piping system, shown in [Fig. 13.7], at a rate of 400 gallons per minute. Find: The velocity in both the 4 and 5-inch pipe sizes and the pressure differential between gauges P 1 and P2 •
Solution: 1. Use Bemoulli's theorem: Z¡
144P
vf
144P?
v~
Pi
2g
P2
2g
+ - -1 + - = Z2 + --- + - +
5" Welding Elbow
h
L
P,
5" Schedule 40 Pipe
4" Schedule 40 Pipe P,
FLOW
5" Schedule 40 Pipe
Eltva.!i2!Jl::1.:. O
-!-,....__;;;_,;11.-..ll..,..
The empirical relation between Saybolt Universal Viscosity and Saybolt Furo! Viscosity at 100 F and 122 F, respectively. and Kinematic Vi'scosity is taken from A.S.T.M, D2161-63T. At other temperatures, the 3aybolt Viscosities va1·y only slightly.
µ.
100 10--~-
.01
Saybolt Universa! Seconds Centistokes x 4.6347 Sayboit Furo! Seconds = Centistokes x 0.4717
1000 90~ -80 700 600
.01 .009 .008 .007 .006 .005 200 35
60---.
s
!
¡¡¡
(_)
10
20
-;j'. .0004
10
20
o:
z::l
--
1.50
...
~
~
-
----
0.92 4
68105
2
/l,. - Reynolds Number based on
4
68106
d2
Figure 13.14. Flow coefficient C for nozzles (data from "Fluid Meters, Part I," 4th edition, American Society of Mechanical Engineers, 1937).
e
1ij
e
M75 Ñ o.55
... ~',,' , 2
.625 1.&0
~
~
6810'
Qj
1il
0.94
2
-~ .s
675 a..
-~
L.--
!ij
a
45 40 JI
0.20
o
~ "' o::
Korifice
~
132
1 C2 4
/3
e for square-edge
Flow-
e 1.3 1
l. 2 l.
,.._ ....__
d,
=~·;¡;-=.SO
_.__
·-¡-
1.0
o. 9 1 1
o. 8
¡
,/
I\\
-.70 =.65 =.60 =.50
.~
I~ v ... "' __.. __.. I~ ~ v" t:-¡,.... 1/
~¡,,
,, [A
~ ~
/
..--
--..........
--
~
~
'
\
1\ \~ !'--...._ r--."f'....."- !"-.... ,... ........ r-- ~ r-t:'t--r--..._
~
-i-
l./~
-~
t--
~
175 r--;;::: ~V/1 f.-._
r-- t-- ,.... ....
,._ ...
11
"" ~ 8 \:: ,____
v"~
0.5 0.4
/
=.75
,/
0.7 0.6
17 ./
11
d,
~o-d;
= 401-
~
= =
.301- (_/ o ... :
~
6
'¿Q
8 10
4Q60BOJ02
4
6
4
8 10'
6 8 10•
Rr - Reynolds Number based on d 2
--
0.78 0.76
-
0.7 4
-
0.71
--,_ --¡...._
j
..._
·º.75 º.,
r-- ¡...._ t--
L
o.115f
-¡..
o.70 ~
0.7o
.,
~
1---~
0.68
r--..__
o.60
...___
o.55 'O o.50 ~ o.45 &;
0.66 0.64 .0.61 0.60 0.58
1
-
~
e16
...._
o.65
-~
fl
~
o
~.40 0.30
I' 0.10 6
8 10•
6
8 10'
6
8 10•
R,. - Reynolds Number based on d 2
Figure 13.15. Flow coefficient C for square-edge orífices (data from "Fluid Meters, Part 1," 4th edition, American Society of Mechanical Engineers, 1937; G. L. Tuve and R. E.
Sprenkle, "Orífice Coefficients for Viscous Liquids," Instruments, p. 201, November 1933). 434
Q
q
20 000
r w
8 000
·1 10
-JO 000
·ª 000
10
6 000 .
