Control Systems Engineering Exam Reference Manual: A Practical Study Guide, Third Edition [3 ed.] 9781941546567

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Cover Control Systems Engineer (CSE)

Control Systems Engineer

Control Systems Engineering Exam Reference Manual: A Practical Study Guide Third Edition For the NCEES Professional Engineering (PE) Licensing Examination Bryon Lewis, PE, CMfgE, CCNA

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Control Systems Engineering Exam Reference Manual: A Practical Study Guide Third Edition – A New Plant Design Approach For the NCEES Professional Engineering (PE) Licensing Examination Bryon Lewis, PE, CMfgE, CCNA

Controls engineering encompasses a broad range of industries: power, paper and pulp, pharmaceuticals, manufacturing and chemical plants. Although this third edition has been expanded to further include the many different applications used by all of the above, the book will focus on petrochemical applications. The Professional Engineer – Control Systems Engineer (CSE) examination tends to be concentrated toward the application of chemical and pharmaceutical plant design applications of code and control systems. I have tried to introduce the new upcoming engineer to the depth of knowledge they will need to acquire in order to tackle very large projects that may present themselves in the future of their career. I have tried to present a firsthand view of what a large plant looks like and how to break it down into small parts that are easily engineered and designed, while combining these many small parts into a large and complex working system that will run safe and smoothly.

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Cover Concept and Design by Bryon Lewis, PE, CMfgE, CCNA Copyright © 2016

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Notice from the Publisher

The information presented in this publication is for the general education of the reader. Because neither the author nor editor nor the publisher has any control over the use of the information by the reader, both the author and the publisher disclaim any and all liability of any kind arising out of such use. The reader is expected to exercise sound professional judgment in using any of the information presented in a particular application. Additionally, neither the author nor editor nor the publisher have investigated or considered the effect of any patents on the ability of the reader to use any of the information in a particular application. The reader is responsible for reviewing any possible patents that may affect any particular use of the information presented. Any references to commercial products in the work are cited as examples only. Neither the author nor the publisher endorses any referenced commercial product. Any trademarks or trade names referenced belong to the respective owner of the mark or name. Neither the author nor editor nor the publisher makes any representation regarding the availability of any referenced commercial product at any time. The manufacturer's instructions on use of any commercial product must be followed at all times, even if in conflict with the information in this publication.

Copyright © 2016 by ISA 67 Alexander Drive P.O. Box 12277 Research Triangle Park, NC 27709 All Rights Reserved ISBN: 978-1-941546-56-7

No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher.

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This Reference Manual Covers All Subject Content for the PE/CSE Examination This book thoroughly covers all subject content currently listed in the NCEES PE/CSE examination specifications for the Professional Engineer in the discipline of Control Systems Engineering as of 2016. This review reference manual encompasses 18 of the most important subjects that may be encountered in control systems engineering for the NCEES PE/CSE examination. I have compiled numerous college text book subjects into this one comprehensive guide. ISA offers books on most of these subjects that covers this information in extensive detail. The text book subjects covered in this manual are: Fluid Mechanics Fundamentals of Instrumentation Process Analyzers Control Valves Pressure Relief Valves Process Control Theory Digital Fundamentals Motor Controls Industrial Electronics Electrical System Design for Industrial Plants Fluid Power Systems Conveying Technology Fundamentals of Industrial Networking Process Technology ISA Documentation Standards Safety Instrumented Systems State and Federal Codes for Process Plant Installations Control Systems Design for Process and Manufacturing Plants

Plan Your Study Time If your only job is engineering and designing control systems, then you should be able to adequately prepare for the PE/CSE exam in 4 weeks. If you are very familiar with control systems, then you should be able to adequately prepare for the PE/CSE exam in 8 weeks. If you are new to control systems engineering and only have 4 years of experience, most of these subjects are not taught or covered in college. You should plan to spend a period of 12 to 18 weeks studying this review material to be thoroughly prepared for the PE/CSE examination. You should try to complete at least one module a week. This manual has 28 study modules. You may want to combine some of the smaller modules and study them at the same time, such as instrumentation subjects. With important subject modules like Safety Instrumented Systems (SIS) and documentation, you should plan on dedicating a significate amount of time to the subject. These subjects encompass a significate percentage of the time spent on questions when taking the CSE examination.

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Table of Contents Cover Control Systems Engineer (CSE) ................................................................................................ i

Notice from the Publisher .................................................................................................................... iii This Reference Manual Covers All Subject Content for the PE/CSE Examination ............................... iv Plan Your Study Time ........................................................................................................................... iv Table of Contents .................................................................................................................................... 1 Introduction to This Study Guide ........................................................................................................ 19

About the Author ................................................................................................................................ 19 People who have contributed to the previous editions of this manual ............................................. 20 Tips on How to Use This Study Guide ................................................................................................ 21

Using Thumbnails to Navigate ............................................................................................................ 22 Using Bookmarks to Navigate ............................................................................................................. 23 Important File Attachments - Open by clicking on the paper clip! ..................................................... 24 How to Print this Manual .................................................................................................................... 24 Welcome to Control Systems Engineering ........................................................................................ 25

Licensing as Professional Engineer / Control Systems Engineer (CSE)................................................ 25 Why Become a Professional Engineer?............................................................................................... 28 This is the third edition of this study manual...................................................................................... 30 The new and expanded sections include: ........................................................................................... 30 Recommended Flow Chart of Study for the CSE ............................................................................... 31

Overview of Recommended Flow Chart of Study for the CSE ............................................................ 32 Examination General Information........................................................................................................ 33

State Licensing Requirements ............................................................................................................. 33 Eligibility .............................................................................................................................................. 33 Exam schedule..................................................................................................................................... 33 Description of Examination ................................................................................................................. 34 Exam content ...................................................................................................................................... 34 I. Measurement ............................................................................................................................ 34 II. Signals, Transmission, and Networking..................................................................................... 35 III. Final Control Elements .............................................................................................................. 35 IV. Control Systems ........................................................................................................................ 36 V. Safety Systems .......................................................................................................................... 37 VI. Codes, Standards, Regulations ................................................................................................. 37 Exam Scoring ....................................................................................................................................... 37 Reference Materials for the Exam ....................................................................................................... 39

Recommended Books and Materials to Take to the Exam ................................................................. 39 Books and Materials for Testing ......................................................................................................... 40 Books for Additional Study ................................................................................................................. 40 Courses for Additional Study .............................................................................................................. 41 ISA Control Systems Engineer (CSE) PE Review .................................................................................. 41 Industrial Network Training ................................................................................................................ 41 Control Systems Engineer (CSE) Supplement Course ......................................................................... 42 Online Process Plant @ Learn Control Systems.com .......................................................................... 42

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Process Measurement Standards and Terminology ......................................................................... 43

Overview of process measurement, control and calibration ............................................................. 43 Process Signal and Calibration Terminology ....................................................................................... 44 Definition of the Range of an Instrument ........................................................................................... 44 Definition of the Span of an Instrument ............................................................................................. 45 Definition of the use of Zero in Instrumentation ................................................................................ 45 Live-Zero ........................................................................................................................................ 45 Elevated-Zero ................................................................................................................................. 45 Suppressed-Zero ............................................................................................................................ 45 Illustrations of range and span terminology ....................................................................................... 46 Illustrations of measured variable, measured signal, range and span ............................................... 47 Applications of Fluid Mechanics in Process Control ........................................................................ 49

Relationship of pressure and flow ...................................................................................................... 49 Applications of the formulas ............................................................................................................... 52 Summary of fluid mechanics for process control ............................................................................... 56 Temperature Measurement and Calibration ....................................................................................... 57

Temperature measurement devices and calibration.......................................................................... 57 Thermocouple - worked examples (how to read the thermocouple tables) ...................................... 59 RTD (Resistance Temperature Detector) ............................................................................................ 60 Installing RTDs and Thermocouples into a process stream ................................................................ 63 Typical RTD and thermocouple applications....................................................................................... 64 Pressure Measurement and Calibration ............................................................................................. 65

Pressure measurement and head pressure ........................................................................................ 65 Applying pressure measurement and signals - worked examples ...................................................... 66 Differential pressure and meter calibration ....................................................................................... 66 Pressure change in a pipe for a given flow rate .................................................................................. 67 Pressure change across the flow element for a given flow rate ......................................................... 67 Pressure calibration of transmitter ..................................................................................................... 68 Level Measurement and Calibration.................................................................................................... 69

Applying level measurement and calibration - Worked examples ..................................................... 69 Level displacer (Buoyancy) .................................................................................................................. 72 Bubbler level measurement ................................................................................................................ 74 Density measurement ......................................................................................................................... 75 Interface level measurement .............................................................................................................. 76 Radar and Ultrasonic level measurement ........................................................................................... 78 Time of flight technology ............................................................................................................... 78 Ultrasonic level measurement ....................................................................................................... 78 Radar (non-contact) ....................................................................................................................... 78 Guided Wave Radar (GWR)............................................................................................................ 79 Capacitance level measurement ........................................................................................................ 79 Radiometric (gamma) level measurement ......................................................................................... 80 Level gauging system in a tank farm .................................................................................................. 80 Calculating the volume in tanks .......................................................................................................... 81 Flow Measurement and Calibration..................................................................................................... 83

Applying flow measurement devices .................................................................................................. 83 Turndown ratio in a flow meter .......................................................................................................... 83 ISA standard flow meter symbols ....................................................................................................... 83 Flow meter applications chart ............................................................................................................ 84 2

Pressure tappings (Impulse Line Taps) ................................................................................................ 84 Orifice tap dimensions and impulse line connections ........................................................................ 85 Various Types of Flow Meters ............................................................................................................. 88 Applying the Bernoulli principle for flow control................................................................................ 89 Types of Head Pressure based meters ................................................................................................ 90 Venturi meter................................................................................................................................. 90 ISO 5167 Orifice Plate and Orifice plate ......................................................................................... 90 Dall tube ......................................................................................................................................... 90 Pitot-Static tube ............................................................................................................................. 90 Multi-hole pressure probe ............................................................................................................. 90 Cone meters ................................................................................................................................... 90 Annubar meters (also reference averaging pitot tubes) ............................................................... 91 Differential head meter calculations................................................................................................... 91 Classic fluid mechanics model............................................................................................................. 91 “K” value flow coefficients ............................................................................................................. 92 The beta ratio ...................................................................................................................................... 95 Pipe Size Is Important - Remember! .............................................................................................. 96 Standard Flow Measurement Equations............................................................................................. 97 Spink - Flow Measurement Equation .................................................................................................. 97 The basic Spink equation derived .................................................................................................. 98 The basic Spink equation for liquid ................................................................................................ 99 The basic Spink equation for gas and vapor .................................................................................. 99 The basic Spink equation for steam ............................................................................................... 99 Applications of the Beta and Spink factors ............................................................................... 100 Table 3 – The Spink Factor (S) ........................................................................................................... 101 ISO 5167 - Flow Measurement Equation .......................................................................................... 102 The expansibility factor ................................................................................................................ 102 The discharge coefficient ............................................................................................................. 103 The ISO 5167 equation explained ................................................................................................ 103 Solve for the Reynolds number ‘Re’ ............................................................................................ 104 Solve for the coefficient ‘C’ .......................................................................................................... 104 Solve for mass flow rate: ............................................................................................................. 105 Solve for volumetric flow rate ..................................................................................................... 105 Equation Comparison Summary .................................................................................................. 106 Sizing orifice type devices for flow measurement - worked examples............................................. 106 Mass flow measurement and control ............................................................................................... 109 Applying mass flow measurement with an orifice - worked example .............................................. 112 Turbine meter applications ............................................................................................................... 113 Turbine flow meter - worked example ........................................................................................ 116 Weight Measurement and Calibration ............................................................................................... 119

Weight measurement devices and calibration ................................................................................. 119 Load cells ........................................................................................................................................... 119 Load cells for (flow, level, force) applications in process ................................................................. 120 Process Analyzers .............................................................................................................................. 121

Electrical conductivity and pH correction ......................................................................................... 121 How are pH and electrical conductivity measured? ......................................................................... 121 Control of pH values in processes ..................................................................................................... 121 Typical pH correction control scheme ......................................................................................... 122 Control of conductivity...................................................................................................................... 123 Instrument specifications and operating parameters ................................................................. 123 3

Common Plant Analyzers .................................................................................................................. 123 Boiling Point Analyzers................................................................................................................. 123 Vacuum Distillation Analyzer ....................................................................................................... 123 Flash Point Analyzer ..................................................................................................................... 124 Cloud Point Analyzer .................................................................................................................... 124 Freeze Point Analyzer .................................................................................................................. 124 Pour Point Analyzer ..................................................................................................................... 124 Color Analyzer .............................................................................................................................. 124 Combustion and Analyzers................................................................................................................ 124 Combustion furnace and air-fuel ratio control ............................................................................ 125 Air-Fuel ratio control utilizing CO and O2 concentrations ........................................................... 125 BMS - Burner Management Safety .............................................................................................. 125 OSHA Requirements .................................................................................................................... 125 Carbon dioxide (CO2) reading ...................................................................................................... 126 Examples of Process Analyzers ......................................................................................................... 126 Select the appropriate analyzer and configuration .......................................................................... 127 Typical Analyzer Piping and Control Schematic ................................................................................ 128 Process Control Valves and Actuators ............................................................................................. 129

Process control valves ....................................................................................................................... 129 Considerations when sizing a control valve ...................................................................................... 130 Flow Coefficient Cv ...................................................................................................................... 130 Specific Gravity ............................................................................................................................ 130 Operating Conditions ................................................................................................................... 130 ISA standard valve symbols ............................................................................................................... 131 ISA standard pressure regulating valve symbols............................................................................... 131 Valve actuators.................................................................................................................................. 132 ISA standard actuator symbols .................................................................................................... 132 Limit switches on a valve - ISA standard symbol .............................................................................. 133 Calculating the size of the actuator ............................................................................................. 133 Example actuator sizing ............................................................................................................... 134 Split ranging control valves ............................................................................................................... 135 Valve positioner applications ............................................................................................................ 137 ISA standard valve positioner symbols ........................................................................................ 137 Summary of positioners ............................................................................................................... 138 When should a positioner be used? ............................................................................................ 138 Electrical positioners .................................................................................................................... 138 Control valve application comparison chart ..................................................................................... 139 Understanding flow with valve characteristics ................................................................................. 140 What is the ΔP for valve sizing? ................................................................................................... 140 System piping ΔP pressure drops................................................................................................. 140 Control valve ΔP pressure drop ................................................................................................... 141 Graph of the Inherent valve characteristics (off the shelf).......................................................... 142 Which valve characteristic trim to use?....................................................................................... 142 Characteristic distortion in valves................................................................................................ 143 Gain and Rangeability (turndown ratio in valves) ....................................................................... 145 Proper control valve sizing ............................................................................................................ 146 Oversized valves present problems ............................................................................................. 147 Experiment and understand Installed valve characteristics ........................................................ 149 Summary of control valve characteristics .................................................................................... 150 Control Valve Sizing ........................................................................................................................... 151 The Valve Sizing Equations.......................................................................................................... 151 4

The Basic equation for liquid flow ............................................................................................... 151 The basic equation for gas flow ................................................................................................... 151 The basic equation for steam flow .............................................................................................. 151 Sizing valves for liquid - worked example ......................................................................................... 153 Sizing valves for gas - worked example ............................................................................................. 155 Sizing valves for vapor and steam - worked example ....................................................................... 158 Sizing valves for two phase flow - worked example ......................................................................... 161 Two Phase Flow Worked Example ............................................................................................... 163 ΔP Valve Limitations - Very Important!............................................................................................ 165 Flowing Quantity (the turndown ratio of a valve) ....................................................................... 165 Flashing ........................................................................................................................................ 166 Joule-Thomson Effect (J-T) – auto refrigeration in valves ........................................................... 166 Choked Flow................................................................................................................................. 166 Maximum ΔP and Maximum Flow (qmax) in Valves Applications ...................................................... 167 Determining qmax (Maximum Flow Rate) ..................................................................................... 167 Determining ΔPmax (the Allowable Sizing Pressure Drop) ............................................................ 168 Cavitation in valves ...................................................................................................................... 169 Check for cavitation and choked flow in a control valves - worked examples ................................. 170 Fluid Velocities through Control Valves ............................................................................................ 174 Viscosity Correction for Sizing Valves ............................................................................................... 175 Pressure Relief Valves and Rupture Disks ....................................................................................... 177

Pressure Relief Valves (PRV) and Pressure Safety Valves (PSV) ........................................................ 177 Important Note: (Do Not Throttle Pressure Relief Valves) .......................................................... 177 EPA regulations ............................................................................................................................ 178 Regulation details ........................................................................................................................ 178 PRD bypass ................................................................................................................................... 179 Pilot operated safety valve .......................................................................................................... 180 Bellow or balanced bellow and diaphragm ................................................................................. 181 Weight loaded PRV operation ..................................................................................................... 181 Venting Atmospheric and Low-Pressure Storage Tanks ................................................................... 183 API Standards for pressure relieving systems ................................................................................... 186 CFR Standards for pressure relief required by federal law ............................................................... 187 API Standard 2000 – Venting atmospheric and low-pressure storage tanks .............................. 187 API Standard 2003 – Protection against ignitions from static, lightning, and stray currents ...... 188 API Standard 2350 – Overfill protection for storage tanks in petroleum facilities...................... 188 API Standard 2510 – Design and construction of LPG installations ............................................. 189 NFPA 30 – Flammable and combustible liquids code .................................................................. 190 Important excerpts from NFPA 30 code: .................................................................................. 190 Chapter 4: Tanks Storage .......................................................................................................... 190 Chapter 5: Piping Systems ......................................................................................................... 191 Chapter 6: Container and Portable Storage Tanks .................................................................... 191 Chapter 7: Operations ............................................................................................................... 192 ASME VIII code for sizing relief valves and rupture disks ............................................................ 193 Introduction to ASME VIII.......................................................................................................... 195 Overview Section VIII - Pressure Vessels................................................................................... 195 ASME VIII – Pressure relief requirements ................................................................................. 195 ASME VIII - Pressure limits in sizing........................................................................................... 196 Table 5 - ASME standard nozzle orifice data..................................................................................... 196 ISA pressure relief valve and rupture disc symbols .......................................................................... 197 Sizing equations for relief valves and rupture disks ......................................................................... 198 ASME VIII code equations USCS units .......................................................................................... 198 5

A Note about sonic or choked flow ............................................................................................. 199 Variables for PRV and PSV sizing equations................................................................................. 199 Sizing rupture disks - worked examples ............................................................................................ 201 Sizing pressure relief valves - worked examples ............................................................................... 203 Review of Feedback Control Fundamentals .................................................................................... 209

Compare Open Loop Control to Closed Loop Control ...................................................................... 209 Open Loop Example – A Mathematical Analysis ............................................................................... 209 Closed Loop Example – A Mathematical Analysis ............................................................................. 211 The Transfer Function for the Automobile ....................................................................................... 213 Review of Frequency Response Fundamentals .............................................................................. 215

Electrical Application – A First Order System .................................................................................... 215 Bode Plot of First Order System ........................................................................................................ 216 Calculate the data for the Bode Plot ................................................................................................. 217 Creating a Bode Plot – First Order System using Frequency ............................................................ 220 Hydraulic Application – A First Order System ................................................................................... 221 Process Control Theory and Controller Tuning ............................................................................... 223

Degrees of Freedom in Process Control Systems ............................................................................. 223 Controllers and control strategies (models-modes) ......................................................................... 225 Process Loop Gain (Gp) ..................................................................................................................... 227 Process Signal Linearization .............................................................................................................. 228 Signal Filtering in Process Control ..................................................................................................... 230 Appling Signal Filters .................................................................................................................... 230 Filter Time Constant and Sample Time ........................................................................................ 231 Example of Filter Time Selection ................................................................................................. 232 DCS/PLC Sample and Scan Time Consideration ................................................................................ 233 Sampling time .............................................................................................................................. 233 Time per scan cycle ...................................................................................................................... 233 Tuning of Process Controllers ........................................................................................................... 234 Closed Loop Tuning of the Controller .......................................................................................... 234 Example: Tune Using Ultimate Gain (continuous cycling) ........................................................ 235 Open Loop Tuning of the Controller ............................................................................................ 236 Example: Tuning using Process Reaction Curve (Step Response) ............................................. 238 Advanced Tuning Methods for Controllers ....................................................................................... 239 The Integral Criteria Method ....................................................................................................... 239 Lambda Tuning Concepts ............................................................................................................. 239 Example Reactor Ratio Timing ..................................................................................................... 242 IMC Tuning Method ..................................................................................................................... 243 PID Controller Models.................................................................................................................. 244 Trial and Error Tuning Method .................................................................................................... 244 Dead Time and PID Control.......................................................................................................... 244 PID Tuning Video - Parameters in Action .......................................................................................... 244 Process Characteristics from the transfer function .......................................................................... 245 Poles, Zeros, and Dampening from the Transfer Function ............................................................... 245 Find the Poles from the Function ................................................................................................ 246 Find the Damping from the Function........................................................................................... 246 Find the Time Constant ................................................................................................................ 247 Find the Period ............................................................................................................................. 247 Find the Time Constant from the Period ..................................................................................... 247 Find Overshoot and Peak Value ................................................................................................... 247 Block Diagram Algebra ...................................................................................................................... 248 6

Example of Block Diagram Algebra Reduction .................................................................................. 249 Nyquist Stability Criterion ................................................................................................................. 250 Routh Stability Criterion .................................................................................................................... 251 Check for Stability using Routh (Example) ........................................................................................ 254 Communications and Industrial Control Networks ......................................................................... 257

Overview of Corporate and Plant Networks ..................................................................................... 257 Open System Interconnect (OSI) and TCP/IP network layer model.................................................. 259 7 Layers of networking in the OSI model ..................................................................................... 259 Physical (Layer 1) ....................................................................................................................... 259 Data Link (Layer 2) ..................................................................................................................... 259 Network (Layer 3) ...................................................................................................................... 259 Transport (Layer 4) .................................................................................................................... 259 Session (Layer 5) ........................................................................................................................ 260 Presentation (Layer 6) ............................................................................................................... 260 Application (Layer 7) ................................................................................................................. 260 Cisco Network Certification – IIOT (Industrial Internet of Things) for IT and OT ..............................260 The typical network model .......................................................................................................... 261 The Network Essentials ................................................................................................................ 263 Overview of Industrial Networks ...................................................................................................... 264 The most popular industrial networks and their applications are below.................................... 264 HART Networks ............................................................................................................................ 265 Traditional HART Network......................................................................................................... 265 A Wired HART Network ............................................................................................................. 266 A Wireless HART Network ......................................................................................................... 266 PROFIBUS and AS-i Networks ...................................................................................................... 267 Reasons for choosing PROFIBUS ............................................................................................... 267 PROFIBUS DP ............................................................................................................................. 267 PROFIBUS PA ............................................................................................................................. 268 PROFINET................................................................................................................................... 268 AS-i ............................................................................................................................................ 268 PROFIBUS Fieldbus Message Specification (FMS) ..................................................................... 269 PROFIBUS................................................................................................................................... 269 PROFIsafe .................................................................................................................................. 269 PROFIdrive................................................................................................................................. 269 Use of the OSI Networking Layers ............................................................................................. 269 PROFIBUS/AS-i/PROFINET Certifications: ................................................................................. 269 FOUNDATION Fieldbus . ...................................................................................................................... 270 Reasons for choosing FOUNDATION Fieldbus . ................................................................................ 270 H2 or HSE (High Speed Ethernet) .............................................................................................. 270 FOUNDATION H1 ......................................................................................................................... 270 Typical FOUNDATION Segments ................................................................................................. 271 Use of the OSI Networking Layers ............................................................................................. 271 Rockwell and ODVA (CIP) Networks ............................................................................................ 272 ControlNet ............................................................................................................................. 272 DeviceNet .............................................................................................................................. 273 EtherNet/IP............................................................................................................................ 274 CompoNet ............................................................................................................................. 274 DH485, DH+, RIO ................................................................................................................... 274 Modbus Networks........................................................................................................................ 275 Traditional Modbus Networks................................................................................................... 275 Communication and Devices ..................................................................................................... 275 7

Protocols.................................................................................................................................... 275 EtherCAT ...................................................................................................................................... 276 SERCOS ......................................................................................................................................... 276 Summary - Automation and Process Control Networks ............................................................. 277 Plant Facility Monitoring and Control System (FMCS) ................................................................ 277 BACnet ......................................................................................................................................... 278 LonWorks ..................................................................................................................................... 278 Typical Building Automation Network ......................................................................................... 278 Networked intelligent and smart devices .................................................................................... 279 PID control in intelligent networked devices ............................................................................... 279 PROFIBUS Control Blocks ............................................................................................................. 280 The Rosemount 333 Tri-Loop to split multiple variable signals................................................... 280 The Application of Digital Logic in Control Systems ...................................................................... 281