B
4 000
6 ~3000
Jnternal Pipe D1ameter, lnches
lndex
6
000
4 000 3 000
R,
lOOO
10 000 6000 4 000
2 llOO ¡ 000
000
llOO
400
300 ~
GOO
200
~
e
100 llO 50
~o ~ ~
w
~
"'
~
o
40 30
e
~~
-
!•
l 000 600 400
\
'~
10
¡::
70
-~m
65
fü
1 3/4
l.5
lll
1/1
"' ~
';; w
' ~
.02
200 100 50 40
~ ~
"
o
~
w
o \' •\
10
·-
IH-~o
lO
~
io
"'
~
·-
;,;: 2\\
.6
.4
f
.02
.03
.04
.o
~ Friction Factor !or Clea11
Stoel Pipe
11l-di
"
30-'l~
'
.2
"'
.!
.004 .003
.6 .4
.002l1
.3
.8
.6
.2
:!JO
300
3
~
3*
-;;
55
w
~ "-
©
¡¡¡
·-
-;;;
·;;
b
';; w
N
©
Z.i
!lJ ~ ~
-;;¡
w
·¡¡;
'
~
""
"" 10
1
.
45
JO
16
15
18 1{)
'!JO 500 6lllJ
"
~
"-
:
11 14
! .8
"-
,_,
·8
100
.006
6IJ
1.5 :;.
;;; .O!
o
©
~
9
.O! .008
U"I
p
3/4
l.O
~
·-
¡;:
lO 8
t
.6
.4 .5 .6 .7 .8
3 1
1000
.5
©
w
400-¡¡
~f
d
20 24
-14
Figure 13.16. Reynolds number for liquid flow friction factor for clean steel pipe.
40
TABLE 13.1. Equlvalents of Absolute (Dynamic) Vlscoslty TO OllTAIN - -
¡
Poise
~e
tPoundm Ft Sec
Grsm
*Pound¡ Sec
Cn;i. Sec
Ft'
Poundal Sec Ft'
~ (100 µ)
(µ',)
(µ,)
O.O!
2.09 (I0- 5)
6.72 (10-•)
l
2.09 (!O-•)
0.0672
47 90ll
479
1
g or 32.2
1487
14.87
l.or .0311
1
Centipoi1e
'.>lULTlPLY
Dyne Sec
1 C•ntipoi••
(µ)
'\"'" (µ) 11'.
Poi se Gram CmSec Dyne Sec
1
(100 µ)
100
~
1
Slugo Ft Sec
1
(µ'e)
•:Pound1 Sec
Ft•
1
tPoundm Ft Sec Poundal Sec
Ft'
(µ,)
1
1
1
1 1
fJ
1
*Pound¡= Pound of Force
To convert absolute or dynamic viscosity from one set of units to another, locate the given set of units in the left hand column and multiply the numerical value by the factor shown horizontally to the right under the set of units desired.
tpoundm = Pound of Mass
Asan example, suppose a given absolute viscosity of 1 poise is to be converted to slugs 1 foot second. By referring to the table, we find the conversion factor to be 2.og ( I0-3). Then, 2 (poise) times 2.og ( 1 o-3) = 4.18 (10-3) = 0.00418 slugs. foot second.
TABLE 13.2. Equivalents of Kinematic Viscosity TO OBTAI\;--
Centistokes
\!LLTIPLY
l Ceñtistokes
Stokes
Cm' Sec
BY
~ (,)
(,)
11'
Ft 2 Sec
(IOO ,)
(,')
0.01
1.076 (I0-5)
Stokeo
Cm' Sec Ft 2 Sec
(100 ,)
(/)
92 900
929
11
To convert kinematic viscosity from one set of units to another, locate the given set of units in the left hand column and multiply the numerical value by the factor shown horizontally to the right, under the set of units desired.
436
!.076 (10-')
100 11
As an example, suppose a given kinematic viscosity of o. 5 square foot.isecond is to be con verted to centistokes. By referring to the table, we, find the conversion factor to be g2,goo. Then, 0.5 (sq ft/sec) times q2,goo = 46,450 centistokes.