Overview of Digital Logic................................................................................................................... 281 Digital Logic Gate Symbols ................................................................................................................ 281 Digital Logic Gate Truth Tables ......................................................................................................... 282 ISA Binary Logic ................................................................................................................................. 283 Relay Ladder Logic............................................................................................................................. 284 Standard RLL Symbols ....................................................................................................................... 285 Sealing Circuits .................................................................................................................................. 285 Control System Architectures ........................................................................................................... 286 DCS Plant Wide Control System Architecture - Networked......................................................... 286 PLC Control System Architecture ................................................................................................. 288 PLC (Programmable Logic Controller) vs PAC (Process Automation Controller) ......................... 288 Controller Application Function Comparison Chart..................................................................... 289 SCADA Control System Architecture ............................................................................................ 289 PLC Programming Languages ....................................................................................................... 290 PLC Programming (LD) ladder diagram or (RLL) relay ladder logic ........................................... 291 PLC Programming (ST) structured text ...................................................................................... 291 PLC Programming (FBD) functional block diagram ................................................................... 292 PLC Programming (SFC) sequential function chart ................................................................... 292 Writing a Program and Developing a HMI for a Small Systems ................................................... 293 RSLogix 5000, ControlLogix PIDE (PID Enhanced) Function Block Diagram ................................. 294 Motor Control and Logic Functions .................................................................................................. 297

Plant Electrical System ...................................................................................................................... 297 Motor Control Center (MCC)............................................................................................................. 297 Typical MCC Design ........................................................................................................................... 298 Typical Motor Controller.............................................................................................................. 298 How to Control a Motor .................................................................................................................... 299 Starter Auxiliary Contacts ............................................................................................................ 299 Overload and Fault....................................................................................................................... 299 The basic NEMA stop-start station ................................................................................................... 300 Typical Motor Control Schematic ................................................................................................ 300 NEMA and IEC Terminal Designations .............................................................................................. 301 NEMA Standards Publication ICS 19-2002 (R2007) ................................................................... 301 Relays and Contacts .................................................................................................................. 301 Coil Lettering and Relay Socket Numbers (NEMA and IEC Numbers) ......................................... 301 Standard Symbols ....................................................................................................................... 303 Standard Symbols (Continued) .................................................................................................... 304 NEMA and IEC Comparisons ........................................................................................................ 305 8

Stop-Start Station Control Circuit Schematic ............................................................................... 306 Starter Control Circuit Schematic ................................................................................................ 306 Relay Ladder Logic (RLL) and Function Blocks................................................................................... 307 RLL and Their Boolean Functions ................................................................................................. 307 Putting Ladder Logic into the PLC ................................................................................................ 308 Example of a Safety System in a PLC............................................................................................ 309 Safety Logic in the PLC ................................................................................................................. 310 Alarming on Sensor Input Failure .............................................................................................. 310 The PLC Logic for Valve and Alarm Monitoring ........................................................................... 311 Schematic to Programming Languages ..................................................................................... 311 The Application of Analog Circuits in Control Systems ................................................................. 313

Overview of Analog Signals ............................................................................................................... 313 Typical Analog Loop Wiring Diagram ........................................................................................... 313 Simplified signal transmitters that maintain constant flow rate for measurement variable ...... 314 Constant Current Loops and Ohm’s Law ..................................................................................... 315 Current Loop Fundamentals ........................................................................................................ 315 The 4-20 mA Current Loop........................................................................................................... 315 Using Current to Transmit Transducer Data ................................................................................ 316 Current Loop Components ........................................................................................................ 316 Current Loop System ................................................................................................................. 316 Designing a Current Loop System ................................................................................................ 317 Choosing a Power Supply .......................................................................................................... 317 Adding More Transducers and Instruments ................................................................................ 318 Devices in Series ........................................................................................................................ 319 A typical Current Loop Repeater.................................................................................................. 320 Active and Passive Current Loops ................................................................................................ 321 Sinking and Sourcing Devices ....................................................................................................... 322 What is the difference between PNP and NPN? ....................................................................... 322 PNP Sensor verses NPN Sensor ................................................................................................. 323 Overview of Motion Controller Applications .................................................................................... 325

Motion Control Systems.................................................................................................................... 325 The basic architecture of a motion control system contains: ..................................................... 325 Stepper Motor ............................................................................................................................. 325 Closed-Loop Stepper Motor ...................................................................................................... 325 Stepper motor advantages .......................................................................................................... 326 Linear motion control................................................................................................................ 326 Series vs. parallel connection .................................................................................................... 326 Servo motor systems ................................................................................................................... 327 Advanced motion controls ........................................................................................................ 327 Position plus velocity system .................................................................................................... 327 Electro-hydraulic Servo System ................................................................................................... 328 Position and pressure/force control ......................................................................................... 328 Position transducers .................................................................................................................. 328 Fieldbus interfaces .................................................................................................................... 329 Applications of servo systems...................................................................................................... 329 Soft Starter Applications ................................................................................................................... 329 How does a soft starter work? ..................................................................................................... 329 Benefits of choosing a soft starter ............................................................................................... 330 Variable Frequency Drive .................................................................................................................. 330 How does a variable frequency drive work? ............................................................................... 330 9

Conversion from AC to DC to AC PWM ........................................................................................ 331 Volts to Hertz Relationship .......................................................................................................... 334 Important Note about Low Frequency in VFDs ........................................................................... 335 VFDs put Noise into the Electrical System ................................................................................... 335 PID Control with VFD or DC Drive ................................................................................................ 336 Closed loop control with drive electronics................................................................................ 336 Block diagram of PID control with feedback operation available on some VFDs ..................... 336 Drive with built-in PID tension control of web or winding reel operation................................ 336 Electrical Systems and Power Quality .............................................................................................. 337

Filtering Power and Harmonics ......................................................................................................... 337 Harmonic Neutralizing Transformers........................................................................................... 337 Filtering of a Harmonics in Power Systems.................................................................................. 338 Passive Filter ................................................................................................................................ 338 Active Filter .................................................................................................................................. 339 Proper Grounding Procedures .......................................................................................................... 341 Emergency Standby Systems ............................................................................................................ 343

Article 700 – Emergency Systems ..................................................................................................... 343 Article 701 – Legally Required Standby Systems .............................................................................. 343 Article 702 – Optional Standby Systems ........................................................................................... 343 UPS (uninterruptible power supply) ............................................................................................ 343 UPS and Battery Bank Sizing ........................................................................................................ 344 Load Profile Calculation............................................................................................................. 347 Battery Sizing Calculation .......................................................................................................... 348 Worked Example – Sizing the Battery Bank .............................................................................. 349 Backup Generator ........................................................................................................................ 351 BMCS Implementation (Building Monitoring and Controls System) ................................................ 352 Hydraulics and Pneumatics ............................................................................................................... 353

Fluid Power Systems ......................................................................................................................... 353 Hydraulic Systems ........................................................................................................................ 353 Pneumatic Systems ...................................................................................................................... 355 Typical Pneumatic System (this type may be found in a manufacturing or chemical plant) ...... 355 Mechanical Flow Diagram of a Large Compressor .................................................................... 355 Instrumentation Air Header (Fluid Distribution Header or Manifold) ...................................... 355 Pneumatic Schematic of Valve Controller ................................................................................. 356 I/P Current to Pneumatic Positioner ......................................................................................... 356 Instrument Air Cost - Engineering Economics ............................................................................. 357 Assumption .................................................................................................................................. 357 Peak air demand .......................................................................................................................... 357 Vendor data ................................................................................................................................. 357 Include Total Demand .................................................................................................................. 358 Instrument Air Piping and Cost .................................................................................................... 358 Pipe sizing is just like sizing electrical lines ....................................................................................... 359 Caution Using Charts and Graphs ................................................................................................ 359 Interconnects and headers .......................................................................................................... 359 The Target Objectives .................................................................................................................. 359 Eliminate the pressure drop ........................................................................................................ 360 Air Velocity ................................................................................................................................... 360 Crunching the Numbers ............................................................................................................... 361 Recover Wasted Heat to Save Money ......................................................................................... 362 10

Fluid Power Schematic Symbols ....................................................................................................... 363 Overview of Conveying Technologies .............................................................................................. 371

Some common types of conveying systems are as follows: ............................................................. 371 Heavy Duty Roller Conveyors....................................................................................................... 371 Flexible Conveyors ....................................................................................................................... 371 Vertical Conveyors and Spiral Conveyors .................................................................................... 372 Spiral Conveyors .......................................................................................................................... 372 Vertical conveyor with forks ........................................................................................................ 372 Vibrating Conveyors ..................................................................................................................... 372 Pneumatic and Vacuum Conveyors .................................................................................................. 373 Pneumatic Tube Conveyor Systems............................................................................................. 373 Large Complex Pneumatic Conveying Systems............................................................................ 374 Typical Plant Pneumatic Conveying System .............................................................................. 374 HMI for Pneumatic Conveying System ...................................................................................... 374 Dilute Phase Systems ................................................................................................................ 375 Dense Phase Systems ................................................................................................................ 375 Conveying Phase Diagram ......................................................................................................... 376 Pressure Distance Relationships ............................................................................................... 377 Vacuum Conveying ...................................................................................................................... 377 A typical vacuum product transportation system ..................................................................... 378 Vacuum conveying systems and HMI display ........................................................................... 378 Vacuum conveying system HMI display .................................................................................... 378 Blower operating cost of pneumatic systems.............................................................................. 379 Screw conveying systems............................................................................................................. 379 Screw conveyor instruments ..................................................................................................... 380 Mass or bulk flow measurement ................................................................................................. 380 Radiometric measurement for mass flow rate ......................................................................... 380 Load cell measurement for mass flow rate ............................................................................... 380 Mass flow control of conveying system ....................................................................................... 381 Radiometric measurement for mass flow rate ......................................................................... 381 Load Cell (Strain Gauge) measurement for mass flow rate ...................................................... 381 Typical scale systems used on manufacturing lines and in plants ............................................ 382 Chemical Process Technology and Equipment ............................................................................... 383

Process Technologies ........................................................................................................................ 383 Separation Processes ........................................................................................................................ 384 A Typical Horizontal 3-Phase Separator....................................................................................... 384 Industrial Distillation ......................................................................................................................... 384 A Typical Industrial Distillation Process ....................................................................................... 385 A Typical Distillation Unit ............................................................................................................. 385 Industrial Furnaces (Fired Heaters) ................................................................................................... 386 Industrial Furnaces....................................................................................................................... 386 Fired Heater Control Scheme....................................................................................................... 387 Expansion Tanks and Heat Transfer Fluid ......................................................................................... 387 Vapor Pressure, Boiling and Cavitation in Equipment ...................................................................... 389 Vaporization in Equipment .......................................................................................................... 389 Control Valve Applications ........................................................................................................... 389 Pumping Applications .................................................................................................................. 389 Video of Vaporization and Cavitation Phenomenon ................................................................... 390 Heat Exchangers ................................................................................................................................ 391 Flow Arrangement ....................................................................................................................... 391 Shell and Tube Heat exchanger ................................................................................................... 392 11

Dynamic scraped surface heat exchanger................................................................................. 392 Phase-change heat exchangers ................................................................................................. 392 Reboiler as seen on a distillation column.................................................................................. 392 Heat Exchanger BTU Calculation and Control.............................................................................. 393 Example of how to control the heat exchanger: ......................................................................... 393 Condenser (heat transfer) ................................................................................................................. 394 Evaporation Processes ...................................................................................................................... 395 What is evaporation? ................................................................................................................... 395 What is latent heat?..................................................................................................................... 395 What is the boiling point? ............................................................................................................ 395 Various Types of Evaporators and Their Working Principles............................................................ 395 Vertical Falling Film Evaporator ................................................................................................... 395 Horizontal Film Evaporator.......................................................................................................... 396 Low Temperature Vacuum Evaporator........................................................................................ 397 Using the Psychrometric Chart ......................................................................................................... 399 Cooling Towers .................................................................................................................................. 401 Cooling Tower Calculations .......................................................................................................... 401 Cooling tower water loss and make-up ....................................................................................... 402 Cooling tower control scheme and operating cost .......................................................................... 404 Typical pH correction system ....................................................................................................... 405 Chemical Reactors and Control ......................................................................................................... 406 What is a Reactor? .................................................................................................................... 406 Types of Reactors ...................................................................................................................... 406 Basic Control Scheme for a Reactor ............................................................................................ 407 CSTR (Constant Stirred Tank Reactor) ....................................................................................... 407 Hydrocracking Reactor Controls .................................................................................................. 407 Chemical Scrubbers ........................................................................................................................... 408 Wet exhaust gas cleaning ............................................................................................................ 408 Wet gas scrubber ......................................................................................................................... 409 Dry scrubbing ............................................................................................................................... 410 Scrubber waste products ............................................................................................................. 410 Bacteria spread ............................................................................................................................ 410 Dehydration Processes...................................................................................................................... 411 Absorption ................................................................................................................................... 411 Joule-Thompson effect...................................................................................................................... 413 Crystallization Technology ................................................................................................................ 414 Static Crystallization ..................................................................................................................... 414 Falling Film Crystallization ........................................................................................................... 416 Suspension Crystallization ........................................................................................................... 416 Process flow diagram suspension crystallization ......................................................................... 417 Freeze Concentration................................................................................................................... 417 Overview of a small crystallization plant to control .................................................................... 418 Flare and Vent Disposal Systems ...................................................................................................... 418 Types of flares .............................................................................................................................. 418 Flare Control Systems .................................................................................................................. 419 Quality Control Standards for Production of Products ..................................................................... 419 ISA Standards for Documentation..................................................................................................... 421

ISA Instrument or Function Symbol .................................................................................................. 421 ISA Line Type Symbols ....................................................................................................................... 422 Standard Line Types .......................................................................................................................... 422 ISA Identification Letters ................................................................................................................... 423 12

ISA P&ID Identification (Controllers and Readouts) .......................................................................... 424 ISA P&ID Identification (Transmitters, Switches and Alarms) .......................................................... 425 ISA P&ID Identification (Compute, Relay and Elements) ................................................................. 426 Piping and Equipment Symbols......................................................................................................... 427 Standard P&ID (Piping and Instrumentation Diagram) ..................................................................... 428 P&ID Sample 1 (Functions) .......................................................................................................... 428 P&ID Sample 2 (Alarms) ............................................................................................................... 429 P&ID Sample 3 (Separator) .......................................................................................................... 429 EM (Equipment Modules) as in the ISA-88 Standard ................................................................... 430 Cross Limiting Control of Furnace ................................................................................................ 430 Simplified P&ID Sample 1 ............................................................................................................ 431 Simplified P&ID Sample 2 ............................................................................................................ 431 ISA Standard PFD (Piping Flow Diagram) or MFD (Mechanical Flow Diagram) ................................ 432 PFD (Piping Flow Diagram) Sample 1 ........................................................................................... 432 BFD (Block Flow Diagram) ................................................................................................................. 434 BFD Sample 1 ............................................................................................................................... 434 BFD Sample 2 ............................................................................................................................... 434 ISA Standard Loop Diagram .............................................................................................................. 435 Instrument Location and Elevation Plan Drawing ............................................................................ 437 Instrument Index Sheet..................................................................................................................... 438 DCS or PLC I/O List (A List of Inputs and Outputs with Tags and Calibration Data) .......................... 439 ISA Standard (HMI) Graphical Display Symbols and Designations ................................................... 440 HMI Sample 1 ............................................................................................................................... 440 HMI Sample 2 ............................................................................................................................... 441 NFPA 79 Colors for Graphical Displays (Industrial Machinery) ......................................................... 441 Battery Limits of the Plant ................................................................................................................ 442 Overview of Safety Instrumented Systems ...................................................................................... 443

Overview of process safety and shutdown ....................................................................................... 443 SIS (Safety Instrumented Systems) .............................................................................................. 443 Complying with IEC 61511 / ISA-84 .............................................................................................. 443 Other codes related to SIS systems ............................................................................................. 444 ISA and OSHA letter defining the requirements of the implementation of SIS systems .................. 444 Initiating Events of Safety Instrumented Systems ....................................................................... 445 Initiating Event ............................................................................................................................. 445 Examples ...................................................................................................................................... 445 External Events ............................................................................................................................ 445 Equipment Failures ...................................................................................................................... 445 Human Failures ............................................................................................................................ 445 The difference between BPCS and SIS systems ................................................................................ 446 IEC 61508 mandatory and guidelines .......................................................................................... 447 SIF and SIL.......................................................................................................................................... 448 Risk analysis and protection layers .............................................................................................. 448 Designing a SIS System ...................................................................................................................... 449 SIL (Safety Integrity Level) – Unit for Functional Safety .............................................................. 449 SFF – Safe Failure Fraction ........................................................................................................... 450 Probability of Failures on Demand (PFD) ..................................................................................... 451 Probability of Failures per Hour (PFH) ......................................................................................... 451 SIL Capability and Safety System ................................................................................................. 452 SIF (Safety Instrumented Function) ............................................................................................. 453 A typical P&ID of the (SIF) Instrumentation................................................................................. 453 Voting or (Polling of the System) ................................................................................................. 454 13

A typical voting system and its instrumentation for the above P&ID ....................................... 454 Types of Voting (X out of X) ....................................................................................................... 454 Voting Probabilities ...................................................................................................................... 455 The SIS calculations ........................................................................................................................... 455 Quantification of Reliability in almost absolute terms ................................................................ 455 Failure Models – The Bathtub Curve ........................................................................................... 456 Reliability Laws............................................................................................................................. 457 Improving the reliability of a measurement system ................................................................. 457 Safety Integrity Level (SIL) and Availability .................................................................................. 458 Sample of SIL Evaluation ........................................................................................................... 458 Acronyms................................................................................................................................... 458 Metrics used in the reliability engineering field involving SIS .......................................................... 459 2. MTTR = Mean Time to Repair ............................................................................................ 459 3. MTBF – Mean Time Between Failures ............................................................................... 459 4. Availability A(t) and Unavailability U(t) ............................................................................. 460 5. Probability of Failure on Demand (PFDavg) and Periodic Test and Inspection ................. 460 SIS Calculations - worked example .............................................................................................. 462 Calculating PFD (Probability of Failure on Demand) ............................................................. 463 Calculating MTTF (Mean Time to Failure) Based on Failure Rates…......................................463 Calculating MTBF based on failures ...................................................................................... 463 SIS and SIL – worked examples .......................................................................................................... 464 Example 1: Pump Failure Rate (FR) ....................................................................................... 464 Example 2: MTBF over 10 years ............................................................................................ 464 Example 3: PFD and Test Interval .......................................................................................... 465 Recommended SIS Study Material .................................................................................................... 466 Excerpts from Process Safebook 1 – Rockwell Automation ............................................................. 466 Overview of NEC / NFPA and Other Codes ...................................................................................... 469

CFR (Federal Government) Public Safety Standards of the United States........................................ 469 List of NFPA codes (be familiar with these codes) ............................................................................ 472 NFPA 70 – NEC (National Electrical Code)......................................................................................... 472 Voltage Drop Calculations............................................................................................................ 473 Substitute specific resistance (k) for resistance (R) of wire ...................................................... 473 Wire and cable sizing formulas for voltage drop ...................................................................... 473 Voltage drop calculations – worked examples ............................................................................ 474 NEC Article 500 Explosion Proof Installations .............................................................................. 476 Class I Hazardous Location NEC Article 501 ................................................................................. 476 Class I Location Definition ..................................................................................................... 476 Class I Division Definitions ..................................................................................................... 477 Class I Group Definitions ....................................................................................................... 477 Class I Temperature Definition .............................................................................................. 478 Class II Hazardous Location NEC Article 502 ................................................................................ 478 Class II Location Definition .................................................................................................... 478 Class II Division Definitions .................................................................................................... 478 Class II Group Definitions ...................................................................................................... 479 Class II Temperature Class ..................................................................................................... 479 Class III Hazardous Location NEC Article 503 ............................................................................... 479 Class III Location Definition ................................................................................................... 479 Class III Division Definitions ................................................................................................... 479 Class III Group Definitions ..................................................................................................... 480 Use of Zone Classifications........................................................................................................... 480 Classification Comparison (Zone/Division) for a Class I Location.............................................. 480 14

Group Comparison (Zone/ Division) for a Class I Location ........................................................ 481 Protection Methods Comparison Class ..................................................................................... 481 Designation of NEC/CEC Classification......................................................................................... 482 Hazardous Location Classification ............................................................................................. 482 Summary the various hazardous (classified) locations. ............................................................... 483 Hazardous Location Wiring Methods .......................................................................................... 484 Purged and pressurized systems ................................................................................................. 485 Intrinsically safe systems ............................................................................................................. 485 Zener diode barrier (configurations) ......................................................................................... 485 Conventional passive IS Zener barriers ................................................................................. 485 Active (powered) IS isolation barriers ................................................................................... 485 NEC Article 409 and UL 508A ............................................................................................................ 486 What is NEC 409 and UL 508A? ................................................................................................... 486 SCCR (Short-circuit current rating) of industrial control panels .................................................. 486 Components in the power circuit ................................................................................................ 486 SCCR calculations – worked examples ......................................................................................... 487 NEC Articles for Remote Control and Signaling ................................................................................ 488 Article Categories ......................................................................................................................... 488 Cabling Installations and Applications (Types and Ratings) ......................................................... 489 Cables Selection for Installation per NEC Code ........................................................................... 489 Article 725 - Class 1, Class 2, Class 3, Remote-control Circuits .................................................... 491 Power sources .............................................................................................................................. 492 Class 1 methods and materials .................................................................................................... 492 Class 2 and Class 3 methods and materials ................................................................................. 492 Article 800 - Communications Circuits......................................................................................... 493 Examples of Article 725, 727 and 800 in instrumentation and controls ..................................... 494 NEMA Electrical Enclosures Types and Uses ..................................................................................... 496 Non-hazardous location NEMA enclosure types ......................................................................... 496 Table 10 – Indoor Nonhazardous Locations ................................................................................ 497 Table 11 - Outdoor Nonhazardous Locations .............................................................................. 498 Table 12 - Hazardous Locations ................................................................................................... 499 Temperature Rise Calculation ................................................................................................... 499 NFPA 70E Standard for Electrical Safety ........................................................................................... 500 What is NFPA 70E? ....................................................................................................................... 500 What is Arc Flash.......................................................................................................................... 500 Approach / Protection Boundaries .............................................................................................. 501 Arc Flash Analysis ......................................................................................................................... 501 Required Arc Flash Warning Label ............................................................................................... 501 NFPA 77 Static Electricity .................................................................................................................. 502 1.2 Purpose .................................................................................................................................. 502 8.1 General overview ................................................................................................................... 502 8.3.1 Charge generation .............................................................................................................. 503 G.1 Grounding diagrams .............................................................................................................. 504 NFPA 780 Lightning Protection (formerly NFPA 78) ......................................................................... 505 NFPA 780 and NFPA 70 (NEC) ...................................................................................................... 505 Strike-termination devices ........................................................................................................ 505 Connecting conductors to electrodes ....................................................................................... 505 Routing down conductors ......................................................................................................... 506 Conductor and electrode connection ....................................................................................... 506 Earth-grounding electrodes ...................................................................................................... 506 Summary of lightning protection components ............................................................................ 506 Air terminal height .................................................................................................................... 506 15

Conductor bends ....................................................................................................................... 506 Conductor size and material ........................................................................................................ 507 Transient Protection from Lightning Strikes ................................................................................ 507 NFPA 79 Industrial Machinery........................................................................................................... 509 Conductor sizing........................................................................................................................... 509 Conductor colors .......................................................................................................................... 509 Pushbutton functions for color .................................................................................................... 509 Colors for Machine Indicator Lights and Icons Table 10.3.2 ........................................................ 509 NFPA 496 Purged and Pressurized Systems ...................................................................................... 510 Overview of the NFPA 496 articles .............................................................................................. 510 Factors to consider (NFPA 496, Sec. 5-3) ..................................................................................... 510 Location of the control room (NFPA 496, Secs. 5-3.1(c) and 5-3.2) ............................................ 510 Positive pressure air systems (NFPA 496, Sec. 5-4.1) .................................................................. 511 Type X equipment (NFPA 496, Sec. 5-4.4) ................................................................................... 511 Type Y equipment (NFPA 496, Sec. 5-4.5) ................................................................................... 511 Type Z equipment (NFPA 496, Sec. 5-4.5) ................................................................................... 511 Examples of Purged and Pressurized Systems ............................................................................. 512 Basic design of purged enclosures ............................................................................................... 512 Basic design of purged buildings .................................................................................................. 513 40 CFR and EPA - LDAR ...................................................................................................................... 514 The Clean Air Act (CAA)................................................................................................................ 514 What the Law Requires ................................................................................................................ 514 Putting It All Together ......................................................................................................................... 515

Define the Scope of the Plant ........................................................................................................... 515 Define the Control Systems Architecture ......................................................................................... 516 Some Typical Large DCS Architectures .............................................................................................. 517 More on DCS Cabinets and I/O Distribution ..................................................................................... 518 Distributing the Power and Control .................................................................................................. 519 Routing the Cable Trays .................................................................................................................... 520 Choose the Wiring Method ............................................................................................................... 521 Field Distribution Systems................................................................................................................. 522 Class I, Division 2 Installations ..................................................................................................... 523 Class I, Division 1 Installations ..................................................................................................... 523 Modular Wiring Distribution Systems.......................................................................................... 524 Instrument Air Supply and Pneumatic Tubing .................................................................................. 525 Instrument Air Consumption ....................................................................................................... 525 Compressor Types........................................................................................................................ 526 Piping System and Manifold ........................................................................................................ 526 Air Pipe Header ......................................................................................................................... 526 Pneumatic Tubing...................................................................................................................... 526 Air Distribution Manifold (Header) ........................................................................................... 527 Routing of Pneumatic Tubing .................................................................................................... 527 Heat Tracing Systems ........................................................................................................................ 528 Electric Heat Tracing .................................................................................................................... 528 Steam Heat Tracing ...................................................................................................................... 529 Free Heat Tracing Software ......................................................................................................... 530 Determine Scope of Design ............................................................................................................... 530 Electrical Scope ............................................................................................................................ 531 Instrumentation and Mechanical Scope ...................................................................................... 531 Design of Electrical Plans ............................................................................................................. 532 Sample of a possible design for the control network and communications in plant .................. 533 16

Sample of a possible plan for routing of cable tray and conduit in plant .................................... 534 Sample of a possible layout for a MCC building with medium voltage switchgear installed ...... 535 Sample of a possible one-line electrical diagram for the low voltage in the MCC building ....... 536 Sample of a possible ladder diagram for the control of an Allen Bradley frequency drive ......... 537 Sample of a possible electrical field wiring diagram for the frequency drive ............................. 538 Sample of a possible electrical field wiring diagram routing the analog instruments to DCS ..... 539 Locations of Instruments and Piping Design ..................................................................................... 541 Finding the location of an instrument in a plant ......................................................................... 547 Useful Equations for Pumping, Piping and Sizing Valves .............................................................. 549

Find pipe diameter with velocity of flow known .............................................................................. 549 Find flow velocity with pipe diameter known................................................................................... 549 Find pipe diameter with temperature and pressure correction ....................................................... 549 Find flow velocity with temperature and pressure correction ......................................................... 549 Find the Reynolds Number for the flow............................................................................................ 549 Calculate the Piping Head Losses to Size a Control Valve ................................................................. 550 Find the pump motor size (break horsepower) ................................................................................ 551 Calculating the Hydraulic Horsepower of pumps ........................................................................ 551 Calculating the Brake Horsepower of pumps .............................................................................. 552 Correct Pump Head and Flow Rate for Fluid Viscosity ................................................................ 553 Piping Absolute Roughness Values ................................................................................................... 556 Applications of Pumping Systems .................................................................................................... 557

Pump Basics ...................................................................................................................................... 557 Static Head ........................................................................................................................................ 557 Applying Variable Frequency Drives to Pumps to Realize Savings ................................................... 558 Pumps with Variable Frequency Drives (VFD).................................................................................. 558 When Can You Save with a VFD? ...................................................................................................... 559 Sizing a Pump Head with Specific Gravity of the Pumped Fluid ....................................................... 560 How a Piping System Works .............................................................................................................. 561 Calculating Volume in Tanks ............................................................................................................. 564

Cylindrical Tanks Upright .................................................................................................................. 565 Cylindrical Tanks on Side ................................................................................................................... 565 Spherical Tanks.................................................................................................................................. 566 Bullet Tanks ....................................................................................................................................... 566 Examination Sample Questions ........................................................................................................ 567

Sample Questions ............................................................................................................................. 567 Answers to Examination Sample Questions ..................................................................................... 574 Explanations and Proofs of Examination Sample Questions ............................................................ 575 Preparing this Guide for the Exam .................................................................................................... 587

An Avery tab template is included with this guide ........................................................................... 587 Suggested tabbing the guide............................................................................................................. 587 Guide to Using the Fisher Control Valve Handbook ....................................................................... 589

Important Sections to Review ........................................................................................................... 589 Important Pages to Tab ..................................................................................................................... 589 Valve and materials Selection ...................................................................................................... 589 Actuator Sizing Methods.............................................................................................................. 590 Valve Sizing Methods ................................................................................................................... 590 Electrical Apparatus ..................................................................................................................... 590 17

Engineering Data .......................................................................................................................... 590 Piping System Applications .......................................................................................................... 590 Conversions and Equivalents ....................................................................................................... 591 Appendix and Data Tables ................................................................................................................. 593

Table A1 - Thermocouple Table (Type J) ........................................................................................... 594 Table A2 - Thermocouple Table (Type K) .......................................................................................... 596 Table A3 - Thermocouple Table (Type E) .......................................................................................... 599 Table A4 - Thermocouple Table (Type T) .......................................................................................... 601 Table A5 - Platinum 100 Ohm RTD Table in ohms ............................................................................. 602 Table A6 - Properties of Water Specific Gravity and LBs/HR to GPM ............................................... 603 Table A7 - Properties of Water Specific Volume and Density ........................................................... 604 Table A8 - Properties of Water Kinematic Viscosity centistokes ...................................................... 605 Table A9 - Properties of Saturated Steam......................................................................................... 606 Table A10 - Valve Selection – Materials and Applications ................................................................ 611 Valve Terms.................................................................................................................................. 611 Selecting your Valve ..................................................................................................................... 611 Valve Types and Descriptions ...................................................................................................... 612 Valve Selection Overview - Service Application Chart ................................................................. 614 Valve Selection Detailed - Service Application Chart................................................................... 615 Valve Types - Advantages and Disadvantages ............................................................................. 616 Standard Control Valve Body Materials ....................................................................................... 617 Valve Seat Leakage Bubbles per Minute...................................................................................... 619 Valve Trim Material Temperature Limits...................................................................................... 620 Valve Service Temperature Limits for Non-Metallic Materials.................................................... 621 Valve Stem Packing Friction Values (Typical)............................................................................... 622 Valve Stem Packing Temperature – Pressure .............................................................................. 622 Valve Seating Shutoff Pressure .................................................................................................... 623 Abbreviations and Terminology.................................................................................................... 624 Table A11 - Properties and Sizing Cv Coefficients for Fisher ED Globe Valves ................................. 625 Table A12 - Properties and Sizing Cv Coefficients for Fisher Rotary Valves...................................... 628 Table A13 - Numerical Constants for Control Valve Sizing Formulas ............................................... 629 Table A14 - Critical Pressure and Temperature of Elements ............................................................ 630 Table A15 - Pipe Standard Dimensions and Data.............................................................................. 631 Table A16 - NEC Wire Ampacity Table 310.16 .................................................................................. 633 Table A17 - NEC Conductor Properties and Impedance ................................................................... 634 Table A18 - NEC Full Load Motor Currents ....................................................................................... 637 Table A19 - NEC Grounding and Bonding Conductors ...................................................................... 638 Table A20 - Specific Gravity and Gas Constants for Some Common Gases ...................................... 639 Table A21 - Specific Gravity Common Fluids..................................................................................... 641 Table A22 - The kinematic viscosity common fluids ......................................................................... 644 Table A23 - The absolute viscosity common liquids ......................................................................... 651 Table A24 - The absolute viscosity common gases ........................................................................... 653 Table A25 - Density of Elements in English and Metric Units ........................................................... 654 Table A26 - Metric Conversion Tables .............................................................................................. 655 Table A27 - Standard Conditions and Gas Laws ................................................................................ 657 Table A28 - Head Loss in Piping Systems .......................................................................................... 658 Table A29 - Maximal flow velocity in pipes....................................................................................... 659 Table A30 - Pressure Vapor Chart of Common Liquids ..................................................................... 660 References ........................................................................................................................................... 661

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Introduction to This Study Guide This manual helps prepare the PE (Professional Engineer) candidate for the NCEES PE examination in the PE discipline option of Control Systems Engineering (CSE). The CSE examination covers a broad range of subjects, from the electrical, mechanical and chemical engineering disciplines. This examination is not on systems theory, but on sound judgment of the application of process control systems and applicable codes. Basic process control systems (BPCS) and safety instrumented systems (SIS) are presented in detail. Experience in engineering or designing process control systems is almost a necessity to pass this discipline of the NCEES P&P (principles and practices) examination. Study of this reference manual should adequately prepare the experienced engineer or designer to take the CSE examination. This manual presents many practical problems which may be presented on the CSE examination, with explanations and worked solutions. State and federal codes needed for the examination are reviewed and standard documentation and design practices are demonstrated for the design of real world plant control systems. Most state licensing boards in the United States recognize the Control System Engineering (CSE) examination, however some states do not offer the CSE examination, check with your state licensing board to see if they offer the CSE examination. If you live in one of these states that do not offer the CSE, you may choose to pursue licensing in another discipline (such as electrical, mechanical, or chemical engineering). You may also try to arrange to take the CSE exam in a neighboring state. More details about the examination content, application process and also study materials are presented later in this manual.

About the Author Bryon Lewis, PE, CMfgE, CET, CCST III, CCENT Professional Engineer (PE) Certified Manufacturing Engineer (CMfgE) Certified Journeyman Electronics Technician in Industrial electronics (CET) Certified Control System Technician Level III (CCST) Certified PROFIBUS Network Engineer Certified Cisco – Industrial Specialist (CCENT) State of Texas Master Electrician mailto:[email protected] http://www.linkedin.com/in/bryonlewis Bryon Lewis is a licensed as a PE in Control Systems Engineering (CSE). He is a Senior Member of ISA and has held Senior Membership with SME. Mr. Lewis has over 30 years of experience in electrical, mechanical, instrumentation, and control systems. He holds letters of recommendation from Belcan Engineering, S & B Engineers and Constructors, Enron Corporation and Lee College. Bryon’s experience in diversified engineering and competitive projects is as follows: • 12 years of Engineering and Design experience using AutoCAD 9 through 2014. • 16 years of Field experience including start-up and troubleshooting and calibration of instruments. • Projects consist of compressor stations, petrochemical and food process plants. • Turbine and compressor control systems, material handling systems and burner management systems. • Development of P&IDs; MFDs; electrical power distribution systems and control diagrams. • Engineering and implementation of Foxboro I/A and Honeywell DCS systems and security. • Network support including: servers; workstations; routers; switches and cabling. • Allen-Bradley automation and PLC programming for the Allen-Bradley family of processors. Bryon has participated in projects for clients such as Shell Oil, Exxon, Diamond Shamrock, Eli Lilly Pharmaceuticals, Proctor and Gamble (fault analysis), JVC America (solvent recovery project), Keebler Corporation, Mission foods, Enron Transportation and Storage, and Comanche Peak Steam Nuclear Station 1987. The power house addition and computer grounding at the Johnson Space Center in 1985. If there are any questions, please contact Bryon Lewis at his email address.

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People who have contributed to the previous editions of this manual

Chad Findlay, PE Chad graciously reviewed this manual for errors and made numerous suggestions to improve its content. Chad Findlay is a Lead Controls Engineer for General Electric Company where he has worked for 7 years. He develops gas turbine control systems applied to simple and combined cycle power plants. Chad holds a Master's degree in mechanical engineering from the University of California, Davis.

Daniel Masso, PE Daniel also contributed to the review of this manual for errors and made suggestions to improve its content. Daniel Masso has worked as a DCS engineer for Westinghouse and Emerson Electric for 20 years in sales, project and field/start-up engineering capacities in system, control logic and graphic design and programming capacities. He earned a B.Ch.E. from Cleveland State University and continued on a M.S. Ch.E. at Case Western Reserve University and is employed by Emerson Process Management Power and Water Solutions.

Susan Colwell I would like to thank Susan for her patience and help in the publication of this manual. She was extremely helpful in the publication of the first edition. Susan Colwell is the Publishing Director for ISA, International Society of Automation. Susan holds a BA from Franklin Pierce University.

Richard Tunstall I would like to thank Richard for giving me the opportunity to design the first draft of the Lee College process pilot plant under the advisement of the DuPont training department in Deer Park, Texas and the opportunity to study real processes and their associated control systems in 1994. Richard has been a faculty member of the Instrumentation Technology Program at Lee College - Baytown, Texas for since 1991. Richard has earned the following: BS in education from Baylor University Don Thompson Award - 2010 from ISA (International Society of Automation) Lee College Outstanding Faculty with over Ten Years of Experience – 2012

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Tips on How to Use This Study Guide To make the most of this study guide, it may be of interest to use the features built into Adobe Reader. The image below shows where to click, for the display of Page Thumbnails and Bookmarks in this guide. The Bookmarks are a dynamic Table of Contents. See the following images below for illustrations of how thumbnails and bookmarks work. (There is a formula sheet for the exam in the attachments)

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Using Thumbnails to Navigate The Page Thumbnail shows a preview of the pages in this guide. Just click on any thumbnail image to instantly jump to the page in the preview. The default viewing mode in Adobe Reader is one column. If you want to view two columns at the same time as shown below, move your mouse over the divider between the thumbnails and the viewing page and drag the column splitter till you show as many columns as you would like to view at once. I recommend viewing only two columns.

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Using Bookmarks to Navigate The Bookmarks in this guide are the same as the Table of Contents collapsed. Quickly navigate to the subject of interest and click on the “+” to expand the contents of the subject matter under the subject heading. Click on the “-“ to collapse the subject topics. The default viewing mode in Adobe Reader shows wrap around text in the bookmark column. If you would like to read your bookmarks as shown below, move your mouse over the divider between the bookmarks and the viewing page and drag the column splitter till you show as much text width as you desire to view.

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Important File Attachments - Open by clicking on the paper clip! The instructions are on the next page. Files attached to this PDF file:

Formula Sheet.pdf Avery Tabs ready to print for this third edition manual for quick reference in the CSE examination Flow Measurement - API & AGA - Emerson.pdf Flow Measurement - ISO 5167.pdf Managing Industrial Networks with Cisco Networking Technologies (200-401) IIOT Specialist Managing Industrial Networks for Manufacturing with Cisco Technologies (200-601) CCNA RCDD Certification - A Registered Communications Distribution Designer

Avery® Printable Self-Adhesive Tabs 16281, 96 Tabs, 1-1/4" x 1" http://www.avery.com/

See the section in this book “Preparing this Guide for the Exam” for recommended pages to tab for quick reference in the NCEES PE/CSE Examination.

How to Print this Manual The style of this book has a layout for reading on a computer. To maintain this easily read format when printing the book, use skip blank pages in your printer setup. Most printers have an option to “skip blank pages” in the printer setup dialog box. If your printer does not support this option, then just do not print the one blank page that immediately follows this book’s cover page. All other pages are formatted and organized for the printing the information in this book. Also you may choose to manually tell the printer which pages to print. Instead of print all pages, use the print pages option as 1, 3-677. In the Adobe print dialog box, check the print both sides if this option is available for your printer to get the best results as a readable book for the examination. The front and back covers can be color laser printed on glossy card material at Staples, FedEx Kinko's, and Office Depot for less than $5.00 for both. FedEx Kinko's can print and coil spring bind the manual for around $68.00 laser printed black and white or $350.00 laser printed color. They will also coil spring bind only your printed book for less than $10.00. Many printer manufactures sell color inkjet printer for around $100.00 and cartridges for around $40.00, you will need about: (4 each set of color) and (1 each set of black XL). You should be able to print it yourself in color on 24lb paper for around $300.00 dollars and you will still have the printer and some ink left over. I would recommend color printing for full understanding of the information in the graphs. Black and white laser jet printers can be purchased for around $60.00 to $100.00. With 24lb paper you should be able to print a quality document for around $100.00 to $140.00.

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Welcome to Control Systems Engineering Licensing as Professional Engineer / Control Systems Engineer (CSE) A Professional Engineering license must be obtained to perform engineering work for the public and private sectors, in the United States and most countries in the world. In order to protect the health, safety, and welfare of the public, the first engineering licensure law was enacted in 1907 in Wyoming. Now every state regulates the practice of engineering to ensure public safety by granting only Professional Engineers (PEs) the authority to sign and seal engineering plans and offer their services to the public. The title of Engineer cannot be used to advertise for engineering work, without a PE license. The CSE (Control Systems Engineer) takes on responsibilities beyond those of most other disciplines of professional engineering. If the pump quits working, you just don’t have water. If the electrical panelboard fails, you just replace the components. In plant control systems, a failure can mean absolute disaster. Plants explode and many people can die. Even the failure of systems can mean the loss of hundreds of thousands of dollars and up into the millions for loss of product and production. There may also be class action and environmental lawsuits into the billions of dollars. This is why I have taken a complete plant design approach to show the vastness of exposure and experience needed to be a control systems engineer. Just like the saying in the Spiderman movie, “With great power comes great responsibility.” The control systems engineer’s job cannot be taken lightly. People’s lives depend on you knowing what you are doing and getting it right the first time. You cannot guess at control systems engineering. You must know! Being a Professional Engineer is not just answering a minimum of 54 questions on an 8-hour examination. The CSE can’t just say the bottle is in place, now fill it. The CSE has to ask questions like: 1. 2. 3. 4. 5.

Is the bottle in place Is the valve open Is there fluid available to fill the bottle in the tank Is the pump running Is the fluid flowing

6. 7. 8. 9. 10.

Did the bottle fill Did the valve close Did the fluid stop flowing Did the pump stop Did something fail

The CSE must be ready to handle abnormal conditions and upsets at any time. This will be a major part of the programming and a large part of the instrumentation, with increasing concern for safety today and compliance with government regulations now requiring safety instrumented systems (SIS) installed.

Explosions can occur in petrochemical and other similar hazardous plants, even though the electrical and process systems are designed explosion proof per NFPA, ANSI/ISA, API, OSHA, ISO, and other codes.

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A highly modular plant with complex motion controls and industrial networks using advanced diagnostics. In Singapore, ExxonMobil shown below, owns and operates a 592,000-barrel-per-day (bpd) refinery as one of the largest in the world. Singapore employs almost 3,000 people and Exxon resides in 200 countries.

The typical petrochemical plant will require around 1000 workers to build and will take years to complete. Most large petrochemical plants will have land coverage in the upward range of 2,000 to 7,500 acres.

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Why Become a Professional Engineer? Being licensed as a Professional Engineer is an important distinction and can enhance your career options. Many engineering jobs require a PE license to work as an engineering consultant or senior engineer, testify as an expert witness, conduct patent work, work in public safety, or advertise to provide engineering services. Although you may never need to be registered for “legal” reasons, you may find that you need to be a PE to be eligible for engineering management positions. On the average, the PE makes significantly more money than unlicensed engineers. Even if your first job does not require a PE license, you may need it later in your career. In today's economic environment, it pays to be in a position to move to new jobs and compete with others who have a PE license or are on a professional engineering track. It is also highly unlikely that a job requiring a PE license will be outsourced overseas. The following was taken from the NCEES website: What makes a PE different from an engineer? 

Only a licensed engineer may prepare, sign and seal, and submit engineering plans and drawings to a public authority for approval, or seal engineering work for public and private clients.



PEs shoulder the responsibility for not only their work, but also for the lives affected by that work and must hold themselves to high ethical standards of practice.



Licensure for a consulting engineer or a private practitioner is not something that is merely desirable; it is a legal requirement for those who are in responsible charge of work, be they principals or employees



Licensure for engineers in government has become increasingly significant. In many federal, state, and municipal agencies, certain governmental engineering positions, particularly those considered higher level and responsible positions must be filled by licensed professional engineers.

Many states require that individuals teaching engineering must also be licensed. Exemptions to state laws are under attack, and in the future, those in education, as well as industry and government, may need to be licensed to practice. Also, licensure helps educators prepare students for their future in engineering.

I-Foreign Graduate with foreign degree and Satisfy any course deficiencies

The path to follow to be a licensed PE (Professional Engineer)

II 4 years qualifying experience

III FE, intern certificate application

I-US Graduate with ABET degree from the United States

II-No Degree with no degree meet your state’s FE / EIT requirements

IV Pass FE, become certified EIT

V 4 years qualifying experience

V-No Degree The state may not require the FE / EIT with many years of experience

VI PE, licensing application

VII Pass PE, receive license

V-No Degree with no degree meet your state’s PE / CSE requirements

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This is the third edition of this study manual This review reference manual has been greatly expanded at the request of the NCEES CSE (Control Systems Engineer) PE examination committee chairman. It now includes new and expanded chapters on numerous control systems subjects. I have taken a complete systematic approach to understanding how to design a complete plantwide control system, for multiple processes, as might be encountered throughout the control engineer’s career.

The new and expanded sections include:                       

Updated NCEES PE (CSE) option examination content Expanded section on pressure measurement and calibration Expanded section on flow measurement and calibration Expanded section on weight and load cell applications New section on process analyzers Expanded section on process control valve sizing, applications and how to size them for installed real world control of flowing process streams Expanded section on pressure relief and safety valves, their applications and federal regulations and requirements for installation and monitoring per EPA requirements issued September 2015 Expanded section on process control theory and tuning Expanded section on the application of digital logic in control systems (formerly overview of discrete control subjects) Expanded section on the application of analog circuits in control systems (formerly overview of analog control subjects) New section on electrical systems and power quality New section on overview of conveying systems Expanded section on ISA standards for documentation Expanded section on SIS safety instrumented systems, explanation of OSHA requirements, definitions and their application and calculations for installations New section on overview of networks and communications New section on hydraulics and pneumatics New section on overview of motion controller applications New section on motor controls and logic functions New section on chemical processes and equipment New section on applications of basic fluid mechanics in piping systems New section on pumping applications New “Putting It All Together” section on how real plants are built and the use of ISA standard documentation and how plan drawings and details are generated Expanded appendix data tables to include most information needed for the CSE exam

Notes for Reading this Manual: When you see these types of boxes in the guide, the material or example problems may be on the CSE exam. Major topics are in grey background as shown below.

Sample problem: The problem will be stated in this colored area with any parameters needed to solve the problem. The solution will be in this colored area.

Major topics of study will appear in highlighted text of this color. This color will break up the topic Important information for the CSE examination will appear in highlighted text of this color.

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Recommended Flow Chart of Study for the CSE Study Group 1 Review Process Measurement Standards and Terminology

Review Fluid Mechanics for Process Control and Measurement

Study Group 2

Study Group 3

Study Group 4

Temperature Measurement and Calibration

Weight Measurement and Calibration

Review of Feedback Control Fundamentals

Pressure Measurement and Calibration

Process Analyzers

Review of Frequency Response Fundamentals

Level Measurement and Calibration

Process Control Valves

Process Control Theory and Controller Tuning

Flow Measurement and Calibration

Pressure Relief Valves and Rupture Disks

Network Communications and Industrial Control

Study Group 5

Study Group 6

Study Group 7

Applications of Digital Logic in Control Systems

Overview Motion Controller Applications

Hydraulics and Pneumatics

Motor Controls and Logic Functions

Electrical Systems and Power Quality

Overview of Conveying Systems

Applications of Analog Circuits in Control Systems

Emergency Standby Systems

Chemical Processes and Equipment

Study Group 8 ISA Standards for Documentation Overview of Safety Instrumented Systems Overview of NEC / NFPA and Other Codes Putting it All Together

Study Group 9 Examination Sample Questions and The ISA CSE Study Guide (4-hour practice Examination)

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Copyright © 2016 by ISA

Overview of Recommended Flow Chart of Study for the CSE Note: Recommended flow of study with the manual Control Systems Engineering Exam Reference Manual - A Practical Study from ISA by Bryon Lewis, PE/CSE, CMfgE, CET, CCST, CCNA http://www.isa.org/csereference Study Group 1 Definitions of span, range, zero, suppressed zero, elevated zero, LRV and URV (lower and upper range values) Pressure, Head and relationship between ΔP (pressure) and flow Calculate differential pressure in pipes and head type flow elements Pump head and work done by total energy in fluids Study Group 2 Temperature of liquids, gases and vapors Level of liquids Density and interface level Flow rates of liquids, gases and vapors Mass rate of liquids, gases and vapors Study Group 3 Level of solids and liquids Mass rate of solids and liquids Molecular Composition Flow control of liquids, gases and vapors Pressure control and regulation ASME VIII and NFPA 30 codes for equipment and piping protection from overpressure Study Group 4 Laplace transforms and block algebra reduction Process control modes and loop applications Process system response and tuning of controllers Networks and communications Process control through networking Study Group 5 Digital functions and truth tables Relay ladder logic and motor control applications with NEMA and IEC standards Constant current and constant voltage control loop applications Analog loop signals and impedance Study Group 6 Stepper motor and servo systems (electric and hydraulic) Speed control and VFD operations Pules wave modulation Harmonics and electrical noise Power systems for critical loads Study Group 7 Control with hydraulics and pneumatics Bulk solids transportation Heat exchanger control and BTU calculations Cooling tower operation and control Distillation and separation processes Pollution control and fluid stream cleansing Flare and vent disposal systems Study Group 8 ISA standard P&ID, MFD, BFD, Loop sheets (electrical and pneumatic) and HMI BPCS (basic process control system) and SIS (safety instrumented system) Designing a safety instrumented system using SIL and SIF values SIS calculations for the CSE examination OSHA, NFPA, NEC, CFR and EPA codes Study Group 9 ISA CSE Study Guide (4-hour sample test) ISA PE/CSE examination review course LearnControlSystems.com online and hands on supplement course (putting it all together review)

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Examination General Information State Licensing Requirements Licensing of engineers is intended to protect the public health, safety, and welfare. State licensing boards have established requirements to be met by applicants for licenses which will, in their judgment, achieve this objective. Licensing requirements vary somewhat from state to state but have some common features. In all states, candidates with a 4-year engineering degree from an ABET/EAC accredited program and four years of acceptable experience can be licensed if they pass the Fundamentals of Engineering (FE) exam and the Principles and Practice of Engineering (PE) exam in a specific discipline. References must be supplied to document the duration and nature of the applicant’s work experience.