TABLE 13.3. Equlvalents of Klnematlc and Saybolt Universal Vlscoslty Kinernatic Viscosity, Centistokes V
1.83 2.0 4.0 6.0 8.0 10.0 15.0 20.0
TABLE 13.4. Equlvalents of Klnematlc and Saybolt Furol Vlscoslty Kinematic Viscosity,
Equivalent Saybolt Universal Viscosity, Sec At IOOF Basic Values
Centistokes
32.13 32.85 39.41
45.56 52.09 58.91 77.39 97.77
45.88 52.45 59.32 77.93 98.45
At 122 F
At 210 F
48 50 60
25.3 26.1 30.6
25.2 29.8
70 80 90
35.1 39.6 44.1
34.4 39.0 43.7
100 125 150 175
48.6 60.1 71.7 83.8
48.3 60.1 71.8 83.7
200 225 250 275
95.0 106.7 118.4 130.1
95.6 107.5 119.4 131.4
300 325 350 375
141.8 153.6 165.3 177.0
143.5 155.5 167.6 179.7
400 425 450 475
188.8 200.6 212.4 224.1
191.8 204.0 216.1 228.3
500 525 550 575
135.9 247.7 259.5 271.3
240.5 252.8 265.0 277.2
600 625 650 675
283.1 294.9 306.7 318.4
289.5 301.8 314.1 326.4
V
At 210 F
31.01 32.62 39.14
Equivalent Saybolt Furo! Viscosity, Sec
25.0 30.0 35.0 40.0 45.0
119.3 141.3 163.7 186.3 209.1
120.1 142.3 164.9 187.6 210.5
so.o
55.0 60.0 65.0 70.0
232.1 255.2 278.3 301.4 324.4
233.8 257.0 280.2 303.5 326.7
75.0 80.0 85.0 90.0 95.0
347.6 370.8 393.9 417.1 440.3
350.0 373.4 396.7 420.0 443.4
100.0 120.0 140.0 160.0 180.0
463.5 556.2 648.9 741.6 834.2
466.7 560.1 653.4
200.0 120.0 240.0 260.0 280.0
926.9 1019.6 1112.3 1205.0 1297.7
700 725 750 775
330.2 342.0 353.8 365.5
338.7 351.0 363.4 375.7
300.0 310.0 340.0 360.0 380.0
1390.4 1483.1 1575.8 1668.5 1761.1
800
815 850 875
377... 389.1 400.9 412.7
388.1 400.5 411.9 425.3
400.0 420.0 440.0 460.0 480.0 500.0
1853.9 1946.6 2039.3 1131.0 2224.7 1317.4
90Ó 925 950 975
414.5 436.3 448.1 459.9
437.7 450.1 461.5 474.9
1000 1025 1050 1075
471.7 483.5 495.1 507.0
487.4 499.8 512.3 524.8
Over 500
Saybolt Seconds equal Centistokes times 4.6347
1100 1125 1150 1175
518.8 530.6 542.4 554.1
537.1 549.7 561.2 574.7
1200 1225 1250 1175 1300
566.0 577.8 589.5 601.3 613.1
587.1 599.7 611.1 614.8 637.3
Over 1300
•
t
Saybolt Seconds equal Centistokes times 4.óó73
Note: To obtain the Saybolt Universal viscosity equivalent to a kinematic viscosity determined at
t,
multiply the equivalent Saybolt Universal viscosity at 100 F by 1+ (t - 100) 0.000 064. For example. 10 v at 210 F are equivalent to 58.91 multiplied by 1.0070 or 59.32 sec Saybolt Universal at 210 F. These tables are reprinted with the permission of the AmericanSociety for T esting Meteríais (ASTM) The table at the left was abstracted from Table 1, 02161-ó3T. The table at the right was abstracted . from Table 3, 02161-óH.