Eligibility Some state licensing boards will accept candidates with engineering technology degrees, related-science (such as physics or chemistry) degrees, or no degree, with indication of an increasing amount of work experience. Some states will allow waivers of one or both of the exams for applicants with many years (6– 20) of experience. Additional procedures are available for special cases, such as applicants with degrees or licenses from other countries. Most states have abandoned the no degree statute and will only accept as minimal, an accredited associate degree. Note: Recipients of waivers may encounter difficulty in becoming licensed by “reciprocity” or “comity” in another state where waivers are not available. Therefore, applicants are advised to complete an ABET accredited degree and to take and pass the FE/EIT exam. Some states require a minimum of four year experiences after passing the FE/EIT exam, before allowing a candidate to sit for the PE (principles and practices) exam. Some states will not allow experience incurred before the passing of the FE/EIT exam. It is necessary to contact your licensing board for the up-to-date requirements of your state. Phone numbers and addresses can be obtained by calling the information operator in your state capital, or by checking the Internet at www.ncees.org or nspe.org.

Exam schedule The CSE exam is offered once per year, on the last weekend in October, (typically on Friday). Application deadlines vary from state to state, but typically are about three or four months ahead of the exam date. Requirements and fees vary among state jurisdictions. Sufficient time must be allotted to complete the application process and assemble required data. PE references may take a month or more to be returned. The state board needs time to verify professional work history, references, and academic transcripts or other verifications of the applicant's engineering education. After accepting an applicant to take one of the exams, the state licensing board will notify him or her where and when to appear for the exam. They will also describe any unique state requirements such as allowed calculator models or limits on the number of reference books taken into the exam site.

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Description of Examination Exam format The NCEES Principles-and-Practice of Engineering examination (commonly called the PE examination) in Control Systems Engineering (CSE) is an eight-hour examination. The examination is administered in a four hour morning session and a four hour afternoon session. Each session contains forty (40) questions in a multiple-choice format. Each question has a correct or “best” answer. Questions are independent, so an answer to one question has no bearing on the following questions. All of the questions are compulsory; applicants should try to answer all of the questions. Each correct answer receives one point. If a question is omitted or the answer is incorrect, a score of zero will be given for that question. There is no penalty for guessing.

Exam content The subject areas of the CSE exam are described by the exam specification and are given in six areas. ISA supports Control Systems Engineer (CSE) licensing and the examination for Professional Engineering. ISA is responsible for the content and questions in the NCEES examination. Refer to the ISA web site (http://www.isa.org) for the latest information concerning the CSE examination. For a copy of the latest PE/CSE examination format and content, visit NCEES at: (http://www.ncees.org) The following is an overview of what categories and content might be expected on the examination. The NCEES website will have the latest specifications of what exactly will be the focus of the exam, as the format and specifications change over the years.

I.

Measurement          

Sensor technologies applicable to the desired type of measurement (e.g., flow, pressure, level, temperature, analytical, counters, motion, vision) Sensor characteristics (e.g., rangeability, accuracy and precision, temperature effects, response times, reliability, repeatability) Material compatibility Calculations involved in: pressure drop Calculations involved in: flow element sizing Calculations involved in: level, differential pressure Calculations involved in: unit conversions Calculations involved in: velocity Calculations involved in: linearization Installation details (e.g., process, pneumatic, electrical, location)

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II.

Signals, Transmission, and Networking 

Signals       



Transmission  



Networking (e.g., routers, bridges, switches, firewalls, gateways, network loading, error checking, bandwidth, crosstalk, parity)

Final Control Elements 

Valves         



Types (e.g., globe, ball, butterfly) Characteristics (e.g., linear, low noise, equal percentage, shutoff class) Calculation (e.g., sizing, split range, noise, actuator, speed, pressure drop, air/gas consumption) Selection of motive power (e.g., hydraulic, pneumatic, electric) Applications of fluid dynamics (e.g., cavitation, flashing, choked flow, Joule-Thompson effects, two-phase) Material selection based on process characteristics (e.g., erosion, corrosion, plugged, extreme pressure, temperature) Accessories (e.g., limit switches, solenoid valves, positioners, transducers, air regulators, servo amp) Environmental constraints (e.g., fugitive emissions, packing, special sealing) Installation practices (e.g., vertical, horizontal, bypasses, location, troubleshooting)

Pressure Relieving Devices      

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Different communications systems architecture and protocols (e.g., fiber optics, coaxial cable, wireless, paired conductors, buses, Transmission Control Protocol/Internet Protocol [TCP/IP], OLE Process Control [OPC]) Distance considerations versus transmission medium (e.g., data rates, sample rates)

Networking 

III.

Pneumatic, electronic, optical, hydraulic, digital, analog, buses Transducers (e.g., analog/digital [A/D], digital/analog [D/A], current/pneumatic [I/P] conversion) Intrinsically Safe (IS) barriers Grounding, shielding, segregation, AC coupling Basic signal circuit design (e.g., two-wire, four-wire, isolated outputs, loop powering, buses) Circuit Calculations (voltage, current, impedance) Calculations: unit conversions

Pressure Relieving Valve Types (e.g., conventional spring, balanced bellows, pilot operated) Pressure Relieving Valve Characteristics (e.g., modulating, pop action) Pressure Relieving Valve Calculations (e.g., sizing considering inlet pressure drop, back pressure, multiple valves) Pressure Relieving Device Material Selection based on process characteristics Pressure Relieving Valve Installation Practices (e.g., linking valves, sparing the valves, accessibility for testing, car sealing inlet valves, piping installation) Rupture discs (e.g., types, characteristics, application, calculations)



Motor Controls     



Other Final Control Elements   

IV.

Types (e.g., motor starters, variable speed drives) Applications (e.g., speed control, soft starters, valve actuators) Calculations (e.g., sizing, tuning, location) Accessories (e.g., encoders, positioners, relays, limit switches) Troubleshooting (e.g., root cause failure analysis and correction)

Solenoid Valves (e.g., types, sizing) On-Off Devices/relays (e.g., types, applications) Self-Regulating Devices (e.g., types, sizing, pressure, temperature, level and flow regulators)

Control Systems 

Drawings 



Theory     



Drawings (e.g., PFD-process flow diagrams, P&IDs–piping and instrumentation diagrams [or drawings], loop diagrams, ladder diagrams, logic drawings, cause and effects drawings, electrical drawings.)

Basic processes (e.g., compression, combustion, evaporation, distillation, hydraulics, reaction, dehydration, heat exchangers, crystallization, filtration) Process dynamics (e.g., loop response, P-V-T pressure volume temperature relationships, simulations) Basic control (e.g., regulatory control, feedback, feed forward, cascade, ratio, PID, splitrange) Discrete control (e.g., relay logic, Boolean algebra) Sequential control (e.g., batch, assembly, conveying, CNC)

Implementation        

HMI (e.g., graphics, alarm management, trending, historical data) Configuration and Programming (e.g., PLC, DCS, hybrid systems, SQL, ladder logic, sequential function chart, structured text, function block programming, data base management, specialized controllers) Systems Comparisons and Capabilities (e.g., advantages and disadvantages, of systems architecture, distributed architecture, remote I/O, buses) Installation Requirements (e.g., shielding, constructability, input/output termination, environmental, heat load calculations, power load requirements, purging, lighting) Network Security (e.g., firewalls, routers, switches, protocols) System Testing (e.g., FAT-factory acceptance test, integrated systems test, site acceptance test) Commissioning (e.g., performance tuning, loop checkout) Troubleshooting (e.g., root cause failure analysis, and correction)

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V.

Safety Systems 





VI.

Basic Documentation  Basic documentation (e.g., safety requirements specification, logic diagrams, test procedures, SIL selection report) Theory  Reliability (e.g., bathtub curve, failure rates)  SIL selection (e.g., risk matrix, risk graph, LOPA) Implementation  Safety systems design (e.g., I/O assignments, redundancy, segregation, software design)  Safety integrity level (SIL) verification calculations  Testing (e.g., methods, procedures, documentation)  Management of changes (e.g., scope of change, impact of change)

Codes, Standards, Regulations          

American National Standards Institute (ANSI) American Petroleum Institute (API) American Society of Mechanical Engineers (ASME) International Electrotechnical Commission (IEC) Institute of Electrical and Electronics Engineers (IEEE) International Society of Automation (ISA) National Electrical Code (NEC) National Electrical Manufacturers Association (NEMA) National Fire Protection Association (NFPA) Occupational Safety and Health Administration (OSHA)

Exam Scoring NCEES exams are scored independently. There are no pre-specified percentages of candidates that must pass or fail. Assisted by a testing consultant, a panel of licensed CSEs uses recognized psychometric procedures to determine a passing score corresponding to the knowledge level needed for minimally-competent practice in the discipline. The passing score is expressed as the number of questions out of 80 that must be answered correctly. The method used for pass-point determination assures that the passing score is adjusted for variations in the level of exam difficulty and that the standard is consistent from year to year. Starting in October 2005, candidates have received results expressed either as “Pass” or “Fail”; failing candidates no longer receive a numerical score. Published passing rates are based on first-time takers only, omitting the results for repeat takers.

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Reference Materials for the Exam Recommended Books and Materials to Take to the Exam I have included a review of all subject material that is in the NCEES PE/CSE examination specifications and almost any data you may need to look up for questions on the examination. The list of recommended books and materials for testing in this guide, have been listed to help you pass the CSE examination. Use a book you are comfortable with. A substitution with the same material and information may be used. The list of recommended books and materials for additional study can be helpful in the review of subjects and preparation for the examination. See http://www.isa.org for more books that may help give you knowledge and deeper insight into various subjects in instrumentation and control systems. Remember to keep the review simple. The test is not on control systems theory studies, but rather on simple general functional design. Again keep your studies simple and practical; control systems theory will only encompass about 3% of the examination.

National Council of Examiners for Engineering and Surveying Non-profit organization The National Council of Examiners for Engineering and Surveying is a national nonprofit organization composed of engineering and land surveying licensing boards representing all U.S. states and territories. Founded: 1920 NCEES on Wikipedia

NCEES on LinkedIn Click on any link above to visit the site

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Books and Materials for Testing 

NCEES APPROVED CALCULATOR (Have a spare with new batteries installed). I recommend the TI-36X Solar (any light). Practice with the calculator you will be using. (See http://www.ncees.org for a current list of approved calculators.)



ISA-5.1-1984 (R1992) - INSTRUMENTATION SYMBOLS AND IDENTIFICATION



ISA-5.2-1976 (R1992) - BINARY LOGIC DIAGRAMS FOR PROCESS OPERATIONS



ISA-5.3-1983 - GRAPHIC SYMBOLS FOR DISTRIBUTED CONTROL/ SHARED DISPLAY INSTRUMENTATION, LOGIC, AND COMPUTER SYSTEMS



ISA-5.4-1991 - STANDARD INSTRUMENT LOOP DIAGRAMS



Fisher or Masoneilan Control Valve Sizing Handbook / Catalog (most data needed for the CSE examination is in this reference manual)



A Safety Relief Valve Book (could be useful) (most data needed for the CSE examination is in this reference manual)

Books for Additional Study 

The Control Systems Engineering (CSE) Study Guide, Fifth Edition, ISA (I highly recommend purchasing this 4-hour review exam)



Instrumentation for Process Measurement and Control, Third Edition, CRC Press, LLC – Norman A. Anderson. (Foxboro)



Basic and Advanced Regulatory Control: Systems Design and Application Third Edition, ISA – Dr. Harold Wade.



Measurement and Control Basics, Fifth Edition, ISA – Thomas A. Hughes



Process Control: A Practical Approach, Wiley – Myke King



Crosby® Pressure Relief Valve Engineering Handbook



Pentair Pressure Relief Valve Engineering Handbook



Alfa Laval Pump Handbook



Programmable Controllers: Theory and Implementation, Second Edition (Bryan and Bryan)



Visit the site: http://learncontrolsystems.com for free study materials, utilities and online training



See ISA (International Society of Automation) for a list of recommended books for study and review

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Courses for Additional Study

ISA Control Systems Engineer (CSE) PE Review 

ISA (International Society of Automation) offers an instructor-led Control Systems Engineer (CSE) PE exam review course at different locations across the nation. The ISA Control Systems Engineer (CSE) information page: http://www.isa.org/isa-certification/cse-licensure-preparation

This course is typically taught by Gerald Wilbanks, P.E. He is a registered professional engineer in four states, a member of NSPE, and ASQ, and an International Former President (1995) of the International Society of Automation (ISA). Gerald is a graduate of Mississippi State University with a B.S. in electrical engineering and was recognized as the Engineer of the Year in 1991 by the Engineering Council of Birmingham. He is a Distinguished Engineering Fellow of MSU and is a Life Fellow member of ISA. He has served as an instructor in many courses, seminars, and other educational sessions for ISA and in his own business.

Gerald Wilbanks, P.E.

See the ISA web site http://www.isa.org for more books and training materials on advanced and basic subjects. ISA offers webinars with instructor-led training in many aspects and topics of process control and networking, as well as the popular topic of networking security. They offer several online study courses specializing in instrumentation and process control for people needing an introduction to the fundamentals of instrumentation. As an ISA member, many of the training videos and ISA/ ANSI standards are free.

Industrial Network Training 

Siemens Automation Free Training PROFINET and PROFIBUS one-day seminars PI North America and the PROFI Interface Centers throughout North America. Webinars are also available on-demand. Certified Courses PROFItech certification courses are available to allow attendees to gain the designation "Certified Network Engineer." Developer, installers, and other courses are available for both PROFINET and PROFIBUS technology and training is also available for AS-i networks.



Fieldbus Center The Fieldbus Center at Lee College, Baytown, Texas offers instructor-led training in the study and certification of FOUNDATION Fieldbus and other process control systems. The training center uses industrial standard equipment and instruments, utilizing the Emerson DELTAV DCS (distributed control system) for programming and as a host system. The Fieldbus Center at Lee College was the first national F OUNDATION Fieldbus training center, established by Chuck Carter with a grant from the National Science Foundation. It is supporting most manufacturers in the instrumentation industry. On a note, Chuck Carter was also one of my instructors when I attended Lee College in 1994.

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Chuck Carter

Control Systems Engineer (CSE) Supplement Course 

Integrated Systems offers online study courses in Controls Systems Engineering (CSE) as a supplement to the ISA (CSE) PE REVIEW course. It includes study materials and streaming videos of instructor-led training. These courses use a live small scale online process plant to demonstrate real world applications of calculations and the tuning and response of real process systems. The online plant is live and interactive at scheduled times during your studies. The plant includes a small MCC and multiple Automation PLCs utilizing typical plant control systems, instrumentation and I/O as seen every day in a large plant or manufacturing environments. Topics include PLC programming, process equipment sizing, instrumentation calculations and calibration procedures, industrial networking configuration and troubleshooting, motor controls, electrical installations and codes, instrumentation and electrical safety grounding, applications of fluid mechanics for process control and measurement. The student has three months to complete their studies and the courses are led by the author of this exam reference manual. Visit http://learncontrolsystems.com or http://www.integrated.cc for more information on training and to run the process plant online for free.

Online Process Plant @ Learn Control Systems.com

Integrated Systems uses the plant shown to teach process and manufacturing control systems to engineers and technicians in the Learn Control Systems courses. It is used to demonstrate in-depth training on various applications of industrial instrumentation and industrial networking, including multivariable control systems. The plant is accessible through a standard web browser and uses live video feed of high definition web cameras, with a wide view and a zoomed close up view of the instrumentation readings. All variables are set and read over the internet in real time via a web browser. The full course work will be in an HMI format, just like you would use in a real process plant. Desktop remote sessions can be scheduled for personal programming of the PLCs. (The free online demo mode has limited access to control functions. It serves as a course preview.)

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Process Measurement Standards and Terminology Overview of process measurement, control and calibration The process control industry covers a wide variety of applications: petrochemical; pharmaceutical; pulp and paper; food processing; material handling; even commercial applications. Experience designing process control systems is almost a necessity to pass the Control Systems Engineer PE examination. Process control in a plant can include discrete logic, such as relay logic or a PLC; analog control, such as single loop control or a DCS (distributed control system) as well as pneumatic; hydraulic and electrical systems. The Control Systems Engineer must be versatile and have a broad range of understanding of the engineering sciences. The CSE is typically referred to as I & E (Instrumentation and Electrical), though the CSE must have in-depth knowledge of mechanical and process systems. The Control Systems Engineer (CSE) examination encompasses a broad range of subjects to ensure minimum competency. This book will review the foundations of process control and demonstrate the breadth and width of the CSE examination. We will then review the basic process control elements, their theory of operation and then apply the elements to real-world application. We will then review the calculations for sizing of the elements, as well as the applicable laws, standards and codes governing the installation of a process control system.

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Process Signal and Calibration Terminology The most important terms in process measurement and calibration are range, span, zero, accuracy and repeatability. Let us start by first defining Span; Range; Lower Range Value (LRV); Upper Range Value (URV); Zero; Elevated Zero; Suppressed Zero.

Definition of the Range of an Instrument Range: The region in which a quantity can be measured, received, or transmitted, by an element, controller or final control device. The range can usually be adjusted and is expressed by stating the lower and upper range values. NOTE 1: For example: Full Range Adjusted Range LRV URV a) 0 to 150°F None 0°F 150°F b) –20 to +200°F –10 to +180°F –10°F +180°F c) 20 to 150°C 50 to 100°C 50°C 100°C NOTE 2: Unless otherwise modified, input range is implied. NOTE 3: The following compound terms are used with suitable modifications in the units: measured variable range, measured signal range, indicating scale range, chart scale range, etc. See Tables 1 and 2. NOTE 4: For multi-range devices, this definition applies to the particular range that the device is set to measure. Range-limit, lower: LRV (Lower Range Value) The lowest value of the measured variable that a device is adjusted to measure. Range-limit, upper: URV (Upper Range Value) The highest value of the measured variable that a device is adjusted to measure. NOTE 1: The following compound terms are used with suitable modifications to the units: measured variable lower range-limit, measured signal lower range-limit, etc. See Tables 1 and 2. Range-limit, upper: URV (Upper Range Value) The highest value of the measured variable that a device is adjusted to measure. NOTE 2: The following compound terms are used with suitable modifications to the units: measured variable upper range-limit, measured signal upper range-limit, etc. See Tables 1 and 2, Span: The algebraic difference between the upper and lower range-values.

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Definition of the Span of an Instrument Span: The algebraic difference between the upper and lower range-values. NOTE 1: For example: Range: 0 to 150°F, Span 150°F Range: –10 to 180°F, Span 190°F Range: 50 to 100°C, Span 50°C NOTE 2: The following compound terms are used with suitable modifications to the units: measured variable range, measured signal range, etc. NOTE 3: For multi-range devices, this definition applies to the particular range that the device is set to measure. See Tables 1 and 2.

Definition of the use of Zero in Instrumentation Live-Zero The lower range value (LRV) is said to be set to zero, as a reference point, whether it is at zero or not. This LRV can be 0%; -40°F; 4 mA; 1V or 3 PSI. All LRVs are an example of the ZERO (Live Zero), in process control signals or elements. Elevated-Zero The lower range-value of the range is below the value of zero. The LRV of the range must be raised to Live Zero, for the instrument to function properly. The output signal of the measured value will always be 0 to 100%. If the LRV of the range is too low, the instrument may not be able to reach 100% output. NOTE: For example:

input signal = (-100 in H2O to 25 in H2O) output signal = (4 mA to 20m A)

The output signal may only reach 12 mA for 25 in H2O (100%) input, due to limitation in the electronics or pneumatics. Therefore, the Elevate jumper must be set in the transmitter or an elevation kit must be installed in a pneumatic transmitter. See Table 1. Suppressed-Zero The lower range-value of the span is above the value of zero. The LRV of the range must be lowered to Live Zero, for the instrument to function properly. The output signal of the measured value will always be 0 to 100%. If the LRV of the range is too high, the instrument may not be able to reach 0% output. NOTE: For example:

input signal = (50 in H2O to 200 in H2O) output signal = (4 mA to 20 mA)

The output signal may only reach 6 mA for 50 in H2O (0%) input, due to limitation in the electronics or pneumatics. Therefore, the Suppress jumper must be set in the transmitter or a suppression kit must be installed in a pneumatic transmitter. See Tab1e 1.

45

Illustrations of range and span terminology

Table 1 – Examples of range and span terminology TYPICAL RANGES

NAME

RANGE

LOWER RANGE VALUE

UPPER RANGE VALUE

SPAN

SUPPLEMENTARY DATA

0

+100

—

0 to 100

0

+100

100

—

20

+100

SUPPRESSED ZERO RANGE

20 to +100

20

+100

80

SUPPRESSION RATIO = 0.25

-25

+100

ELEVATED ZERO RANGE

–25 to +100

–25

+100

125

—

–100

0

ELEVATED ZERO RANGE

–100 to 0

-100

0

100

—

–100

–20

ELEVATED ZERO RANGE

–100 to –20

-100

-20

80

—

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Illustrations of measured variable, measured signal, range and span

Table 2 – Examples of measured variable, measured signal range and span TYPICAL RANGES

THERMOCOUPLE 0 2000°F TYPE K T/C

– 0.68

+ 44.91 mV

FLOWMETER 0 10,000 lb/h

0

100 in H2O

0

10 x1000=lb/h

4

20 mA

1

5 Volts

47

TYPE OF RANGE

RANGE

LOWER RANGE VALUE

UPPER RANGE VALUE

SPAN

MEASURED VARIABLE

0 to 2000°F

0°F

2000°F

2000°F

MEASURED SIGNAL

–0.68 to +44.91 mV

–0.68 mV

+44.91 mV

45.59 mV

MEASURED VARIABLE

0 to 10 000 lb/h

0 lb/h

10,000 lb/h

10,000 lb/h

MEASURED SIGNAL

0 to 100 in H2O

0 in H2O

100 in H2O

100 in H2O

SCALE AND/OR CHART

0 to 10,000 lb/h

0 lb/h

10,000 lb/h

10,000 lb/h

MEASURED SIGNAL

4 to 20 mA

4 mA

20 mA

16 mA

MEASURED SIGNAL

1 to 5V

1V

5V

4V

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Applications of Fluid Mechanics in Process Control Relationship of pressure and flow In a pipe, the static pressure distributed across the pipe is even during no flow. You have the same pressure at both ends of the pipe because the total energy in the system is at equilibrium. As the fluid flows, it is accelerated through the pipe. There is a pressure drop across the pipe. The static pressure is a measurement of the potential energy in the fluid. It is changed to the form of kinetic energy and is used up in the form of heat and vibration doing work on the pipe to overcome the friction of the pipe.