*OVER 1300 CENTISTOKES AT 122 F: Saybolt Fluid Sec = Centistokes x 0.4717 toVER 1300 CENTISTOKES AT 210 F: Log (Saybolt Furo! Sec - 2.87) 1.0276 ll.og (Centistokes)] - 0.3975
437
TABLE 13.5. Physical Properties of Water Temperature
of Water
Saturation P;ressure
1
t
P'
Degrees Fahrenheit
Pounds per Square Jnch Absolute
32
'
50 60
0.08859 0.12163 0.17796 0.25611
70 80 90 100
0.36292 0.50683 0.69813 0.94924
1
Specific Volume
v
1 1
1
1
Weight Density
Weight 1
p
1
1
Cubic Feet Per Pound
1
1
Pounds per Cubic Foot
Pounds Per Gallon
1
0.016021 0.016019 0.016023 0.016033
62.414 62.426 62.410 62.371
8.3436 8.3451 8.3430 8.3378
0.016050 0.016072 0.016099 0.016130
62.305° 62.220 62.116 61.9%
8.3290 8.3176 8.3037 8.2877
140
1.2750 1.6927 2.2230 2.8892
0.016165 0.016204 0.016247 0.016293
61.862 61.7132 61.550 &1.376
8.2698 8.2498 8.2280 8.2048
150 160 170 180 190
3.7184 4.7414 5.9926 7.5110 9.340
0.016343 0.016395 0.016451 0.016510 0.016572
61.188 60.994 60.787 60.569 60.343
8.1797 8.1537 8.1260 8.0969 8.0667
il.526 14.123 14.696 17.186
0.1)16637 0.016705 0.016719 0.016775
60.107 59.862 59.812 59.613
8.0351 8.0024 7.9957 7.9690
24.%8 35.427 49.200 67.005
0.016926 0.017089 0.017264 0.01745
59.081 58.517 57.924 57.307
7.8979 7.8226 7.7433 7.6608
134.604 247.259 422.55 680.86
0.01799 0.01864 0.01943 0.02043
55.586 53.648 51.467 48.948
7.4308 7.1717 6.8801 6.5433
45.956 42.301 37.397 27.307
6.1434 5.6548 4.9993 3.6505
40
110 120 130
1
200 210 212
220 240
260 280 300
350 400 450 501)
550
1
1
1045.43 1543.2 2208.4 3094.3
600
650 700
0.02176
0.02364 0.02674 0.03662
Specific gravity of water at
60
F = 1 .oo
Weight per gallan is based on 7.48052 gallons per cubic foot. All data on volume and pressure are abstracted from ASME Steam Tables (1967), with permission of publisher, The American Society of Mechanical Engineers, 345 East 47th Street, New York, N. Y. 10017. TABLE 13.6. Weight Density and Specific Gravity of Various liquids Liquid
Temp. Weight 1Specific Density Gravity 1
p
Deg
1cb~.- P~.r
Fahr.
óO 10 32 32 Brine, 10% Na Cl 1 32 BunkcrsCFue!Max. 60 Carbon Disulphide 32 Distillate 60 Fue! 3 Max. 60 Fue! 5 Min. 60 Fue! 5 Max. 60 Fue! 6 Min. 1 óO Gasolinc 60 Gasoline, Natural 60 Kerosene 60 M.C. Residuum 60 1
Ace tone 1 Ammonia,. Saturated Benzenc Brinc, IOC;~ Ca Cl
438
49.4 40.9
s
¡Temp.' Weight Specific Density Gravity p
1
I
0.792 0.656 0.899 1 !.091 1 1.078 1.014 80.6 1.292 1 52.99 1 0.850 56.02 0.898 60.23 0.966 61.92 0.993 1 1 0.993 1 61.92 0.751 46.81 0.680 42.42 0.815 50.85 0.935 58.32 1 1 Sb.I 68.05 67.24 63.25
Liquid
i Deg
Mercury Mercurv MercurY Mercury Mercury
Milk OliveOil Pentanc SAE 10 Lubej SAE 30 Lube! SAE 70 Lubet Sal t Creek Crude 32.6º API Crude 35 .6' API Crude 40' API Crude 48' AP! Crude
20 40 1
60 80
1
100
...
59 59 60 60 1 60 60 1 60 60 60 1
1
óO
s
1c~: ~tr
Fahr·.
1
1
1
849.74 848.03 113.623 13.596 846.32 !3.568 844.62 13.541 842.93 l '3:'.l.4 t 57.J 0.919 38.9 ' 0.624 54.M 0.876 56.02 0.898 57.12 0.916 52.56 1 0.843 53.77 0.862 52.81 0.847 0.825 51.45 49.16 1 0.788
TABLE 13.7. Equlvalents of Degrees API, Degrees Baumé, Speclflc Gravity, Welght Density, and Pounds per Gallon at 60 F /60 F Degrees on API or Baumé Se ale
o
2 4 6 8
Values for API Scale
Valuea for Baumé Scale Liquida Lighter Than Water
Oil Specific Gravity
Weight Density, Lb/Ft•
s
p
... ... ... ...
. .. ...
. ..
Pounds per-
~cific ravity
Gallon
s ... . .. ... ...
... ... ...
Weight Density, Lb/Ft•
Pounda
G~n
vity
s
p
Weight Density, Lb/Ft•
Pounda per Gallon
p
... . ..