The higher the flow rate, the greater the pressures drop across the pipe. The work done to transfer the fluid through the pipe at higher flow rates becomes greater. Therefore, the pressure drop across the pipe increases as the velocity of the fluid increases through the pipe. It can be seen that the static pressure (available pressure) at the end of the pipe will be lower than the supply or pump pressure at the start of the pipe, due to the fact that work is being done on the pipe. The pump head energy is used up doing work on the pipe. The ∆P measurement across the flow element acts just a little bit different. Flow is measured in the units of ∆P or DP (differential pressure). There is a pressure drop across the orifice element and there will be more pressure drop across the element as the flow rate (the fluid’s velocity) increases. This is the same thing that is happening in the pipe. This is because more work is being done on the element as the velocity increases. But remember the pressure on the downstream side the flow element drops as the velocity increases. How does the pressure for the flow measurement increase? It doesn’t, it is an increase in ∆P or DP (differential pressure), not in the static pressure. We are measuring the ∆P differential pressure across the element and this is an inferred measurement of flow rate. Flow rate equals the velocity (distance per time) multiplied by the area of the pipe. We achieve the measurement of velocity by differential pressure. The difference between the upstream pressure and the downstream pressure across the element is a measurement of the difference in height in two different water columns. This difference in height is a direct proportional measurement of the velocity of the fluid flowing through the pipe. The pump endows potential energy into the fluid and accelerates the fluid upward into a measurable column of water. The water column is typically measured in feet of HEAD PRESSURE, but can be measured in PSI. The water is constantly “falling” down the pipe toward the other end of the pipe and the

49

pump has to constantly accelerate the water upward against the pull of gravity to keep the water column up in the air. The potential energy endowed into the water column turns into kinetic energy, as the water column falls. The kinetic energy is used to overcome the resistance of the pipe and the work done on the pipe as the fluid flows to the other end. If there is energy left over in the fluid, it is again transformed back into to potential energy at the other end of the pipe, as an available pressure at the end of the pipe. This potential energy left over can now fall through a pipe or device or some equipment and do work and then finally resting at a state of equilibrium. At this point all of the energy endowed into fluid by the pump will be used up. Note: The image at the right shows the pump has to develop enough head to raise the fluid to the pipe’s top elevation plus enough head to overcome the friction loss of the piping (suction and discharge). You will also need to add head for any differential pressure across the valve and the orifice or head type meter. 2

The velocity of the fluid is measured as the fluid falls. V =2gH, where “H” is the height in feet (the head). The volumetric flow rate can then be an inferred measurement of the height of the water column. By knowing the size of the pipe and the coefficient of the orifice and the properties of the fluid, we can accurately measure the volumetric flow rate of the fluid. As the fluid flows through the opening of the orifice restriction, kinetic energy is transformed into potential energy in the form of a difference of water column on each side of the restriction orifice element. The height of the water column is the “SCALED” velocity of the fluid through the pipe. Remember the slower the fluid travels, the less work it has to do. The fluid has to accelerate through the small opening in the orifice to maintain the same mass flow rate through the pipe. Remember mass in has to equal mass out. Energy is lost doing work on the orifice plate and the pressure drops on the exit side of the orifice. This can be seen in the profile of the vena contracta of the fluid flowing and the ∆P (differential pressure) across the orifice element. As the fluid exits the small opening into the much larger area of the pipe, the fluid decelerates and a portion of the kinetic energy endowed into the fluid by the pump, is transformed back into potential energy. This potential energy can be seen in the form of a water column, of varying height, on the entry and exit sides of the orifice. If the pipe were blocked at the exit end, the water would squirt out the taps on both sides of the orifice and the two water columns of equal height would become obvious. Again as the fluid starts to accelerate through the pipe and through the orifice, the fluid’s potential energy tends to change back into kinetic energy to do work. This means the water columns start to fall on both side of the orifice. The exit side will fall even more than the entrance side, due to the fact that work is done on the orifice restriction element, as the flow rate increases. The difference in height the column falls on the exit side compared to the upstream column, is its scaled velocity of the flow rate. The higher the fluid’s velocity, the more work is done on the orifice and the pressure drops even more on the exit side of the orifice. This gives a greater ∆P (differential pressure)

50

across the orifice. Note that as the pressure drops in the pipe due to increased velocity, the ∆P at the measurement meter becomes greater! This is because the total system pressure (total hydraulic head) is decreasing by doing work on the pipe and the potential energy (pressure head) is being transformed back into kinetic energy (velocity head) to do the work. The lower the fluid’s velocity through the orifice, the higher the pressure on the exit side of the orifice. This means there is less difference between the pressure on the high side (entry side) water column and the low side pressure (exit side) water column. Therefore, there is less measured ∆P (differential pressure) across the orifice when the fluid decelerates, even though the pressure increased on the exit side of the orifice and everywhere in the pipe system. Note as the fluid flow approaches a stop, the two water columns are almost even in height. The pressure differential, ∆P, becomes almost nothing. The static pressure on the exit side of the orifice, which represents the potential energy in the fluid, becomes greater. The pipe system will try to reach equilibrium or uniform distribution of static pressure across the pipe system as the work across the pipe becomes less and less. The kinetic energy will change back into potential energy. Remember the total energy in the system equals the kinetic + potential + work done. As the fluid starts to accelerate down the pipe once again, the exit side water column starts to drop in height. The potential energy (pressure head) is once again being transformed back into kinetic energy (velocity head), to do work across the element and pipe. The distance in height the exit side water column falls compared to the height of the entry side water column is the “SCALED” velocity of the flowing fluid. Since we know the fluid’s specific gravity (s.g.), we can now calculate the fluid’s height as if it were a column of water. Remember (F=m*a) and weight is a measure of the force exerted by the pull of gravity. Pressure equals (density * height) and force equals (pressure * area), therefore the pressure measurement is a representation of the fluid’s height. Stack 231 cubic inches of water on top of each other, to form a tall column of water, with a base of 1 square inch. The column of water will be 231 inches tall. Divide the height of the column of water, 231 inches, by the weight of one (1) gallon of water, 8.324 pounds at 60°F. The result will be 27.691 or 27.7 inches of water column per pound of water, over a one square inch of area. Therefore 27.7 inches H 2O, of head pressure, equals one (1) PSI. Therefore, the column of water can be measured in pounds per square inch (psi), not just “HEAD PRESSURE” as a height of inches of water in the measurement meter. Just by knowing the height of the column we can determine the pressure it can excerpt and the inferred amount work it can do. A column of fluid with a lesser weight or density compared to water has specific gravity less than one (1). Specific gravity is the ratio of the density or weight of a fluid compared to the density or weight of water. The more dense the fluid is, the more mass it has, therefore the more force it excerts due to the acceleration of gravity (F=m*a). So a fluid with a specific gravity less than one (1) cannot excerpt as much

51

force as water because it has less mass. Therefore, a column of fluid with a specific gravity less than 1 excerpts less pressure on a measurement meter, compared to the pressure excerpted by a column of water. This is why we divide the pressure head by the specific gravity to give it a “gain” of force equal to that excerpted by water, the industrial standard of measurement. From the previous demonstration, it can be seen that a column of fluid with a specific gravity less than 1, needs to be taller than a column of water, to excerpt the same pressure on the measurement meter. If we had a fluid, such as a solvent, it may have a s.g. of (0.7874). We use the industrial standard of water to calibrate the meter. So to measure the height of the column of solvent in the standard of calibration with water, the column of solvent needs to be taller than a column of water to excerpt the same force on a weight scale. It would seem that the taller column of solvent would be falling faster than the velocity we need to measure and it is. It has less mass; therefore, it needs to be accelerated faster than the column of water to develop more force on impact. This force at impact will be the same force generated by the column of water falling from a lower height and the pressure on the measurement element will be the same. It can be seen we have an equivalent force and an equivalent pressure on the meter, for the two different height columns of fluid. In level measurement, the column of water used to calibrate the meter will less than the column of solvent being measured. The water must fall from a lower height to excerpt the same pressure as the taller column of solvent. So if we have a s.g. of 0.7874 for the solvent, the column of water will be 0.7874 times the height of the solvent column or 78.74% of the intended height measurement. This will produce a 78.74” column of water (100” H2O * 0.7874 s.g. = 78.74” H2O). The solvent column will be 100” tall but will appear to be only 78.74” of water to the measurement meter. Zero to 100% output will equal 0 to 100” of solvent. The height of solvent needed to produce a pressure equal to that of 100 cm of water is shown to the right. The solvent column height is taller than the column of water, 100 cm / (s.g. = 0.7874). So the column of solvent equals 100 cm / 0.7874 = 127 cm. It can be seen that both columns produce the exact same pressure at the bottom of the “U” tube. The same thing is happening in the flow meter. The solvent is less dense than water and excerpts less pressure on the meter for the same flow rate as water. 10 gallons a minute of water traveling down a pipe or conveyor weights (10 * 8.33 lb. = 83.3 lbs.). 10 gallons a minute of solvent traveling down a pipe or conveyor weights (10 * 8.33 lb. * 0.7874 s.g. = 65.59 lbs.). The pressure the solvent excerpts on the scale is less for the same volumetric flow rate. Again the flow meter will be calibrated in water with a lower measure of water column applied to the meter to read the desired flow rate of solvent.

Applications of the formulas Let’s do a quick overview of how we use fluid mechanics in process control measurements and then we will discuss how we get the formulas and how fluid mechanics are used in detail in the following sections of this guide to provide safe and accurate control of process plants.

Part One Let’s look at the flow measurement formula for calibration. We have 100 gpm of water flowing in a 3” schedule 40 pipe (ID=3.068”) with a s.g. of 1 and the orifice diameter is 1.534”. The “Beta Ratio” is the pipe inside diameter divided by the orifice hole diameter.

Q( gpm)  5.667 SD 2

h Gf 52

The Beta Ratio = 0.5 (3.068 /1.534 =0.5). From Table 3: Beta = 0.500, S = 0.1568

100( gpm)  5.667  0.1568 3.068 100( gpm) 5.667  0.1568 3.068  2  100( gpm)   h       8.3639   1 

11.95612 

2



2

h 1

h 1

2

h 1

142.95" H 2 O  h Now we will have 100 gpm of solvent flowing in a 3” schedule 40 pipe (ID=3.068”) with a s.g. of 0.7874.

Q( gpm)  5.667 SD 2

h Gf

From Table 3: Beta = 0.500, S  0.1568

100( gpm)  5.667  0.1568 3.068 100( gpm) 5.667  0.1568 3.068

2



2 h   100( gpm)         8.3639   0.7874  h 11.95612  0.7874 142.95  0.7874   h

2

h 0.7874

h 0.7874 2

112.56" H 2 O  h It can be seen we need less water to calibrate the flow meter in the calibration standard of water, to measure the flow of solvent.

53

Part two Let’s apply Bernoulli’s principal to the pressure drop in pipes: For a change in the static pressure anywhere in the piping system: 2

F  p2   1  p1  F2 

p F  p2 F 2 1 1

2 2

This is practical for a pressure meter to measure the available pressure at a flow rate, but it does not tell the loss of pressure across the piping system or flow element. We have 100 gpm of water flowing through 100 foot of 2” schedule 40 pipe (ID=2.067”) at 60°F (cST=1.22). The pump is producing 100 feet of water or 43.32 psi. When the pump is running at full speed and the pipe is blocked by a valve at the exit end of the pipe, the pressure of 100 feet of head is distributed evenly throughout the pipe. We crack open the valve until the water is flowing at 100 gpm. Let’s calculate the head drop (delta pressure drop) across the pipe. First find the velocity of the fluid:

velocity( ft / sec) 

9.56( ft / sec) 

gpm *0.4085 ID2 (inches)

100*0.4085 2.0672 (inches)

Find the Reynolds number for the pipe:

Re =

3160 * flow rate( gpm) * Specific Gravity Note: for liquids Pipe ID(inches) * Viscosity (cST )

125,310Re 

3160 * 100 * 1 2.067" ID * 1.22(cST )

Find the head loss across the pipe using the Darcy-Weisbach equation: Find the friction factor: Friction factor for Darcy-Weisbach equation Note: e = 0.00015 for steel pipes

1 6     e *12 10 3  f  0.0055  0.0055  20,000   Re    Pipe ID(inches)   1 6  3 10  0.00015 *12   0.0217  0.0055  0.0055  20,000     2.067"  125,310 

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Find the head loss in the piping system: 2  Length( ft ) * 12  V  ft / sec  hL  f  *  64  Pipe ID(inches ) 

2  100' * 12  9.56  ft / sec  17.99 feet  0.0217  * 64  2.067" 

There is a head loss (pressure drop) across the pipe of 17.99 feet of water (or 7.8 psi) at 100 gpm. This leaves 82 feet of head (100’ – 18’ = 82’) or 35.52 psi, at the end of the pipe to do work across a control valve or overcome a pressure in a vessel. Note: Usually there is no more than a 10 psi differential of pressure across the control valve. It is recommended that an additional 10% to 40% increase in pump head be added to the required system pump pressure for normal pumping through the piping system, minus the required head to overcome any vessel pressure (pressurized tank, vessel or column). We only need to add the 10% to 40% extra head to the pump head that is needed to overcome the friction loss of the pipe and to do the foot-pounds of work to accelerate the fluid through the pipe. Important Note: You cannot size the pump for just the pressure drop across the piping system due to friction loss and flow rate. The valve will not work. There must be extra head pressure across the valve or the valve will not function. The ∆P across the valve for 10% should be: 17.99 psi * 0.10 = 1.799 psi or 4.153 feet of head for the valve sizing calculation. There will be 1.799 psi across the valve, if there is a 10% increase in the pump head for the piping system. The ∆P across the valve for 40% should be: 17.99 psi * 0.40 = 7.196 psi or 16.61 feet of head for the valve sizing calculation. There will be 7.196 psi across the valve, if there is a 40% increase in the pump head for the piping system. Let’s now calculate the head loss at 50 gpm:

First find the velocity of the fluid: 50*0.4085 4.78( ft / sec)  2.0672 (inches) Find the Reynolds number for the pipe:

62,655Re =

3160 * 50 * 1 2.067" ID * 1.22(cST )

Find the friction factor:

1 6  10  3  0.00015 *12   0.0217  0.0055  0.0055 20,000     2.067"  62,655  Find the head loss across the pipe: 2  100' * 12  4.78  ft / sec  4.8 feet  0.0232  * 64  2.067" 

55

There is a head loss (pressure drop) across the pipe of 4.8 feet of water (or 2.08 psi) at 50 gpm. This leaves 95.2 feet of head (100’– 4.8 ’= 95.2’) or 41.24 psi, at the end of the pipe to do work across a control valve or overcome a pressure in a vessel. Note: The psi drop across the control valve increases as the flow slows down and the valve absorbs the remaining pressure left in the system across the control valve. The difference of the system pressure is the pump head minus the head loss across the piping system and minus any head needed to overcome entry into a pressurized vessel. Just like I*R=E, the valve has more resistance to flow as it closes down, so the pressure drop across the valve increases to maintain the flow rate. So even though the control valve is trying to slow down the flow rate of the fluid, the fluid will try to maintain its flow rate as the valve absorbs the extra pressure in the system. The control valve controls the flow by burning up the extra energy head in the fluid as it flows through the piping system. We will discuss this in much more detail in the section on control valves.

1 gpm  1 CV *

1 Ppsig

Visit http://www.learncontrolsystems.com/studymaterials/ for more resources to study. A piping system calculator can be downloaded for free from my web site. It is an Excel Spreadsheet to show real-world system results, with generated graphs of response curves of valve characteristics for a given system. Liquid System Sizer - version 2.7 (Size Pump, Valve, Orifice, Transmitter and Piping System) http://www.learncontrolsystems.com/studymaterials/System-Sizer.htm

Summary of fluid mechanics for process control The ∆P across the orifice decreases as the velocity of the fluid decreases. It can be seen that the pressure on the exit side of the orifice increases as the fluid’s velocity decreases and the pressure drop across the pipe decreases (less work is being done). The velocity being measured is a “SCALED” velocity. It is scaled by the orifice size; the beta factor “the Spink Factor" or flow coefficient; the pipe ID and the specific gravity (s.g.) of the fluid. Velocity equals the “square root of (2gH)”. The fluid’s velocity through the pipe may be much different than the measured differential height of the two water columns that are being measured to obtain the fluid’s velocity. Depending on the orifice size and the beta factor (say 0.3), for a given flow rate, the ∆P may be 1,000 inches of water column differential across a small orifice opening. The fluid has to do much more work to get through the high resistance of the small opening. The ∆P could be only 100 inches water column differential for a much larger beta ratio (say 0.7). The larger opening has less resistance and therefore much less work is being done to flow through it. Therefore less potential energy has to change into kinetic and the height of the water column on the exit side of the orifice is much higher than with a beta ratio of (say 0.3). Therefore there is less ∆P across the orifice for the same flow rate that has been “SCALED” to calculate the volumetric flow rate. Remember the pump will have to produce enough head pressure to provide energy for the work to be done on the piping system and any valves or head type meters at the maximum flow rate. The valve cannot just be sized for some selected differential pressure; it must be sized for the pump head pressure not being used to do work on the rest of the piping system. The valve differential pressure must be checked at maximum flow, normal flow and minimum flow rates, to ensure the valve will control the flow rate properly. Now we will discuss most process measurement subjects in detail, including the application of the fluid mechanics we just reviewed. These basic principles work for level, flow, orifice sizing, valve sizing, pump sizing, pipe sizing and understanding the basics of process operations.

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Temperature Measurement and Calibration Temperature measurement devices and calibration In the process industry, temperature measurements are typically made with thermocouples, RTDs (Resistance Temperature Detector) and industrial thermometers. Industrial thermometers are typically of the liquid (class I), vapor (class II), and gas (class III) type. Standard Thermocouple Configurations Single Grounded

Single Ungrounded

Dual Grounded Unisolated

Dual Ungrounded Unisolated

In plants there are five major types of thermocouple (TC) configurations used. They are shown to the left. The first two thermocouples are welded or grounded, as shown, to the outside metal protective sheathing. The bottom three thermocouples are ungrounded and should never touch the metal protective sheathing; otherwise they are shorted to ground

Dual Ungrounded Isolated

Most Popular Types Used in Process Plant Temperature Measurements J-Type

K-Type

The four major thermocouples used in the process industry for temperature measurement are: JType, E-Type, K-Type, and T-Type. The red wire is always the negative wire with thermocouples.

E-Type

T-Type Thermocouple terminal junction blocks should be made of the same material as the thermocouple wire that is being connected to terminal. This will prevent additional thermocouple (TC) junction points from being introduced in the temperature signal. Some companies use standard terminal strips, this can cause an error in the signal.

Thermocouple Extension Wiring Thermocouples should be extended with thermocouple extension wire and thermocouple termination blocks, but can be extended with standard copper wire and standard terminal blocks. This is due to the fact that the voltages generated at the extension junctions almost cancel each other out with very little error. One side is positive (the color: yellow, white, purple, etc.) and the other side is negative (always red, except in some extension wires).

57

Thermocouple millivolt tables for the examination can be found in the Table A1 – Thermocouple Table (Type J) through Table A4 – Thermocouple Table (Type T) in the Appendix section of this guide.

Thermocouple Linearity Chart

Thermocouple Makeup Material and Color Code TC Type

THEMOCOUPLE MATERIAL

RANGE FOR CALIB. DEG F

USEFUL RANGE DEF F

E

TC COLORS

Chromel (+) Constantan (-)

-300 to 1830

200 to 1650

Purple Wire Jacket Purple (+) Red (-)

J

Iron (+) Constantan (-)

-320 to 1400

200 to 1400 (300 to 800)

Black Wire Jacket Black (+) Red (-)

K

Chromel (+) Alumel (-)

-310 to 250

200 to 2300

Yellow Wire Jacket Yellow (+) Red (-)

R

Platinum 13% Rhodium (+) Platinum (-)

0 to 3100

1600 to 2640

Green Wire Jacket Black (+) Red (-)

S

Platinum 10% Rhodium (+) Platinum (-)

0 to 3200

1800 to 2640

Green Wire Jacket Black(+) Red (-)

-300 to 750

-310 to 660

Blue Wire Jacket Blue (+) Red (-)

T

Copper (+) Constantan (-)

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Thermocouple - worked examples (how to read the thermocouple tables) Sample problem: What is the Millivolt (mV) output of a Type “J” thermocouple at 218°F and referenced to a 32°F electronic ice bath?

Find the nearest temperature in Table A1 - Thermocouple Table (Type J) in the appendix of this guide. The nearest temperature in the first column is 210. Look at the column headers at the bottom of the chart. Find the column header labeled 8. Follow the column up to the row with the 210 value. Where they meet is a total of 210°F + 8ºF = (218°F). Read the value of mV. The answer is: 5.45 mV

Sample problem: What is the Millivolt (mV) output of a Type “K” thermocouple at 672°F from the data given? Assume the thermocouple is linear.

Given: 670°F = 14.479mV 672°F = mV 680°F = 14.713mV We will have to interpolate the mV value for the desired temperature as follows: Interpolation:

 deg desired - deg lower value   mV    mV upper value - mV lower value     deg upper value - deg lower value    mV lower value Therefore the new mV for 672°F:

 672 - 670   14.526    14.713 - 14.479    14.479  680 - 670   The mV at 672°F is 14.526 mV This can be verified in Table A2 –Thermocouple Table (Type K) in the appendix.

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RTD (Resistance Temperature Detector) The process control industry also uses RTDs (Resistance Temperature Detectors) for many applications, for example, when precise temperature measurement is needed, such as mass flow measurements or critical temperature measurements of motor bearings. RTDs typically come in 10-ohm copper and 100-ohm platinum elements. Their resistance is typically very linear over the scale. Resistance values for the examination can be found in the Table A5 - Platinum 100 Ohm RTD Table in ohms, in the appendix section of this guide.

Typical wiring configurations and uses of RTDs 2-wire RTD

Good for close applications, at the transmitter.

3-wire RTD

4-wire RTD

Good for further distance applications. Remote from the transmitter.

Best application and usually uses 20 mA driving current and a voltage measurement.

RTD - worked examples Sample problem: A RTD is platinum and has a resistance of 100 ohms at a temperature of 32°F and an alpha 0.2178 ohms per °F. What is the resistance of the RTD at a temperature of 240°F?

Find the difference in the temperature first. 240°F – 32°F = 208°F Now find the resistance for the differential temperature: 208°F * 0.2178 ohms/deg F = 45.3 ohms Now we add the change in resistance to the resistance at 32°F: 100 ohms + 45.3 = 145.3 ohms Referring to Table-A5. Platinum 100 Ohm RTD Table in ohms, in the appendix. The resistance value for the RTD can be interpolated and found for a given temperature.

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Sample problem: In the bridge circuit below, if R1 and R2 are 200 ohms and the RTD is at 60°F. What resistance should R3 measure, to balance the circuit and give the meter a reading of 0 volts? The RTD is platinum and measures 100 ohms at 32°F with an alpha of 0.2178 ohms per °F.

Find the difference in the temperature first. 60°F – 32°F = 28°F Now find the resistance for the differential temperature: 28°F * 0.2178 ohms/°F = 6.0984 ohms Now we add the change in resistance to the resistance at 32°F: 100 ohms + 6.0984 = 106.0984 ohms The resistor R3 needs to be 106 ohms to balance the bridge and give 0 volts at the meter.

Sample problem: In the bridge circuit above, R1 and R2 are 200 ohms. R3 is150 ohms. The excite voltage to the bridge is 10 volts. If the meter is reading 0.4 volts (the positive is on the right side and the negative on the left side) what is the temperature at the RTD?

Find the voltage on the left side of the bridge. This is the voltage we will add to the meter voltage on the right side. We will use the voltage divider theorem to find the voltage across R1.

VR1 

R1 200 (10V )  (10V )  5V R1  R2 200  200

This means the voltage across the RTD is 5.0V + 0.4V = 5.4 volts. We will now use the voltage divider theorem to find the resistance of RTD.

VRTD 

RRTD RRTD (10V ) ; 5.4V  (10V ) RRTD  RR 3 RRTD  150

Solving for RRTD :

 RRTD  5.4   10  RRTD  150  61

5.4  RRTD  10   10  RRTD  150  10  RRTD  0.54  RRTD  150      RRTD  150   RRTD  150  0.54( RRTD  150)  RRTD 0.54 RRTD  0.54(150)  RRTD 0.54 RRTD  81  RRTD 0.54 RRTD - 0.54 RRTD  81  RRTD - 0.54 RRTD 81  RRTD - 0.54 RRTD 81  (1  0.54) RRTD 81  (0.46) RRTD 81 (0.46) RRTD  0.46 0.46 176.087  RRTD We can prove that the 176.087 ohms for the RTD is correct by plugging the value into the voltage divider formula to find the 5.4 volts at the meter.

VRTD 

176.087 (10V )  5.4V 176.087  150

We have the ohms of the RTD, now we can find the temperature. 100 ohms = 32°F, So subtract the difference in ohms 176.087 – 100 = 76.087 ohms.

Divide the 76.087 ohms by the alpha 0.2178 ohms per °F.

F 

76.087 ohms

 0.2178 ohms   deg F   

 349.34 F

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Add the 32°F bias for 100 ohms to the 349.34°F for 76.087 ohms and we get: 349.34°F + 32.00°F = 381.34°F.

Installing RTDs and Thermocouples into a process stream

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Typical RTD and thermocouple applications

A complete assembly with a 4-20 mA transmitter in an explosion proof housing

Industrial RTD or Thermocouple with head A straight and tapered thermowell is shown

Various Industrial Thermometers Threaded for mounting in tanks and pipes

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Pressure Measurement and Calibration Pressure measurement and head pressure Pressure is measured in typically two different forms. Pounds per square inch (psi) or in head pressure. Head pressure is measured in inches or feet of water column (H2O). Head pressure is independent of the tank’s height or area. The transmitter measures head pressure. Head pressure is the measure of the potential energy in the system. The transmitter measurement is from how high is the fluid falling. The distance the fluid falls indicates the force generated (F=ma). This is why the density of the fluid must be known to calibrate a pressure transmitter for a process, to obtain the fluid mass. The calibration process uses specific gravity (s.g.), the ratio of a known density of a fluid divided by the density of water (H2O). To illustrate these facts, we will start with one gallon of water. The gallon of water equals 231 cubic inches and weighs approximately 8.324 pounds at 60°F. Pressure is measured in PSI (pounds per square inch). Only one (1) square inch of area is needed to calculate the height of the water and the force it is excerpting. Remember force divided by area = pressure. Stack 231 cubic inches of water on top of each other, to form a tall column of water, with a base of one (1) square inch. The column of water will be 231 inches tall. Divide the height of the column of water, 231 inches, by the weight of one (1) gallon of water, 8.324 pounds. The result will be 27.691 or 27.7 inches of water per pound of water, over a one square inch of area. Therefore 27.7 inches H2O, of head pressure, equals one (1) PSI. By knowing the specific gravity of the fluid to be measured, multiplied by the height of the tank in inches, an equivalent value in inches of water can be found. The transmitter can now be calibrated in inches of water, regardless of the fluid. If the tank’s fluid has a s.g. equal to 0.8 and a height of 100 inches tall, then the height in inches of H2O will be: (100” of fluid * 0.8 s.g. = 80” of H2O). Pressure transmitters are purchased in different sizes of measurement. They are in ranges of inches H2O, psig (the “g” stands for gauge pressure) or psia (the “a” stands for absolute pressure). When the symbol psid (the “d” stands for differential pressure) is called for, a standard psig transmitter is used. Most industrial pressure transmitters are differential pressure transmitters. They act on differential forces applied to each side of the transmitter. The force is produced by the pressure in the system multiplied by the area of the diaphragm.