...
... ...
... . .. . .. . .. ...
1.0000 1.0140 1.0284 1.0432 1.0584
62.36 63.24 64.14 65.06 66.01
8.337 8.454 8.574 8.697 8.824
...
...
Liquida Heavier Than Water ~ific
...
. .. ...
14 16 18
1.0000 0.9861 0.9725 0.9593 0.9465
62.36 61.50 60.65 59.83 59.03
8.337 8.221 8.108 7.998 7.891
1.0000 0.9859 0.9722 0.9589 0.9459
62.36 61.49 60.63 59.80 58.99
8.337 8.219 8.105 7.994 7.886
1.0741 1.0902 1.1069 1.1240 1.1417
66.99 67.99 69.03 70.10 71.20
8.955 9.089 9.228 9.371 9.518
20 22 24 26 28
0.9340 0.9218 0.9100 0.8984 0.8871
58.25 57.87 56.75 56.03 55.32
7.787 7.736 7.587 7.490 7.396
0.9333 0.9211 0.9091 0.8974 0.8861
58.20 57.44 56.70 55.97 55.26
7.781 7.679 7.579 7.482 7.387
1.1600 1.1789 1.1983 1.2185 1.2393
72.34 73.52 74.73 75.99 77.29
9.671 9.828 9.990 10.159 10.332
30 32 34 36 38
0.8762 0.8654 0.8550 0.8448 0.8348
54.64 53.97 53.32 52.69 52.06
7.305 7.215 7.128 7.043 6.960
0.8750 0.8642 0.8537 0.8434 0.8333
54.57 53.90 53.24 52.60 51.97
7.295 7.205 7.117 7.031 6.947
1.2609 1.2832 1.3063 1.3303 1.3551
78.64 80.03 81.47 82.96 84.51
10.512 10.698 10.891 11.091 11.297
40 42 44 46 48
0.8251 0.8155 0.8063 0.7972 0.7883
51.46 50.86 50.28 49.72 49.16
6.879 6.799 6.722 6.646 6.572
0.8235 0.8140 0.8046 0.7955 0.7865
51.36 50.76 50.18 49.61 49.05
6.865 6.786 6.708 6.632 6.557
1.3810 1.4078 1.4356 1.4646 1.4948
86.13 87.80 89.53 91.34 93.22
11.513 11.737 11.969 12.210 12.462
50 52 54 56 58
0.7796 0.7711 0.7628 0.7547 0.7467
48.62 48.09 47.57 47.07 46.57
6.499 6.429 6.359 6.292 6.225
0.7778 0.7692 0.7609 0.7527 0.7447
48.51 47.97 47.45 46.94 46.44
6.484 6.413 6.344 6.275 6.209
1.5263 1.5591 1.5934 1.6292 1.6667
95.19 97.23 99.37 101.60 103.94
12.725 12.998 13.284 13.583 13.895
60 62 64 66 68
0.7389 0.7313 0.7238 0.7165 0.7093
46.08 45.61 45.14 44.68 44.23
6.160 6.097 6.034 5.973 5.913
0.7368 0.7292 0.7216 0.7143 0.7071
45.95 45.48 45.00 44.55 44.10
6.143 6.079 6.016 5.955 5.895
1.7059 1.7470 1.7901 1.8354 1.8831
106.39 108.95 111.64 114.46 117.44
14.122 14.565 14.924 15.302 15.699
70 72 74 76 78
0.7022 0.6953 0.6886 0.6819 0.6754
43.79 43.36 42.94 42.53 42.12
5.854 5.797 5.741 5.685 5.631
0.7000 0.6931 0.6863 0.6796 0.6731
43.66 43.22 42.80 42.38 41.98
5.836 5.778 5.722 5.666 5.612
1.9333 ...
120.57
16.118
80 82 84 86 88
0.6690 0.6628 0.6566 0.6506 0.6446
41.72 41.33 40.95 40.57 40.20
5.577 5.526 5.474 5.424 5.374
0.6667 0.6604 0.6542 0.6482 0.6422
41.58 41.19 40.80 40.42 40.05
5.558
90 92 94 96 98 100
0.6388 0.6331 0.6275 0.6220 0.6166 0.6112
39.84 39.48 39.13 38.79 38.45 38.12
5.326 5.278 5.231 5.186 5.141 5.096
0.6364 0.6306 0.6250 0.6195 0.6140 0.6087
39.69 39.33 38.98 38.63 38.29 37.96
5.306 5.257 5.211 5.165 5.119 5.075
10 12
. ..