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Applying pressure measurement and signals - worked examples Differential pressure and meter calibration Differential pressure or differential head pressure is used to calibrate transmitters for pressure, level, flow and density measurements. The transmitter has a high side, marked with an H, and a low side, marked with a L. The low side will typically go to atmospheric pressure or to a fixed height wet leg measurement. The high side will typically go to the tank, where the varying height of fluid is to be measured. When calibrating an instrument remember: The low side is the negative scale, below zero, and the high side is the positive scale, above zero. The transmitter’s sensor element is static in position or elevation and therefore the transmitter itself is always equal to zero elevation. This will be discussed in detail in the section on Level Measurement. Transmitters can be purchased in ranges of 25 in. of H2O, 250 in. of H2O, 1000 in. of H2O, 300 psi and 2000 psi. The formula for calibration is: (high side inches x s.g.) – (low side inches x s.g.) = lower or upper range value. Note: Gives LRV when empty or minimum and URV when full or maximum

Sample problem: A pressure gauge is reading 25 pisg. It is attached to a tank filled with a fluid. The bottom of tank is 65 feet above the ground. The pressure gauge is 5 feet above the ground. The fluid has a specific gravity of (0.7 s.g.). What is the level of the fluid in the tank?

First convert the psi gauge measurement to feet of head measurement. 25 psi * 2.31 feet per psi = 57.75 feet of H2O. Next find the elevation of the bottom of tank in relation to the elevation of the pressure gauge. Tank bottom in feet – pressure gauge elevation in feet, equals the height in feet to the bottom of tank. 65 feet– 5 feet = 60 feet of head to bottom of the tank. Note: Head is always measured in the standard of inches or feet of water column (WC / w.c.). Multiply the head between the bottom of the tank and the pressure gauge times the s.g. to get the head equal to H2O. 60 feet of fluid * 0.7 s.g. = 42 feet H2O to bottom of tank from the pressure gauge. Next subtract (the height from the pressure gauge to the bottom of the tank in feet of H2O), from (the total height of fluid in feet of in H2O above the pressure gauge), to find (the height of the fluid in the tank in H2O). (57.75 feet of H2O total head) – (42 feet of H2O below the tank) = (feet of fluid in H2O in the tank). (57.75 feet total) – (42 feet to bottom tank from the pressure gauge) = 15.75 feet in H2O in the tank Next convert height in feet of H2O to height of fluid with a specific gravity (s.g.) of 0.7: 15.75 feet of H2O / 0.7 s.g. = 22.5 feet of total height of the fluid column in the tank

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Pressure change in a pipe for a given flow rate On the CSE examination you will be asked to correlate signals and measurements using Flow, Pressure and the Output in (4 mA to 20 mA) signals. A change in flow in a pipe will cause a change in the head pressure across the pipe and measurement element. If the flow decreases in the pipe the pressure in the pipe will increase at any point along the pipe. If the flow rate increases, the pressure in the piping system decreases. If the flow rate decreases, the pressure in the piping system increases. This is because the total head of the system remains constant due to the head pressure developed by of the pump. The total energy head being endowed into the pump and piping system, remains constant. This can be seen with a pump at a constant speed and two pressure gauges, one at each end of the pipe and a hand valve at the end of the pipe. 2

F  h1  1   h2  F2 

h1 F12  h2 F22

Sample problem: There is a flow rate of 300 gpm in a piping system. There is a pressure gauge reading 100 psi somewhere in the piping system. If the flow rate is decreased to 240 gpm. What is the new pressure gauge reading in psi in the piping system?

Find the new pressure at the point of the gauge in the piping system for a flow rate of 240 gpm. 2

F   300  h2  h1  1   100    156.25 psi  240   F2  2

Pressure change across the flow element for a given flow rate If the flow in the pipe increases, the head pressure on the outlet of the measurement element will decrease. This correlation can be demonstrated by the following equations for differential head pressure (∆P) across the orifice element (a fixed resistor) or smaller section of pipe (venturi or dall tube). See the section on applications of basic fluid mechanics in process control. 2

hF h F 2 1 2

2 2 1

F  h1  2   h2  F1 

Sample problem: a) A flow of 250 gpm has a head pressure measurement of 309 inches of H2O. If the flow is decreased to 150 gpm, what is the new head pressure (∆P) in H2O for the

measurement element? b) What would be the new output to the PLC or DCS, in a mA signal, if the transmitter was calibrated in 0 to 400 inches of H2O? The signal is calibrated for 4 mA to 20 mA. Answer: a) Find the new head pressure for 150 gpm.

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2

F   150  h2  h1  2  ; 309    111.24 in H 2O  250   F1  2

b) Find the mA output: The output signal is the square root of the ratio of change in head pressure (new measurement) to the full scale calibrated range of the transmitter. First find the % of head pressure in the scale of 0 to 400 inches H2O. 111.24 % head   0.2781 400 The output is a 4 mA to 20 mA current signal. The span is 16 mA (20 mA – bias of 4 mA) Since the flow rate is a squared function, we must first extract the square root of the % measurement to find the % of output signal.

output mA = 0.2781*16 mA +4 mA bias=12.44 mA

Pressure calibration of transmitter Sample problem: The pressure in a pipe is to be measured. The maximum pressure is measured as 462 feet of head of natural gas. It is to be displayed in units of psig. What is the calibration of the transmitter to display this pressure in 0 to 100% psig on the display? The minimum pressure measurement will be zero feet of head? Find the psig for the given maximum head pressure: psig = feet head / 2.31 psig per foot of head Maximum measurement in psig: 200 psig = 462 / 2.31 Next find the calibration range to order the transmitter: The formula for calibration is: (high side psi) – (low side psi) = lower or upper range value. Note: Gives lower range value when minimum and upper range value when maximum LRV = 200 – 0 = 200 psi URV = 0 – 0 = 0 psi The transmitter will be calibrated as: 0 to 200 psig

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Level Measurement and Calibration Applying level measurement and calibration - Worked examples

TUNED-SYSTEM

BALANCED SYSTEM

WET LEG

WET/DRY LEG

The calibration procedure below is as follows. The level in a vessel or tank can be measured by a number of methods: differential pressure; displacement of volume; bubbler tube; capacitance; sonar; radar; weight, to name a few. This book will focus on differential pressure, displacement of volume, and bubbler tube for the examination. REMEMBER:

(high side inches x s.g.) – (low side inches x s.g.) = lower or upper range value.

See Example 1. The low side of the transmitter is open to atmosphere. Atmospheric pressure is pushing on the low side. The high side of the transmitter is connected to the tank; it also has atmospheric pressure pushing on it. The atmospheric pressures on each side of the transmitter cancel out. In the example, the first line of math will be the LRV and the second line of math will be the URV. The tank has 100 inches of fluid with a s.g. of 1.0. The calibrated Range of the instrument will be 0” to 100” of water or H2O. The Span of the transmitter is: (100” x 1.0 = 100”) See Example 2. The low side of the transmitter is open to atmosphere. Atmospheric pressure is pushing on the low side. The high side of the transmitter is connected to the tank; it also has atmospheric pressure pushing on it. The atmospheric pressures on each side of the transmitter cancel out. In the example, the first line of math will be the LRV and the second line of math will be the URV. The tank has a 100-inch level and the tube dropping down below the tank adds 20” of fluid height, with a s.g. of 1.0. The calibrated Range of the instrument will be 20” to 120” of water or H2O. Remember the minimum measurement cannot be lower than the fixed tube height of 20”. Suppress the zero with the hard wire jumper or set the variable in the transmitter and make 20” a live zero for the instrument. In pneumatic instruments a suppression kit must be installed. The Span of the transmitter is: (100” x 1.0 = 100”)

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Example 1: Open Tank Zero-Based Level Application Tank Level = 0 to 100 inches s.g. = 1.0 (switch jumper to normal zero)

LRV = (0” x 1.0) – (0” x 1.0) = 0” = 4 mA URV = (100” x 1.0) – (0” x 1.0) = 100” = 20 mA Calibrate range from 0” to 100” H2O

Example 2: Open Tank Suppress the Zero Tank Level = 0 to 100 inches s.g. 1.0 (switch jumper to suppress zero)

LRV = (20” x 1.0) – (0” x 1.0) = 20” = 4 mA URV = (120” x 1.0) – (0” x 1.0) = 120” = 20 mA Calibrate range from 20” to 120” H2O

See Example 3. The low side is connected to the top of the closed tank. The high side is connected to the bottom of the closed tank. The tank’s pressure does not matter, because the pressures in low and high side lines cancel each other out. Since the tank is pressurized, a “wet leg” or “reference leg” must be used. This is the piping going from the low side of the transmitter to the top of the tank. It will be typically filled with some other type of product, such as glycol or silicon. This prevents moisture from accumulating in the line. If moisture accumulates in the line, it will give an error in the transmitter reading. The wet leg has 100 inches of fluid with a s.g. of 1.1. In the example, the first line of math will be the LRV and the second line of math will be the URV. The tank has 100 inches of fluid with a s.g. of 1.0. The calibrated range of the instrument will be -110” to -10” of water or H2O. Elevate the zero in the transmitter with the hard wire jumper or set the variable in the transmitter and make -110” a live zero for the instrument. In pneumatic instruments a suppression kit must be installed. The Span of the transmitter is: (100” x 1.0 = 100”) See Example 4. The low side is connected to the top of the closed tank. The high side is connected to the bottom of the closed tank. The tank’s pressure does not matter, because the pressures in the low and high lines cancel each other out. The wet leg has 120 inches of fluid with a s.g. of 1.1. The first line of math will be the LRV and the second line of math will be the URV. The tank has 100 inches of fluid and the tube dropping down below the tank adds 20” of fluid height with a s.g. of 0.8. The calibrated Range of the instrument will be 116” to -36” of water or H2O. Remember the minimum measurement cannot be lower than 20” on the high side, due to the fixed 20” height of the tube dropping below the tank. Elevate the zero and make -116” a live zero. The Span of the transmitter is: (100” x 0.8 = 80”). REMEMBER: (high side inches x s.g.) – (low side inches x s.g.) = lower or upper range value. Note: Gives lower range value (LRV) when empty and upper range value (URV) when full.

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Example 3: Closed Tank Elevate the Zero

Example 4: Closed Tank Elevate the Zero (transmitter below tank) Tank Level = 0 to 100 inches s.g. = 0.8, Wet Leg: s.g. = 1.1 Height = 120” (switch jumper to elevate zero)

Tank Level = 0 to 100 inches s.g. = 1.0, Wet Leg: s.g. = 1.1 Height = 100” (switch jumper to elevate zero)

LRV = (0” x 1.0) – (100” x 1.1) = -110” = 4 mA URV = (100” x 1.0) – (100” x 1.1) =-10” = 20 mA Calibrate range from -110” to -10” H2O

Rosemount transmitters with seal for density and level applications

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LRV = (20” x 0.8) – (120” x 1.1) = -116” = 4 mA URV = (120” x 0.8) – (120” x 1.1) = -36” = 20 mA Calibrate range from -116” to -36” H2O

Rosemount suggested mounting with Wet/Dry Leg to prevent freezing

Level displacer (Buoyancy) The displacer tube for liquid level measurement is based on Archimedes principle that, the buoyancy force exerted on a sealed body immersed in a liquid is equal to the weight of the liquid displaced. There are two types of displacer transmitters in common use today: torque tube and spring operated.

f 

Vd f 231

(8.338)G f

Where: f = buoyancy force in lbf Vd f = total volume of displaced process fluid in cubic inches Ls = the submerged length of the displacer in process fluid 231 = cubic inches in one gallon of water 8.338 = weight of one gallon of water in pounds Gf = specific gravity of displaced process fluid

Sample problem: a) What is the force upward on the 30” displacer, if the displacer is 4” in diameter and submerged 10” in a fluid, with a specific gravity of 0.72? b) What is the mA output and percent output of the process signal?

Answer: a) Find displaced volume:

   D2    16  3 Vd f     Ls    10  125.66 in 4 4     Find displacement force upward

f 

Vdf 231

(8.33)G f 

125.66 (8.338)(0.72)  3.266 lbf 231

b) Find displacement force upward for the total 30 inches submerged :

   D2    16  3 Vd f     Ls     30  376.99 in  4   4  f 

Vd f 231

(8.338)G f 

376.99 (8.33)(0.72)  9.798 lbf 231

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Find the % output and mA:

%

3.26  0.333 100  33.3% output 9.79

 0.333 16mA  4mA  9.328mA output

Various types of displacement measuring devices and transmitters

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Bubbler level measurement The bubbler tube or dip tube measures the level of the process fluid by measuring the back pressure on the bottom of the tube. This back pressure is the force excerpted from the weight of the fluid in the tank against the tube opening. The tube will have to build up enough pressure for the gas to escape through the process fluid above the opening. The dip tube will have a static back pressure equal to the height or head of the process fluid above the bottom of the opening, as the bubbles escape the dip tube. This simple level measurement has a dip tube installed with the open end close to the bottom of the process vessel. The lowest level that can be measured is from the bottom of the tank to the bottom of the dip tube. If the bottom of the dip tube is 2 inches of the bottom, the minimum level that can be measured is 2 inches. The maximum height that can be measured is only limited to the air supply pressure minus the minimum measureable level. A flow of gas, usually air or nitrogen, is passed through a regulator to reduce the pressure. Then the flow of the gas will be controlled and monitored by passing through a rotameter (flow meter). It then makes its way down the dip tube and the resultant backpressure, due to the hydraulic head of the process fluid, forces back on the pressure transmitter. The pressure in the bubbler tube or dip tube equals the head pressure of level of the fluid in the vessel and a proportional signal is sent to the PLC or DCS. With a transmitter standard level calibration in inches of water, the signal out will vary proportionally with the change in level of the process fluid.

Sample problem: a) What is the head pressure measurement of a bubbler tube submerged 24” in a fluid with a specific gravity (s.g.) of 0.85? b) What is the percent output and mA output, if the transmitter is calibrated for a tube 100” long and the transmitter is calibrated 0 to 85 inches H2O (100 inches * 0.85 s.g.= 85 inches H2O)? Answer: a) Find the head pressure of the process fluid

h  LDipTubeG f  24  0.85  20.4 inches H2 O (the water only excerpts a force of 20.4 inches H2O against the bottom of the tube) b) Find percent and mA output The transmitter is calibrated for 0 to 85 inches H2O which equals = 0% to 100%

%

20.4  0.24 100%  24% output 85

The transmitter output is a 4mA to 20 mA current signal. The span is 16 mA (20 mA – bias of 4 mA) (0.24 * 16 mA) + 4 mA (bias) = 7.84 mA output, which equals 24% of the input measurement scale into the control room. The control room computer (DCS or PLC) is scaling the input signal to value of 0 inches to 100 inches for the tank level. You can see 24% signal reads as 24 inches in the tank for the control room.

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Density measurement Head pressure and volume displacement can be used to measure density. By using a differential head pressure transmitter, calibrated in inches of water, connect the high and low lines to the tank at a fixed distance of separation, such as 10”. Both taps of the density transmitter must be completely submerged below the top of fluid whose density is being measured. The height measured in inches of water divided by 10” (in our example), is the (s.g.) of the unknown fluid. Example: The density transmitter is measuring 7 inches H2O, the s.g. = 0.7 (7”/10” = 0.7). See figure 2 below. With the specific gravity (s.g.) known from the density transmitter, and a second level transmitter calibrated in inches of H2O, the tank level can be found. The level measurement can be divided by the (s.g.) measurement from the density transmitter, to show the true height of the process fluid in the tank.

Sample problem: Find the density of the hydrocarbon product and the interface level of the

water in the bottom of the tank in figure 2. The wet leg (sealed diaphragm leg) has a s.g. equal to 1.1 Remember: [(high side * s.g.) – (low side * s.g.)] = LRV or URV Density: LRV = (0” * 1.0) – (10” * 1.1) = -11” H2O (transmitter not covered with fluid or tank empty) URV = (10” * s.g.) – (10” * 1.1) = ?” H2O (transmitter completely covered with process fluid) o

URV = (10” * 0.825) – (10” * 1.1) = -2.75” H2O (for Crude oil 40 API) o Find s.g. for crude oil 40 API: [(-11) – (-2.75)] = 8.25” so… 8.25”/10” = 0.825 s.g. URV = (10” * 0.7874) – (10” * 1.1) = -3.126” H2O (for ethyl alcohol) Find s.g. for ethyl alcohol: [(-11) – (-3.126)] = 7.874” so… 7.874”/10” = 0.7874 s.g. s.g. process signal = mA = [16 * 0.7874] + 4 = 16.5984mA or 78.74% signal. Level: (% Level signal / % Density signal) * Tank Level = level of process fluid in the tank. Note: The tank level measurement can be any height and the fluid to be measured of any density. Remember to elevate the zero on the density transmitter.

Figure 1

Figure 2

Using a bubbler arrangement to measure level with a varying density of process fluid: Connect the high and low lines to the dip tubes as shown above in figure 1, at a fixed distance of separation in height, such as 2” or 10”. We will use a 2” height differential between the bottoms of the tubes. The maximum distance above L1 equals 20” of process fluid.

Sample problem: Find the density and level in the tank in figure 1, using a bubbler arrangement. Density is calculated as LRV = (0” * s.g.) – (0” * s.g.) = 0” H2O (Density minimum, tank empty) URV = (0” * s.g.) – (2” * 1.0) = -2” H2O (Density equals H2O, L2 submersed and fluid at bottom of L1)

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Remember to elevate the zero in the transmitter! Since any level above L1 will cancel out in the density transmitter, the output is simply the percent signal which equals the s.g. of the process fluid. Example: -2” * 0.7874 = -1.5748” H2O (for ethyl alcohol) -1.5748”/-2” = s.g. = 0.7874 or 78.74% signal. Level is calculated as: For a 15” level of ethyl alcohol above L1: % mA = (15” * s.g.) = 11.811” H2O = (11.811” level)/( 20” max level) = 0.59055 or 59.055% signal At DCS/PLC the display will show Level/Density = 59.055/78.74 = 0.75 or 75% level. Level = 0.75 * 20” = 15” level

Interface level measurement The combined level of the fluids in the tank must be above the top tap of the level transmitter connected to the tank. The distance “h” is the height between the high and low side taps and must be at a known constant distance. We want the lower tap (high side) to see the difference in height in the higher specific gravity fluid in the bottom of the tank, minus the lower specific gravity fluid in the top of the tank. Say we are trying to measure the level of water in a tank holding a hydrocarbon product. If we know the s.g. of the hydrocarbon, we can calibrate the transmitter to an output of zero % signal, due to cancellation of forces (pressure * area) on both sides. Then when the heavier water product enters the tank we can measure this extra weight by the force it is excerpting on the transmitter in inches of water for an interface height. If we do not know the density of the hydrocarbon product, we will do what we did in the previous examples for finding the density of a fluid in a tank. We will put the density transmitter on the upper fluid level and then divide the bottom level measurement by the density multiplier.

If the wet leg and the lighter hydrocarbon product in the tank are the same fluid, the two levels (or forces) will cancel each other out when there is no water in the tank. (The s.g. of the hydrocarbon product must be known and consistent, otherwise a density transmitter should be used to perform the level calculation for accuracy). The height in H2O in the tank = [(height of H2O) + (height of the lighter fluid * s.g.)] The height in H2O in the wet leg = (height of the lighter fluid in the wet leg * s.g.) The signal height in inches of H2O from the transmitter = [(height of H2O) + (height of the lighter fluid * s.g.)] - (height of wet leg * s.g.) = measurement inches H 2O

Sample problem: Find the interface level in the tank. The distance between taps is h = 100 inches Hydrocarbon s.g. = 0.7 (can be found from the density transmitter) Water (H2O) s.g. = 1.0 Maximum interface level to be measured = 50 inches (50% full)

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First find the maximum level measurement in inches H2O on each side of the transmitter: The tank level (high side): (50” H2O ) + (50” hydrocarbon * 0.7) = 50 + 35 = 85 in H2O The wet leg level (Low Side) : (100” hydrocarbon * 0.7) = 70 in H2O Max inches H2O seen by the transmitter: (high side) – (low side) = 85 – 70 = 15 in H2O Our transmitter will be calibrated to: 0” to 15” H2O = 4 to 20 mA signal. We are at 50% full, therefore 100% transmitter signal or 20 mA. At 20 mA the DCS or PLC will see 100% input. We will convert that signal to the actual height of water in the tank. Find the difference of s.g. of the two fluids: 1.0 s.g. (H2O) – 0.7 s.g. (hydrocarbon) = 0.3 = 30%

   15  15 in H 2 O  = = 50 inches = 100% of the maximum interface level  1.0 water  - 0.7 s.g. process fluid  .   0.3 s.g.    Proof it works: The transmitter is measuring 3.75 in H2O. Percentage of measurement = (measured inches by transmitter) / (full scale measurement or span). This equals 3.75”/15” = 0.25 or 25% signal. 25% signal means the tank should have 12.5 inches of water in the bottom of the tank. (measured inches H2O by transmitter) / (difference in specific gravities) = Actual height of tank water.

 3.75 in H 2 O   1.0 water  - 0.7 s.g. process fluid  

  3.75  = = 12.5 inches = 25% of the maximum interface level   0.3 s.g.  

Transmitter calculation: (high side): (12.5” H2O) + (87.5” hydro * 0.7) = 12.5 + 61.25 = 73.75 in H2O (low side): (100” * 0.7) = 70 in H2O (high side) – (low side) = 73.75 – 70 = 3.75 in H2O 3.75” at the transmitter = 25% of signal = 3.75”/0.3 Δs.g. = 12.5” of water in the tank. 25% of the maximum allowable level of 50” in the tank would equal 12.5” of water. Application Hint: The analog signal will be 25% or 8 mA. If we were using a 14-bit analog input card, 14 the bit count would be 2 or 16384 bits or steps. 16384 bits / 20 mA = 819.2 bits per mA. We need to subtract our bias of 4 mA, so 4 mA * 819.2 bits = 3276.8 or 3277 bits. We subtract to get the full scale bit count: 16384 bits – 3277 bits = 13107 bits = 100% or full scale. 100% span equals 13107 bits to the PLC or DCS. The bits will be scaled in the PLC to floating point. Bits for level: 25% signal = 0.25 * 13107 = 3276.75 or 3277 bits input signal. 3277 bits (signal) / 13107 bits (full scale) = 0.250019 (the PLC scaled register value) Bits for density: 70% signal = 0.7 * 13107 = 9174.9 or 9175 bits. Remember we want the difference of the specific gravities so: 1.0-0.7 = 13107 – 9175 = 3932 bits. Δ s.g. = (3932 bits / 13107 bits) = 0.29999237 (the PLC scaled register value) Water interface height in inches = transmitter measurement height in inches / delta density. [0.250019(% level signal from transmitter) * 15 inches(full scale measurement)] / 0.29999237(Δ s.g.) = 12.50127 inches water in the tank.

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Radar and Ultrasonic level measurement Time of flight technology Time of flight devices are much newer technology than hydrostatic devices and consist of ultrasonic and radar devices (non-contact and guided wave). Radar is an acronym for Radio Detection and Ranging. Radar devices used for level measurement operate with electromagnetic radiation at wavelengths of 1.5 to 26 gigahertz. They are commonly known as microwaves. Non-contact radar and guide wave radar operate using the same principle.

Ultrasonic level measurement Ultrasonic waves are not electromagnetic waves; they are mechanical sound waves. The speed at which mechanical waves travel is well known, about 1096 feet per second (334 meters/second) through air at 68°F. The level of the media can be determined by measuring the amount of time it takes for the ultrasonic wave to travel to the liquid, reflect and travel back to the device. Most ultrasonic transmitters and receivers operate from 10 KHz to 70 KHz, well above the frequency of audible sound waves. In order for ultrasonic waves to be reflected, they need a media with a certain mass (density). In level measuring applications, there must be enough mass in the media (density) to reflect the sound waves. Equations: L = E – D and D = C x T/2 L = media level E = distance from measuring device to zero level D = distance from measuring device to media C = speed of sound or speed of light T = amount of time for sound or light to travel from device to liquid and back Based on the figure to the right the level of media can be determined from the time it takes for sound waves or electromagnetic waves to travel from the measuring device to the media and back to the measuring device.

Advantages Accuracy independent of density changes, dielectric or conductivity No calibration with medium required Some come with SIL 2 and 3 ratings

Disadvantages Minimum density required Foam is an issue False measurements with turbulent surfaces No vacuum (10 psia), no high pressures (44 psia)

Radar (non-contact) Non-contact radar devices use microwaves in the 6 to 26 gigahertz range to measure liquid level in tanks. Like the speed of sound, the speed of light (electromagnetic radiation) is well known, 186,000 miles per second. Based on equations 1 and 2 above, the level can be calculated by knowing the dimensions of the tank and measuring the amount of time it takes for the microwaves to reflect off the process media. Why do radar level devices use microwaves compared to other types of energy in the electromagnetic spectrum? Microwaves have little effect from type of gases, temperature, pressure, buildup and condensate. However, the ability for the process medium to reflect or not reflect microwaves needs to be taken into account. You can determine this ability to reflect light or microwaves by looking at the dielectric number of the media.