5.506 5.454 5.404 5.354
... ... ... ... ... ... ... ... ... ... ... ... ... ...
... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
...
... ... ...
...
. .. . .. . .. ... . .. ... ... ... . .. ...
439
TABLE 13.6. Commercial Wrought Steel Pipe Data (Schedule Wall Thickness-per ASA B36. Hl1950)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - .;¿·· ''~~]
Schedule Wall 'l'hicknes.-Per ASA 836.10-1950 Nominal Pipe Size
Outside Diarneter
Thickness
lnches
Inches
ln:hes
14 16 18 20 24 30
0.250 0.250 0.250 0.250 0.250 0.312
13.5 15.5 17.5 19.5 23.5 29.376
lnches 14 16 18 20 24 30
108 12 14 16 1!1 20 24 30
1
1
8.6251
Hl.75 12.75 14 Hi 18 20 24 30
0.250 0.250 0.250 0.312 0.312 0.312 0.375 0.375 0.500
Inside Diamete• 1
F~et
¡ 1
1.125 1.291 1.4583 l.625 1.958 2.448
Inside Diameter Functions (In lnches)
d'
18.12510.6771166.02 10.25 0.8542 105.06 12.25 13.376 15.376 17.376 19.250 23.25 29.00
1
182.25 240.25 306.25 380.25 552.25 862.95
1.021 150.06 l.lll 178.92 1.281 236.42 1.448 301.92 l.604 370.56 1.937 540.56 2.417 841.0
d'
1
536.38 1076.9 1838.3 2393.2
111038. 4359.3 22518. 32012. 55894. 91156. 1373i7. 292205. 707281.
7133.3 112568. 24389.
1
d'
1
33215. 57720. 93789. 144590. 304980. 744288.
13635.2 5246.3
1 8.6251 0.2771 8.07110.6726165.14
d'
1
2460.4 3723.9 5359.4 7414.9 12977. 25350.
1
1
448400. 894660. 1641309. 2819500.
7167030.
1
1
35409. 113141. 275855. 428185. 859442. 1583978. 2643352. 6793832. 20511149.
Sq.ª In.
1
143.14 188.69 240.53 298.65 433.74 677 .76
21864218.
~,~ >5
T:ransverse lnternal Area
Sq
~t. • ~;
0.994 l.311) l.670 2.074 3.012 4.707
, •.
151.8510.3601 82.52 117 .86 '140.52 185.69 237.13 29!.04 424.56 660.52
...
0.5731 0.8185 0.9758 1.290 l.647 2.021 2.948 4.587
•• ·;: ;·,,. ..i.> ;':../ •w
:":!
1
8 1 525.75 4243.2 34248. 1 51.1610.3553 ~ 10 10.75 0.307 10.136 0.8447 Hl2.74 1041.4 10555. 106987. 1 80.69 0.5603 . 1 12 12.75 0.330 12.09 1.0075 146.17 1767.2 21366. 258304. 114.80 0.7972 14 14 13.25 li.1042 175.56 2326.2 30821. 408394. l 137.88 0.9575 -~--+----7---~---'----'-"-----'------+------!---------'---'----!---.:...c:.__ ::;}' 16 16 0.375 15.25 1.2708 232 ..% 3546.6 54084. 824801. 182.65 1.268 18 18 0.438 17.124 293.23 5021.3 85984. 1472397. 230.30 1.599 20 20 o.soo 19.oo 1.5833 36i..oo 6859.o 130321. 2476099. 283.53 1.969 ·.;~ 24 24 0.562 22.876 1.9063 523.31 H971. 273853. 6264703. 411.00 2.854 .··~~-·-~¿; 30 30 0.625 28.75 2.3958 826.56 23764. 683201. 19642160. 649.18 4.508 .:.