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The dielectric number is a measure of the polarization power of an insulating material or how much charge can be stored in a type of material vs. air. Water has a dielectric number of 80 and is considered a great reflector of microwaves. Air has a dielectric number of 1 and is considered a poor reflector of microwaves. Aqueous mixtures tend to work well with radar due to the high dielectric number. However, while hydrocarbon based liquids can be measured, the measuring ranges may be lower due to lower dielectrics numbers. Petroleum oil has a dielectric number of 2 while gasoline has a dielectric number between 2 and 3. Because, ambient conditions have little effect on microwaves, radar devices are generally accepted as the most accurate level devices – some can measure level to ±0.5 mm or ±0.02 inches. This is one of the main reasons why suppliers, processors, and sellers of crude oil and other highcost materials will use a radar device as part of their tank gauging equipment to accurately measure level.

Guided Wave Radar (GWR) Guided wave radar devices use the same principle as non-contact radar devices – it has the ability to transmit and receive reflected microwave energy. Guided wave (sometimes called TDR – Time Domain Reflectometry) operates at 1.5 GHz. While the electronics are mostly the same as non-contact radar, the big difference is the wave guide. The wave guide is a metal rod or rope which guides the energy to the process media. See the image to the left. The wave guide directs approximately 80% of the available energy down the guide within an 8” radius. GWR is suitable for a variety of level measurement applications including: Unstable Process Conditions - Changes in viscosity, density, or acidity do not affect accuracy Agitated Surfaces - Boiling surfaces, dust, foam, vapor do not effect device performance - Recirculating fluids, propeller mixers, aeration tanks Extreme Operating limits - GWR performs well under extreme temperatures up to 600ºF (315ºC) - Capable of withstanding pressures up to 580 PSIG (40 Bar)

Fine Powders and Sticky Fluids

- Paint, latex, animal fat and soy bean oil - Saw dust, carbon black, titanium tetrachloride, salt, grain - Oils or grease in tanks

Capacitance level measurement Commercial capacitance level transmitters are proven devices and were first introduced in the 1950’s. They are also extremely versatile in that they can measure the continuous level and point level (a predetermined measurement point) of liquids, slurries, liquidliquid interface as well as point level of solids. Capacitance technology for level devices has also become known as reactance, admittance or RF technology. The capacitance calculation for empty and full is important because a minimum change of capacitance of about 10 pF is needed for measurement. Last but not least, foam can be tricky with capacitance probes. If the foam is conductive, the capacitance probe will see the liquid and the foam as the complete level. Capacitance transmitters and switches can come with SIL 2 and 3 ratings.

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Radiometric (gamma) level measurement Similar to radar devices, gamma level devices use electromagnetic radiation emitters and receivers to measure the level. Gama devices can be used for liquids and solids in tanks. Gamma devices use electromagnetic radiation at a different part of the electromagnetic spectrum. They use gamma rays which have much higher frequency and therefore smaller wavelengths vs. microwaves. A source of gamma radiation, usually Cesium 137 or Cobalt 60 depending on the application, is placed in a lead source container. The container can be closed (emitting no radiation) or open (emitting gamma radiation). A detector, capable of measuring the amount of radiation from the source, is installed on the other side of the tank. If the tank is empty, the detector receives most of the available gamma radiation. If the tank starts to be filled with liquid or solid, as the level increases, the media will attenuate (absorb) some of the available gamma radiation. When the tank is full, the detector receives very little radiation compared to the empty tank scenario. This is an excellent level transmitter for difficult level measurements, such as catalyst levels in tanks that are in series with other tanks or the piping is in the way. Gama devices can also be used to measure the thickness of materials as well, not just levels. Gama devices can also be used as Irradiators. Irradiators are devices or facilities that expose products to radiation to sterilize them, such as spices and some foods, milk containers, and hospital supplies. Gamma level devices have been proven to be safe and reliable, if safety procedures and regulations are followed. The safety of personnel is number one and the amount of radiation over time that an employee can receive is well known and documented. All of this must be taken into account when purchasing gamma level devices. However, used safely, some of the most critical level measurements can be made with a gamma device.

Level gauging system in a tank farm

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Calculating the volume in tanks With a head pressure measurement, the height of the liquid in a tank can be measured. This is simple with standard cylindrical tanks, but much more difficult with irregular shaped tanks. Calculating the volume in tanks will probably not be on the CSE exam, but the formulas to calculate the volume in these tanks is derived from calculus and included in the appendix of this guide. It will show how to calculate the volume of spherical tanks and bullet tanks, so the volume can be calculated in the PLC or DCS. See the section Calculating the Volume in Tanks for the volume formulas.

The tank ends can be flat (so the tank is just a horizontal cylinder). Tanks can come with different heads (end caps). They can be dished (ASME F&D, or Flanged & Dished), 2:1 elliptical or hemispherical. TANK VOLUME CALCULATION

Horizontal Cylinder

  D   D  2   2 -h   D  -1 2 0.5 -  -h   Dh-h   L   cos    2    D  2   2   

HEAD VOLUME CALCULATION ASME F&D

Elliptical Head

Hemispherical Head

0.215483h 2 1.5D-h 

 6

 3

h 2 1.5D-h 

h 2 1.5D-h 

The liquid volumes in a horizontal cylinder, and ASME F&D, 2:1 elliptical and hemispherical heads are -1 given by these equations. The (cos ) or (arccos) or (arcos) function must return radians, NOT degrees. In the appendix, the volume for the tank section plus both heads combine into one formula. These formulas can be modified using the formulas above for more accuracy with different heads (end caps). The total volume of liquid in the tank is simply the liquid volume in the cylinder plus 2 times the liquid volume in the heads. (Hint: multiply tank diameter “D” x % level signal to get “h” (the height shown on the HMI or display), and then calculate the total tank volume with the math formula in the appendix. .

81

82

Flow Measurement and Calibration Applying flow measurement devices Like level measurement, flow measurement is also head pressure and zero elevation based. Head pressure is the measure of the endowed potential energy in the system. The transmitter measurement is from how high the fluid falls, it is velocity squared. The velocity is squared due to the fact that the fluid is constantly being accelerated through the pipe, as potential energy is endowed into the fluid by the pump‘s head pressure. Head pressure is lost across the orifice element due to the fact that, energy loss is the product of energy flow multiplied by the resistance thought which it flows (see figure at right). Sizing of the orifice will be discussed in detail in the subsection on Orifice Type Meters. You should familiarize yourself with the different types of flow meters, their applications, and their ISA symbols. The ISA P&ID symbols are shown below.

Turndown ratio in a flow meter The turndown ratio of a flow meter is its ability to measure with acceptable accuracy the ratio of maximum flow rate measurement to minimum flow rate measurement. This is also known as the rangeability of the flow meter. Turndown ratio is important when choosing a flow meter technology for a specific application. If a gas flow to be measured will have a maximum measured flow rate of 1,000,000 scfm (standard cubic feet per minute) and a minimum measured flow rate of 100,000 scfm, the meter needs to have a minimum turndown ratio of 10:1 (1,000,000 / 100,000). For example, if the meter had an advertised turndown ratio of 20:1 and maximum flow rate measurement of 2,000,000 scfm, then the minimum measureable flow rate would be 100,000 scfm. The turndown ratio of each type of meter is limited by constraints of the manufacturing process and materials used, as well as practical application considerations. For example, orifice meters create a pressure drop in the measured fluid proportional to the square of the velocity.

ISA standard flow meter symbols

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Flow Nozzle

Magnetic Meter

Orifice Meter

Pitot Meter

Sonic or Doppler

Turbine Meter

Venturi Tube Meter

Vortex Meter

Flow meter applications chart

Sensor

Rangeability

orifice

3.5:1

2-4% of full span

venturi

3.5:1

1% of full span

flow nozzle

3.5:1

2% full span

elbow meter

3:1

5-10% of full span

-low pressure loss

-very poor accuracy

Annubar

3:1

0.5-1.5% of full span

-low pressure loss -large pipe diameters

turbine

20:1

0.25% of measurement

-wide rangeability -good accuracy

-poor performance with dirty or sticky fluids -high cost -strainer needed, especially for slurries

1% of measurement

-wide rangeability -insensitive to variations in density, temperature, pressure, and viscosity

-expensive

0.5% of measurement

-high rangeability -good accuracy

-high pressure drop -damaged by flow surge or solids

-good accuracy

-expensive

Vortex shedding

10:1

positive displacement

10:1 or greater

Coriolis mass flow

100:1

Accuracy

0.05-0.15% of

measurement

Advantages -low cost -extensive industrial practice -lower pressure loss than orifice -slurries do not plug -good for slurry service -intermediate pressure loss

Disadvantages -high pressure loss -plugging with slurries -high cost -line under 15 cm -higher cost than orifice plate -limited pipe sizes

Pressure tappings (Impulse Line Taps) There are three standard positions for pressure tappings (also called taps), commonly named as follows:  Corner taps placed immediately upstream and downstream of the plate; convenient when the plate is provided with an orifice carrier incorporating tappings  D and D/2 taps or radius taps or vena contracta taps, placed one pipe diameter upstream and half a pipe diameter downstream of the plate  Flange taps placed 25.4mm (1 inch) upstream and downstream of the plate, normally within specialized pipe flanges. These types are covered by ISO 5167 and other major standards. Other types include  2½D and 8D taps or recovery taps placed 2.5 pipe diameters upstream and 8 diameters downstream, at which point the measured differential is equal to the unrecoverable pressure loss caused by the orifice  Vena contracta tappings placed one pipe diameter upstream and at a position of 0.3 to 0.9 diameters downstream, depending on the orifice type and size relative to the pipe, in the plane of minimum fluid pressure. The measured differential pressure differs for each combination and so the coefficient of discharge used in flow calculations depends partly on the tapping positions. 84

The simplest installations use single tappings upstream and downstream, but in some circumstances these may be unreliable; they might be blocked by solids or gas-bubbles, or the flow profile might be uneven so that the pressures at the tappings are higher or lower than the average in those planes. In these situations, multiple tappings can be used, arranged circumferentially around the pipe and joined by a piezometer ring or in the case of corner taps, annular slots running completely around the internal circumference of the orifice carrier.

Orifice tap dimensions and impulse line connections

Flow meter and pressure meter impulse line connections ΔP=The Square of Process Fluid’s Velocity

ΔP=The Process Fluid’s Pressure

Low Side Connected Down Stream of Orifice

Configuration for Flow

Low Side is Open to the Atmosphere

Configuration for Pressure

Orifice carrier for quick change out of orifice, no line flange disassembly

85

Flow meter impulse lines connections Gas or Air Installation (taps on the top side of the pipe) Any condensate will drip back into the pipe

Steam or Liquid Installations (taps on the side of the pipe) Note: avoid bottom taps so impulse lines do not plug with debris or settlements

86

Standard Mass Flow Meter and Orifice Installation

Typical Rosemount Annubar or Pitot Tube installation

87

Various Types of Flow Meters

Click image to watch video of flow meter measuring principals If the Flow Meters video does not run in your PDF viewer, then click the button below to run the MP4 video from the official web site of http://www.learncontrolsystems.com/flow_meters.mp4

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Applying the Bernoulli principle for flow control The process control industry covers a wide variety of applications of elements and final correction devices. The Control Systems Engineer (CSE) examination encompasses a broad range of valve applications and sizing for different head or pressure devices, possibly an orifice meter; a turbine meter; pressure relief valve or safety rupture disk. This manual will cover the essential basics for the CSE examination.

Let’s start by reviewing the energy equation and its applicable laws governing flow control for processes. Relationship of the Energy Equation and flow rate through a pipe or head measurement device:

Z1 

V12 2g



p1



 Z2 

V22 2g



p2

AV  A2V2 1 1



These equations are very useful on the CSE examination

For change in pressure anywhere in the piping system:

F  p2   1  p1  F2  2

p1 F1  p2 F 2

2 2

For change in head pressure across the flow measurement element:

F  h2   2  h1  F1  2

h1 F  h2 F1 2 2

2

For calculating the Reynolds Number of a fluid to determine laminar or turbulent flow characteristics: Re =

Re =

89

3160 * flow rate( gpm) * Specific Gravity

; for liquids

Pipe ID (inches ) * Viscosity (cSt )

7740*Velocity ( ft / sec) * Pipe ID(inches ) Viscosity (cST )

; for liquids

Re =

6.316 * Flow Rate( LB / Hr ) Pipe ID (inches ) * Viscosity (cSt )

Re = 1000

v  m s  D  mm 

  cSt 

; metric

; for vapors

Types of Head Pressure-Based Meters There are several types of flow meter that rely on Bernoulli's principle, either by measuring the differential pressure (ΔP) within a constriction, or by measuring the difference between static and stagnation (impact) pressures to derive the fluid velocity. Venturi meter A Venturi meter constricts the flow in some fashion, and pressure sensors measure the differential pressure before and within the constriction. This method is widely used to measure flow rate in the transmission of gas through pipelines, and has been used since Roman Empire times. The coefficient of discharge of ‘C’, in Venturi meters ranges from 0.93 to 0.97. The first large-scale Venturi meter to measure liquid flows were developed by Clemens Herschel who used them to measure small and large flows of water and wastewater beginning at the end of the 19th century. ISO 5167 Orifice Plate An orifice plate is a plate with a hole through it, placed in the flow; it constricts the flow, and measuring the pressure differential across the constriction gives the flow rate. It is basically a crude form of Venturi meter, but with higher energy losses. There are three basic types of orifice plates: concentric, eccentric, and segmental. Dall tube The Dall tube is a shortened version of a Venturi meter, with a lower pressure drop than an orifice plate. As with these flow meters the flow rate in a Dall tube is determined by measuring the pressure drop caused by restriction in the conduit. The pressure differential is typically measured using diaphragm pressure transducers with a digital readout. Since these meters have significantly lower permanent pressure losses than orifice meters, Dall tubes are widely used for measuring the flow rate of large pipe systems. Differential pressure produced by a dall tube is higher than the venturi tube or nozzle, all of them having the same throat diameters. Pitot-Static tube A Pitot-Static tube is a pressure measuring instrument used to measure fluid flow velocity by differential pressure. The difference of the static pressure and stagnation (impact) pressure. Bernoulli's equation is 2 used to calculate the dynamic pressure which is the kinetic energy of the fluid V =2gh/s.g. (the difference of the height of the water column of the fluid) and therefore the fluid’s velocity. Pitot tubes are often used to measure the air speed of a plane. Multi-hole pressure probe Multi-hole pressure probes (also called impact probes) extend the theory of the Pitot tube to more than one dimension. A typical impact probe consists of three or more holes (depending on the type of probe) on the measuring tip arranged in a specific pattern. More holes allow the instrument to measure the direction of the flow velocity in addition to its magnitude (after appropriate calibration). Three holes arranged in a line allow the pressure probes to measure the velocity vector in two dimensions. Introduction of more holes (e.g., five holes arranged in a "plus" formation) allows measurement of the threedimensional velocity vector. Cone meters Cone meters are a newer differential pressure metering device first launched in 1985 by McCrometer in Hemet, CA. While working with the same basic principles as Venturi and Orifice type ΔP or DP meters, cone meters don’t require the same upstream and downstream piping. The cone acts as a conditioning device as well as a differential pressure producer. Upstream requirements are between 0-5 diameters compared to upstream diameters of up to 22 diameters for an orifice plate or Venturi. Because cone meters are generally of welded construction, it is recommended they are always calibrated prior to service. The inevitably effects of heat caused by welding, can cause distortions and other effects that prevent tabular data on discharge coefficients with respect to line size, beta ratio and operating Reynolds

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Numbers from being collected and published. Calibrated cone meters have an uncertainty up to +/-0.5%. Un-calibrated cone meters have an uncertainty of +/-5.0%. Annubar meters (also reference averaging pitot tubes) A Rosemount Annubar primary element is an averaging Pitot tube similar to a single point pitot tube used to measure the flow of gas, steam, or liquid in a pipe. An Annubar primary element or Annubar averaging Pitot tube provides better accuracy than single point Pitot tubes. The Pitot tube measures the difference between the static pressure and the flowing pressure of the media in the pipe. The volumetric flow is calculated from that difference using Bernoulli's principle and taking into account the pipe inside diameter. The biggest difference between an Annubar averaging Pitot tube and a Pitot tube is that an Annubar averaging Pitot tube takes multiple samples across a section of a pipe or duct. In this way, it averages the differential pressures encountered accounting for variations in flow across the section. A Pitot tube will give a similar reading if the tip is located at a point in the pipe cross section where the flowing velocity is close to the average velocity. The T-Shape cross section of the Rosemount Annubar primary element allows for increased signal strength and reduced signal noise compared to other averaging Pitot tube shapes Important note: Pitot tubes and Annubars must be supported in high velocity fluids, due to vortex sheading. High frequencies can weaken the tube at the welds and it can snap off inside the pipe. See the manufacturer’s instructions for calculations and mounting procedures for installation in high velocity fluids.

Differential head meter calculations

Classic fluid mechanics model The equation for flow through an orifice is a simple one to understand. Only the units are somewhat awkward, but can be easily converted into terms that make them useful. Q = AV Q = The flow in cubic feet per second (ft3/sec). A = The area of the orifice in square feet (ft2). V = The velocity of the liquid in feet per second (ft/sec) Experience shows that the actual flow is quite different than calculated because of the different shapes of the various orifices. Look at the following diagrams and you will see some of these popular shapes. Each has been assigned a "K" value.

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“K” value flow coefficients

We will enter the "K" value into our equation and the new equation becomes: Q = AVK To make the equation easier to handle we can express the velocity "V" as a function of head in feet of water “H”: Note: water column can be expressed as (WC) or (H2O).

V2  H or V  2 gH or V  64.34 * H  8.02 * H 2g Where: g = 32.2 ft/sec2 H = Head across the orifice in feet. Use the differential head across the orifice.

From your previous studies, remember to convert pressure to head, use these formulas:

27.731 in 1 ft 2.31092 ft *  1 psi 12 in 1 psi It would also make sense to convert some of the terms in our equation to terms that are more convenient to use. As an example:

"Q" can be converted from cubic feet per second to gallons per minute: 1 ft3/sec = 448.831 gpm 92

1728 in3 1 gal 7.4805 gal 60sec 448.831gpm   * * 1min 1 ft 3 231 in3 1 ft 3 1 ft 3 The area in square feet ("A”) can be converted to square inches: 2

1 ft = 144 square inches Putting all of this together gives us a new formula that looks like this:

Qgpm 

A *8.02 * 448.831* K * H  25.0 * A * K * H 144

Let's plug in some numbers and calculate a flow through a typical orifice. Where: H = 20 feet A = 0.049 square inches K = 0.62

Qgpm  0.049 * 25.0 * 0.62 * 20 Q = 3.397 gallons per minute If we want to solve for the orifice area:

A

Qgpm 25.0* K * H



3.397 25.0*0.62* 20

 0.049in2

Remember… 27.731 inches = 1 psi and Head Meters are typically in inches of water head, so let’s change the feet into inches (note: lower case “h” is now head in inches):

Qgpm  A * 25.0 * K * H  A * 25.0 * K *

h 12

 A * 25.0 * K * 0.288675* h

Qgpm  A * 7.21688 * K * h Let's plug in some numbers and calculate a flow through a typical orifice. Where: h = 240 inches (20 feet) A = 0.049 square inches K = 0.62

Qgpm  0.049 * 7.21688 * 0.62 * 240

Qgpm

93

= 3.396 gallons per minute

We made our formula more user friendly by substituting in some conversions and now we can make our calculations in gallons per minute and the area of the orifice hole in square inches, but the flow rate formula would be much better if we could measure the orifice diameter rather than the orifice area. This is a much more practical way to size an orifice. Use the following equation:

4A d2 or d  4 

A

Inserting the 0.049 square inches we calculated from the prior formula we get

4*0.049

d



 0.250 inches or 1 inch 4

I took you through this exercise to show you how the formulas we use in obtaining flow rates are derived. We will re-write the flow and orifice diameter formulas again and maybe this time they will be simpler to use. We will start with the flow rate formula and then correct for the orifice formula:

A

d2 4

or d 

4A



so A  0.7854d 2

Substitute the previous formula in the flow equation for “A” and we get…

Qgpm  A * 7.21688* K * h or

 4

d 2 * 7.21688* K * h

Ignoring the rounding errors through the previous equations we get: Qgpm  5.667 * d 2 * K * h The formula for calculating the orifice diameter becomes:

d2 

Qgpm 5.667 * K * h

or... d 

Qgpm 5.667 * K * h

Let's see if the formula still works. Here are the numbers:    

d = .250 or 1/4 inch K = 0.620 Q = required flow rate of 3.4 gallons per minute h = 240 inches

We will begin by solving for flow (Q)

Qgpm  5.667 * 0.252 * 0.62 * 240 = 3.402 gpm Now let's try it to find the orifice size.

d

Qgpm 5.667 * K * h



3.402 1  0.25 inches or inch 54.44 4 94

The formula has proven correct; there is less than 1/1000th of an inch and 6/100th of a gallon error. All of these above numbers were generated assuming that you were moving water through the orifice at 60°F. If you are making calculations for a liquid other than water or at a temperature other than 60°F, you will have to factor in the specific gravity of that liquid compared to water.

The beta ratio

The ratio of

d has a special name. It is called the “beta ratio” of the orifice plate or head measuring D

element. Where: d = Orifice hole diameter or head restriction element throat diameter. D = The exact internal diameter of the pipe carrying the fluid (related to pipe schedule and material) We will be using the beta ratio (  ) over and over in our studies of flow and pressure relief devices.

d greater than 30% (0.3), use is a modifier formula. The upcoming industrial standard D formulas we will use to for solving problems on CSE examination will show the modifier formula gives results that are much greater that the actual flow rate.

Some might say if

The modifier (M) looks like this:

1

M

d 1   D

4

When you are using the modifier, the formulas look like this:

Qgpm  5.667 * d 2 * K * h * M

Qgpm

d

5.667 * K * h * M

Now we will see what happens when a 0.250 inch (1/4) orifice is put into a smaller cross section 0.5 inch (1/2) pipe, assuming the other numbers stay the same: 4

4

 d   0.250       0.0625  D   0.500 

M

1  1.0328 1  0.0625

This means that you would have to multiply by 1.0328 so the 3.402 gpm we got in the last calculation would become 3.514 gpm.

95

Pipe Size Is Important - Remember! The internal diameter of real pipe does not equal the nominal pipe size. Example: 1/2-inch schedule 40 pipe has an internal diameter (0.622) inches and 8-inch schedule 40 pipe equals (7.981) inches. Let’s recalculate the flow equation with the corrected size: 4

4

 d   0.250       0.0261  D   0.622 

M

1  1.0133 1  0.0261

This means that you would have to multiply by 1.0133 so the 3.402 gpm we got in the standard calculation would become 3.447 gpm. That is a difference of 3.514 – 3.447 = 0.067 gpm. This equals 4.02 gallons error in 1 hour (0.067 gpm * 60 min = 4.02 gpm). A typical work year is 8760. That is an error of 35,215.2 gallons in one year. It can be seen in much larger flow rate, these errors can add up to millions of dollars in loss or over charges, due to inaccuracies in measurement. We will address handling these errors in the following standard equations used for real world industrial flow measurements. The Spink equation, taught in the ISA CSE review course and the ISO 5167 equations used by most companies and software. Other factors also affect the accuracy of the measurement     

The placement of the measurement instrument’s line taps. (They are called impulse lines) Solids buildup inside the piping. Calcium in water applications and coke in hot oil applications are typical. (The interior pipe diameter varies). Higher temperature usually hastens the solids buildup. The specific gravity of the fluid being measured, which can also change with temperature. Shape and design of the orifice plate and any defects, such as nicks in the orifice hole of the plate. (nicks can cause up to 1% error in measurement) Shape and design of restriction elements other than just an orifice plate

96

Standard Flow Measurement Equations There are many variations of flow equations. Books dedicated to flow measurement alone, can be over 500 to 1000 pages. They are dedicated to just how to take flow measurements. There are commercially available software packages for calculating flow measurements, such as Flowel. This software can cost in the area of $3,000. Most calculations do not need to be this accurate. The Spink equation is my favorite, but we will list others used by the top manufactures of flow measurement equipment. The most popular standard equations for flow calculation are:  Spink  ISO 5167  AGA3 (now API-MPMS-14.3)  AGA5/7/8  AGA9  API Manual for Petroleum Measurement  See the attachments with this manual for details on how to use these calculations for flow measurement.

Spink - Flow Measurement Equation The basic Spink equation for liquid flow through an orifice plate is:

Volume Flow

Q  5.667 SD 2

Mass Flow

h Gf

Qm  5.667  SD 2

Note:

h Gf

  8.3378

lb. @ 60F  for water gal.

The book, ‘Principles and Practice of Flow Meter Engineering’ by L.K. Spink, first published in 1930, is generally recognized as the first, and for many years the only, definitive collected ‘body of knowledge’ appertaining to industrial flow measurement. Undergoing nine revisions, the last addition was printed in 1978 – 21 years after Spink’s death. Another book of authority on the subject of flow is the ‘Flow Measurement Engineering Handbook’ by Richard Miller. This is a vey in depth book almost 2 inches thick and can be found at most libraries or obtained through inter-library loan. This book is also used by many colleges.

97

The basic Spink equation derived Let us review the math that derives this volumetric flow equation.