0.375 l
l.4270
--;~-,-,~-;--,.-,.,..,......,....,~~;--~~;--~-;-~~--;~~~~..;--~~------;-~~~~~..;--~~-,-~~
% % %
1
0.0681
0.405 o.540 0.675
o.oss 0.091
0.26910.02241 o.364 0.0303 0.493 0.0411
0.07241 0.1325 0.2430
0.01951 o.o4&2 0.1198
0.0052421 0.01756 0.05905
0.00141 0.00639 0.02912
1'
0.05710.00040 :;:;i 0.104 o.ooon,:\¡;.i 0.191 0.00133 "~~j
!1 1 ~:~~ ~:!~~ 1~::i¡ 1~:~:~~1 ~:~~:91 ~:~~~~ 1 ~:!ii~ 1 ~:~~~~º U~j¡g:~~i~! .·~-~-· 1'
l 114,
1.315 l.660
11
0.133 0.14()
1.049 0.0874 l.380 0.1150
l.100 1.904
1.154 2.628
1.210 3.625
1.270 5.005
0.864 0.00600 ;¡¡ 1.495 0.01040 ';;.í
~112 1 t~ 1g:~~: 1~:~!~ 1g:~~~i1 !:~ii 1 ::~;: 1 ,g~~ 1 i~:~i5 1 ;:~~~ 1g:g~jl~ ~1.4'~
!Yz 5
;:¿:: g:i~~~
i::~ g:~~~
i1h
1
6
::~~
i~:~~~
!:= 1g:i;~ !:~~: 1g:5j~~1 ~~:~i 1 11.8.56 !~:~~~ 5.563 0.258 5.047 0.4206 25.47 1
li.625
0.280
6.065 0.5054
36.78
~~:!~!
~~t~!
1
~! 1~H~5 ltili1~u~;1rm~l!~n: 1tfüT 1i~¡~v ~:
i~ 8
HJ
1 ~::g
i~:g
1
i!
8.62510.40617.81310.6511 476.93 0.500 9.750 IJ.8125 61.04 95.06 926,86 5 ~!:~ ~:~~; g:~i: ~:~~~: ~~:~~ ~~~~:¿
116.0 18.0
20 24
20.0 24.0 0.405 0.540 il.675
%
~
1 1%
1
g:~:~ i~::~: ~ ::~;: ~r~:~ 1~~¡j: 5
10.75
16 18
l/s 1/.i
1g:~~ 1~:::: 1~:!~~3 1i~~:~ 1!~~::~
0.656114.68811.22401215.74 0.750 16.500 1.3750 272.25 13168.8 4492.l
0.812º 0.%8 1
o.0951 O.H9 0.126
18.376 l.5313 337.68 22.064 1.8387 486.82 o.21s 0.302 10.01791 0.0252 0.423 0.0353
o.04621 0.0912 0.1789
~:~:g 10.1471 0.54610.04551 0.29811 1.315 ~:~~: ~:~:; ~:~~~ ~:~~~ 1.660
0.191
1.278 0.1065
l.633
1
648.72 1352.8
223.10
1~~~i~:
i~~~!~: 3725.9 9036.4
1
m:~:
i~~~:2
1i~I~~~ l 1;~:~;~:
~~~~~:::
1
29113. 88110.
;¡;~:¿:
11222982. 683618.
114028. 23&9'!4.
2095342. 5229036.
0.009941
0.0275 0.0757
l
1i:~~~ g:g::~~ '.F;~I%~ 1
20.00610.1390
~t;
28.891 0.2006
!iUi;IH~~i :~!~
um c'~~l!~
1~~tig 1 402.07
2.7921
147.9410.332' 1 ,p, 74,66 0.51!15 ,c_,q¡ i~~:~~ g:~!~~ ·~\ll 0
1169.441 i.1766 'ti':j 213.83 1.4849·;~'..~: 265.21 382.35
l.8417 ,,,~·'. 2.6552;.~•.;
0.0011341 IJ.008317
0.0004591 ll.002513
o.0361 o.¡002s.·~·.·.~·.·. 0.072 O.
0.03200
0.01354
0.141 o.
~:!~~~ 1 0.8387 ~:~~~~61 0.8765 2.087
~:;~~ ~:g~i;~ ~)
3275. 8206.
146544 74120:
6205.2 10741.
.•
2ii:~
2.6667
~:~i:~21 0.719 ~:!~~1~:003oq~·.·.·.i._,_· 0.00499'}'°
0.8027 3.409
1.283
0.0089í%'¡i:: '
(confinued on rha next poge}
440
"\:~..,,~.:
-~'
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