V 2  2gH V  2 gH

Q  AV Q  A 2 gH

H

h Note: h is in inches, put it in feet 12G f

Q  A 2g

h 12G f

 A h  2g Q( gpm)  time scaling  volume scaling      12G f  1 144 

   Note: scale inches to feet  

2 g   d 2  60sec 1728 in 3  h Q( gpm)       3  12 4 144 Gf  1min 231 in 

 60sec 1728 in 3  64.34 ft  2 Q( gpm)        d in   3  2 2  1min 231in  12 in sec 4 144 in Q( gpm) 

60 sec 7.4805 gal 2.3155 ft  0.00545 2      d in   ft 2  3 2 min ft in sec  in 

h in Gf h in Gf

Ignoring the rounding errors accumulated, we derive: 60 h h gal Q( gpm)   7.4805 gal  2.3155  0.00545  d 2   5.667  d 2   min Gf G f min

Q( gpm)  5.667  d 2 

h Gf

Add factor for coefficients of friction, viscosity, convergence, and divergence.

Q( gpm)  5.667  Kd 2 

h Gf

98

Note: S = the Spink factor used for sizing orifice flow measurements. Since the K (the constant) and d (orifice diameter) are unknowns:

 D2   d2  Note that  2   1 and S  K  2  D  D  2

We will cancel the orifice diameter (d ) with “S” and we are left with “S” times the pipe internal diameter 2 squared, (D )…

Q( gpm)  5.667  Kd 2 *

D2 h  2 D Gf

= 5.667 

Kd 2 h h * D2  = 5.667 SD 2 2 D Gf Gf

The basic Spink equation for liquid The basic equation for liquid through an orifice or restriction type device is:

Q( gpm)  5.667 SD 2

h Gf

Using the sizing equation and the Spink sizing factor table, we can accurately size the orifice diameter and the dimensions for the orifices taps; pipe taps; nozzle and venturi; lo-loss tube; and dall (flow) tube for flow measurement.

The basic Spink equation for gas and vapor The basic equation for gas or vapor through an orifice or restriction type device is:

Q( scfh)  218.4 SD 2

Tabs Pabs

hPf Tf G f

If the conditions are standard 60°F and 14.7psia then the formula can be reduced to:

Q ( scfh)  7,727 SD 2

hPf Tf G f

; ONLY at 60°F and 14.7 psia conditions

The basic Spink equation for steam W ( pounds per hour )  359SD2 h f Where:

 molecular weight of gas  28.97  is the M.W. of air   liquid weight of fluid   Specific gravity, for a fluid is  liquid weight of water 

G f  Specific gravity, for a gas is Gf

h  Head in inches

Pabs  Reference pressure  psi absolute  99

Pf  Fluid operating pressure  psi absolute 

Tabs  Reference temperature  temperature absolute in Rankin,  F  460

Tf  Fluid operating temperature temperature absolute in Rankin,  F  460 

 f  Specific weight of the steam or vapor in pounds per cubic foot  operating cond . Let's compare the Spink equation to basic fluid mechanics equation we studied earlier. Here are the numbers:   

d = .250 or 1/4 inch (orifice diameter) D = 0.622 inches (½ inch Sch 40 pipe internal diameter) h = 240 inches

We will begin by solving for beta:



0.25 =0.402 0.662

From table 3 – The Spink Factor (S), S=0.0988 for a beta of 0.402 (interpolate):

Q( gpm)  5.667 SD 2

h  5.667 * 0.0988* 0.622 2 * 240  3.356 gpm Gf

Classic fluid mechanics with the “K” factor gave us Qgpm = 3.404 gpm. With the K” factor and “M” factor became Qgpm = 3.445 gpm. The Spinks equation offers a much more accurate measurement than using classical fluid mechanics. The Spink equation has many more modifiers detailed in the Spink ‘Principles and Practice of Flow Meter Engineering’ book, but this simple equation will work fine for the CSE examination. Applications of the Beta and Spink factors Various Orifice plate configurations

Orifice, flow nozzle and venturi tubes

100

Table 3 – The Spink Factor (S) Beta or d/D Ratio

Square Edged Orifice; Flange Corner or Radius Taps

Full-Flow (Pipe) 2½D and 8D Taps

0.100

0.005990

0.006100

0.125

0.009364

0.009591

0.150

0.01349

0.01389

0.175

0.01839

0.01902

0.200

0.02402

0.02499

0.0305

0.225

0.03044

0.03183

0.0390

0.250

0.03760

0.03957

0.0484

0.275

0.04558

0.04826

0.300

0.05432

0.05796

0.08858

0.325

0.06390

0.06874

0.1041

0.350

0.07429

0.08086

0.1210

0.1048

0.375

0.08559

0.09390

0.1392

0.1198

0.400

0.09776

0.1085

0.1588

0.1356

0.1170

0.1267

0.425

0.1109

0.1247

0.1800

0.1527

0.1335

0.1443

0.450

0.1251

0.1426

0.2026

0.1705

0.1500

0.1635

0.475

0.1404

0.1625

0.2270

0.1900

0.1665

0.1844

0.500

0.1568

0.1845

0.2530

0.2098

0.1830

0.207

0.525

0.1745

0.2090

0.2810

0.2312

0.2044

0.232

0.550

0.1937

0.2362

0.3110

0.2539

0.2258

0.260

0.575

0.2144

0.2664

0.3433

0.2783

0.2472

0.292

0.600

0.2369

0.3002

0.3781

0.3041

0.2685

0.326

0.625

0.2614

0.3377

0.4159

0.3318

0.2956

0.364

0.650

0.2879

0.3796

0.4568

0.3617

0.3228

0.675

0.3171

0.4262

0.5016

0.3939

0.3499

0.700

0.3488

0.4782

0.5509

0.4289

0.3770

0.725

0.3838

0.6054

0.4846

0.4100

0.750

0.4222

0.6667

0.5111

0.4430

0.775

0.4646

0.5598

0.4840

0.800

0.5113

0.6153

0.5250

0.6666

0.5635

0.820

101

Nozzle and Venturi

Lo-Loss Tube

Dall (Flow) Tube

Quadrant Edged Orifice

0.0587 0.0700 0.0824 0.0959 0.1106

ISO 5167 - Flow Measurement Equation ISO 5167 (1991) and ASME MFC-3M (2004) - The Most Popular Mass Flow Rate:

qm  K *  * A * 2 g * m * p 

Volumetric Flow Rate:

qv 

C 1 

4

*

 4

d 2 * 2 1p

qm

1

qm = The mass flow rate kg/m3/s qv = The volumetric mass flow rate m 3/s.



= The expansibility factor.

C = The discharge coefficient. p1 = The upstream pressure before the orifice in Pa.

p 2 = The downstream pressure after the orifice in Pa. p = The differential pressure across the orifice in Pa.

1 = The density of the fluid kg/m 3.  = The ratio of orifice diameter to exact interior piping diameter in meters. V = The fluid velocity in meters per second.

The expansibility factor The variable or coefficient expresses the different compressibility of different fluids (gases, steam); that is, molecules are—depending on their form—more or less compressed when passing the orifice, where: ≤ 1. Water and other liquids are considered incompressible and  = 1. This makes calculations much simpler. The size of ε depends on the pressure relation and the isentropic coefficient ‘K’ (note: this is a different ‘K’ than used previously, it is the heat ratio factor); that is, the relation between a relative change in pressure and the corresponding relative change in density. ‘K’ is a property that is different for different media and varies also with the pressure and temperature of the medium. For many gases there are no published data for ‘K’. The standard recommends using CP/CV.



1   K   p  1   0.351  0.256 *  4  0.93*  8  * 1   2     p1    

Expansibility factor

Note:   1 for incompressible fluids

102

The discharge coefficient The variable or coefficient ‘ C ’ determines the relation between the real flow through a ‘primary device’ and the theoretical possible flow. For a given ‘primary device’ this dimensionless parameter is determined using an incompressible fluid. With fixed geometry, ‘ C ’ only depends on the actual Reynolds number ‘Re’. In a way, ‘C ’ can be regarded as a ‘calibration constant’ for a ‘primary device’. Generally in different installations, that are geometrically equivalent and sense the same flow conditions and are characterized by the same Reynolds number, render the same value for ‘ C ’. Remember: ‘Re’ varies with pressure, temperature, viscosity and flow, therefore so does ‘ C ’.

The ISO 5167 equation explained

 106 *   0.5961  0.0261*   0.216 *   0.000521*    ReD  2

C=

0.7

8

 10 *     0.0188  0.0063*   *  3.5 *    ReD  6

0.3

  0.043  0.080* e-10L1  0.123* e7L1  * 1  0.11*   *

4 1  4

1.3 0.031*  M2 -0.8*M1.1 2 * 

=

d D

 19000 *   A   Re D 

 2 * L2  M2     1- 

Re 

DV 1

 English Units

Re 

DV 1

 Metric Units

103

Data on pipe orifice plate medium

Data on upstream pressure tappings Data on downstream pressure tappings

relation between orifice and pipe diameter

Beta Ratio

A function of β and Re D

Reader-Harris Gallagher Equation

M 2 function of β and L 2

Reader-Harris Gallagher Equation

0.8

for example, 40°C, 3m/s flow

Re 

1.968in / 12in / ft  * 9.842ft / sec * 1.92slugs / ft 3 1.35 * 10-5 lb  sec/ ft 2

for example, 40°C, 3m/s flow

Re 

0.050m * 3m / s * 992.2kg / m3  226,900 0.656 * 10-3 N  s / m 2

 229,559

Only the three following pairs of values for L 1 and L 2 are valid:

L1 = L 2 = 0

L1 = L 2 =

corner tappings

0.0254 D

flange tappings

L1 = 1

D and D/2 tappings

L 2 = 0.47

Let's compare the ISO 5167 equation to the Spink equation formula and to basic fluid mechanics. Here are the numbers:      

d = .250 inch = 0.00635 meters D = 0.622 inches = 0.0157988 meters V = 3.5899 ft/s = 1.0942 m/s Operating Temperature = 60°F = 20°C Orifice taps are flange tappings  = 4.02

 

Δh = 240 inches = 8.66426 psi = 6.096 meters H2O p = Δh = 59737.9693 Pa



 = 1.005 N*s/m2 1 = 998.992 kg/m3



Solve for the Reynolds number ‘Re’

Re 

DV 1





0.00635m * 1.0942m / s * 998.992kg / m3  6906.633 1.005 * 10-3 N  s / m2

Solve for the coefficient ‘C’ First we will solve for the needed variables:

 19000 *   A   ReD 

L1 =L2 =

0.8

 19000 * 0.402     6906.633 

0.8

 1.0839

0.0254 0.0254   1.6077 D 0.0157988

 2 * L 2   2 *1.6077  M2      5.3769  1-   1-0.402  Next we will solve for ‘C’ in the three parts as shown previously C1+C2+C3 = C

Data on pipe orifice plate medium: 104

 106 *   C1  0.5961  0.0261*   0.216 *   0.000521*    Re D  2

0.7

8

  0.0188  0.0063*   * 

3.5

 106 *   *   Re D 

0.3

 106 * (0.402)  C1  0.5961  0.0261* (0.402)  0.216 * (0.402)  0.000521*    6906.633  2

0.7

8

 106 * (0.402)    0.0188  0.0063*1.0839  * (0.402) *    6906.633 

0.3

3.5

 0.6127

Data on upstream pressure tappings: C2   0.043  0.080 * e-10L1  0.123* e7L1  * 1  0.11*   *



4 1  4



C2  0.043  0.080 * e-101.6077   0.123* e71.6077  * 1  0.11*1.0839  *

0.4024  0.001016 1  0.4024

Data on downstream pressure tappings: 1.3 C3  0.031*  M2 -0.8*M1.1  0.031*  5.3769-0.8*5.37691.1  *0.4021.3  0.002725 2 *

Sum solutions for “C” as C1+C2+C3 = C

C  0.6127  0.001016 +  -0.002725  0.61099 or 0.611 Solve for mass flow rate:

(Note: This is the same ‘K’ as used in the fluid mechanics examples) C  qm  K *  * A * 2 g * m * p  * d 2 * 2 1p 1  4 4

qm 

0.611 1  0.402

4

*

 4

0.006352 * 2  998.992  59,737.9693   0.2142

Solve for volumetric flow rate

qv 

qm

1

0.2142  0.0002144m3 998.992 3 0.0002144m 60sec 61023.7in3 1gal gpm  * * *  3.39856 or 3.399gpm 1sec 1min 1m3 231in3

qv 

105

Equation Comparison Summary

Fluid 60 °F 0.5 inch Schedule 40 Pipe, Beta = 0.4 Classic Fluid Mechanics (NO beta compensation)

3.404 gpm

Orifice=0.25 in, Head=240 in H2O

Classic Fluid Mechanics (w/ beta compensation)

3.516 gpm

Orifice=0.25 in, Head=240 in H2O

Spink Basic Equation (uncompensated)

3.356 gpm

Orifice=0.25 in, Head=240 in H2O

ISO 5167 Equation

3.399 gpm

Orifice=0.25 in, Head=240 in H2O

Classic Fluid Mechanics (NO beta compensation)

559.894 gpm

Orifice=3.9905 in, Head=100 in H2O

Classic Fluid Mechanics (w/ beta compensation)

578.256 gpm

Orifice=3.9905 in, Head=100 in H2O

Spink Basic Equation

565.997 gpm

Orifice=3.9905 in, Head=100 in H2O

ISO 5167 Equation

564.216 gpm

Orifice=3.9905 in, Head=100 in H2O

Fluid 60 °F 8-inch Schedule 40 Pipe, Beta = 0.5

There is a 0.315% flow rate disagreement between the Spinks and ISO 5167 on the larger flow rate and a 1.27% disagreement on the smaller flow rate.

Sizing orifice type devices for flow measurement - worked examples Note: Table 3 – The Spink Factor (Orifice Sizing Factor) will be used to size the orifice devices

Liquid Sample Problem: Gasoline is carried in a 3-inch schedule 40 pipe (ID=3.068).

A concentric sharp-edged orifice plate, with corner taps, is used to measure the flow. If the Beta Ratio 2 2 (d /D ) is 0.500, maximum flow rate is 100 gpm, and specific gravity G f = 0.75, what is the differential head and span of the flow meter transmitter?

Q( gpm)  5.667 SD 2

h Gf

From Table 3 the Spink factor: Beta = 0.500, S=0.1568

100( gpm)  5.667  0.1568 3.068

100( gpm) 5.667  0.1568  3.068 

2



2  100( gpm)   h       8.3639   0.75 

2

h 0.75

h 0.75

2

106

11.95612 

h 0.75

142.95  0.75  h 107.21  h (span) Calibrate the transmitter from 0% to 100% and 4 mA to 20 mA. We only need 107.21 inches H2O, but you may want calibrate the transmitter in some even span of measurement, like the range of 0 to 110 inches H 2O. 110 inches H2O will provide a full scale flow of 101.29 gpm.

Steam Sample Problem: Dry saturated steam is carried in an 8-inch schedule 80 pipe (ID=7.625). A flow nozzle is used to measure the flow. If the Beta Ratio is 0.450, and the static pressure is 345.3 psig, what is the flow rate with a differential head pressure of 200 inches H 2O across the meter?

W ( pounds per hour )  359SD2 h f Find the density from Table A9 - Properties of Saturated Steam. A gauge pressure of 345.3 gives a specific volume of 1.2895.

Density in

f =

lb = ft 3

1 specific volume in

ft 3 lb

1  0.7755 1.2895

From Table 3 the Spink factor: Beta = 0.4500, S=0.2026

W ( pounds per hour )  359  0.2026 7.625

2

 200 0.7755  52,664.68 lb / hr

Gas Sample problem: Natural gas is carried in a 6-inch schedule 40 pipe (ID=6.065). Flowing temperature is 60⁰F at 30 psig pressure. A concentric sharp-edged orifice plate, with flange taps, is used to measure the flow. If maximum flow rate is 4,000,000 scf per day; specific gravity Gf = 0.60, and the differential head of the flow meter transmitter is 50 inches H 2O. What is the orifice hole bore diameter?

Q( scfh)  218.4 SD 2

Tabs Pabs

hPf Tf G f

Change flow from per day to per hour and temperature and pressure to absolute:

 4,000,000 scf   1 day      166,666.7 scfh day    24 hour 

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166,666.7  218.4 S  6.065 

166,667  218.4S  6.065 

2

2

520 14.7

520 14.7

 50  30  14.7   520  (0.60)

 50  44.7   759, 216.398 S    520  (0.60)

Find the “S” sizing factor:

166,666.7  S  0.2195 759, 216.398 From Table 3: Beta = 0.575 Beta = 0.600

S = 0.2144 S = 0.2369

This will require interpolation:

 S desired - S lower value   Beta     Beta upper value - Beta lower value    S upper value - S lower value    Beta lower value  0.2195  0.2144   Beta     0.600  0.575    0.575  0.5807  0.2369  0.2144   Find the orifice hole diameter:

d = Beta  pipe ID = hole size d  0.5807  6.065  3.522inches For the calibrated range of the transmitter 0 to 50 inches H2O, and a flow rate of 166,666.7 scfh or 4,000,000 scfd, the orifice hole bore diameter = 3.522 inches

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Mass flow measurement and control Note: Mass flow calculations will probably not be presented on the CSE exam. They have been added for information only.

From Bulletin C-404A, Courtesy of the Foxboro Company Mass flow of gas:

w

Substituting Q for V/t:

m M V   p   3    t 10 R  t   T 

Substituting for Q:

Q  k D; k 

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Mk f 3

10 R

w

MQ  p  103 R  T 

Finally, the simplified mass flow equation:

 p wk D  T 

Where: w = mass flow rate, kilogram/second Q = volume flow rate, cubic meters per second p = absolute pressure, Pascal’s T = absolute temperature, Kelvin M = gram molecular weight of gas (g/mol) R = universal gas constant = 8.314 J/K D = flow meter differential pressure in Pascals k = mass flow proportionality constant kf = flow meter proportionality constant Mass Flow Rate in English Units The equation for standard cubic feet is:

Q

m * Z * R * Ta 144* Pa

The equation for mass in lbm is:

m

Q *144* Pa Z * R * Ta

R

1545.34 ; Substituting this equation into the above equation for R we get: Mw

m

Q *144 * Pa * M w ; Solving this equation for mass with the molecular weight: Z *1545.34 * Ta

For standard temperature of 60°F and standard pressure of 14.7 psia, enter the scfh and molecular weight to get lbm per hour mass flow rate. (use Z = 1 for ideal gas)

m

Q * 4.0707 * M w Z *1545.34

We can further simplify the equation for standard temperature of 60°F and standard pressure of 14.7 psia, We reduce the equation to constant multiplied by scfh and the ratio of molecular weight Mw(gas)/ Mw(air 28.966) or Gf (specific gravity), to get lbm per hour mass flow rate. (Z = 1 for ideal gas)

m  0.0763lbm * scfh * G f Where: Q = scf (standard cubic feet) per unit time R = Universal Gas Flow Constant (1545.34 ft•lbf/(lb•mol)(°R)) divided by Mw Z = compressibility factor m = mass flow rate in lbm (pounds mass) per unit time Pa = pressure absolute (psig + 14.7) Ta = temperature absolute (°F + 460) Gf = specific gravity of gas, for example (Mw of gas / Mw of air)

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lbm = pounds of mass Mw = molecular weight of gas acfh = actual cubic feet per hour scfh = standard cubic feet per hour (at 60°F and 14.7 psia) Convert ACFH to SCFH Note: acfh = scfh if both calculations are at 60°F and 14.7 psia. To correct acfh to scfh, multiply acfh by the temperature and pressure correction factors below.

 Tf scfh  acfh   Ts

  Ps     Pf

  

Where: Tf = temperature of flowing gas in °R (°F + 460) Ts = standard temperature of gas in °R (60°F + 460) = 520°R Pf = pressure of flowing gas in psia (psig + 14.7) Ps = standard pressure of gas in psia (14.7) Note: Different standards for pressure and temperature are used in industry, but 14.7 psia (atmospheric pressure) and 60°F are the most common and are used in this review guide for sizing flow elements and control valves. Most of the ISA standard equations use this reference standard.

Note: Using the Rosemount 3051S with built-in advanced diagnostics capabilities, the following can be detected for alarms:     

Cavitation in the process stream A plugged impulse line Water in in the transmitter housing Power supply maybe failing or faulty The signal line has a high impedance due to corrosion in the terminations or connections of the electrical signal loop

The 3051S has a microprocessor capable of statistical analysis of the of the process measurements. These alarms can be read through the digital HART signal or by putting the transmitter in burst mode and splitting out three analog signals through a Rosemount Tri-Loop 333 Note: the alarm signals cannot be used to meet the requirements of SIS applications, they are only for quality control and maintenance.

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Applying mass flow measurement with an orifice - worked example Note: These measurements will be in English units for this application Mass Sample problem: Natural gas is carried in a 6-inch schedule 40 pipe (ID=6.065). Flowing temperature is 85⁰F at 325 psig pressure. A concentric sharp-edged orifice plate, with flange taps, is used to measure the flow. The specific gravity Gf = 0.657 and the Mw = 19. The differential head of the flow meter transmitter is 0 to 50 inches H2O. The Spink factor is 0.2191 and beta ratio is 0.5802. Find the SCFH and the mass flow rate in lbm per hour and lbm per day.

scfh  218.4(0.2191)  36.784  (35.374)

scfh  62,264.161

(50)(325  14.7) 85  460 (0.657)

(50)(325  14.7) 85  460  (0.657)

scfh  (62,264.161)(6.8873)  428,831.956 scfh Find the mass for the scfh of gas knowing the molecular weight (Mw) :

m

Q * 4.07 * M w lbm   428,831.956  0.002634 19   21,461.324 Z *1545.35 hr

Find the mass for the scfh of gas knowing flowing specific gravity (Gf ):

m  0.07612 lbm * scfh * G f   0.07612  428,831.956  0.657   21,446.246

lbm hr

We are showing a disagreement of 15.074 lbm, due to rounding error or approximately an error of 0.07%. I would use molecular weight, it is more exact. We now need to convert lbm per hr to lbm per day

lbm  lbm   24hr    (21, 461.324)(24)  515,071.776   day  hr   day  Real World Application in a Computer (DCS or PLC) The computer will read three signals from the field: pressure (psig), temperature (F) and differential pressure (in H2O). Note: Do NOT extract the square root in the transmitter. This will be done in the computer calculation. TT 100 = 0 to 120°F and 4 to 20 mA (the gas temperature) PT 100 = 0 to 500 psig and 4 to 20 mA (the gas pressure) PT 101 = 0 to 100 in H2O and 4 to 20 mA (the gas flow rate as velocity) The calculation in the computer will be some constant times the square root of the orifice equation. First calculate the scfh flow; this has already been defined in the previous example at a standard pressure and temperature of 14.7 and 60°F.

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scfh  62,264.161

(in H 2 0)( psig  14.7) ( F  460)(G f )

Take the specific gravity out of the square root, it is a constant:

scfh  62,264.161

1 Gf

(in H 2 0)( psig  14.7) ( F  460)

For a specific gravity of .657 the equation becomes:

scfh  76,816.6663

(in H 2 0)( psig  14.7) ( F  460)

Change scfh to lbm per hr and then lbm per hour to lbm per day

 24hr  lbm lbm   scfh  0.002634  M w  ;   scfh  0.002634  M w    hr day  day  Plugging this into the equation above using scfh and Mw = 19 we get:

(in H 2 0)( psig  14.7) (in H 2 0)( psig  14.7) lbm  76,816.6663(0.002634)(19)(24)  92, 264.8 day ( F  460) ( F  460) Testing the PLC equation we get: 515,075.1161 lbm/day That is an error of 3.34015 lbm difference between the calculation previously and the PLC calculation.

Turbine meter applications How Turbine Flow meters Work Turbine flow meters use the energy of the fluid to mechanically rotate a “pinwheel” (rotor) in the flow stream. Blades on the rotor are angled to transform energy from the flow stream into rotational energy. The rotor shaft spins on bearings. When the fluid moves faster, the rotor spins proportionally faster. Shaft rotation can be sensed mechanically or by detecting the movement of the blades. Blade movement is often detected magnetically, with each blade or embedded piece of metal generating a pulse. When the fluid moves faster, more pulses are generated. If a transmitter is used, it processes the pulse signal to determine the flow of the fluid. Transmitters and sensing systems are available to sense flow in both the forward and reverse flow directions.

Industries Where Used In order of largest industry to smallest industry of use, turbine meters are used in oil and gas, water and wastewater, gas utility, chemical, power, food and beverage, aerospace, pharmaceutical, metals and mining, and pulp and paper.

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The Plusses and Minuses of Turbine Meters The cost is moderate. The turbine meter is very good at clean, low viscosity fluids of moderate velocity and a steady rate. Turndown is very good as it can read very low compared to the maximum flow. They are reliable if put in a clean fluid, especially if the fluid has some lubrication properties. They are AGA and API approved for custody transfers. They do cause some pressure drop in the piping system, and should be considered as a factor in gravity flowing systems. They are not reliable for steam and bearings eventually wear out. How to Use Turbine Flow Meters Turbine flow meters measure the velocity of liquids, gases and vapors in pipes, such as hydrocarbons, chemicals, water, cryogenic liquids, air, and industrial gases. High accuracy turbine flow meters are available for custody transfer of hydrocarbons and natural gas. These flow meters often incorporate the functionality of a flow computer to correct for pressure, temperature and fluid properties in order to achieve the desired accuracy for the application. Be careful using turbine flow meters on fluids that are non-lubricating, because the flow meter can become inaccurate and fail if its bearings prematurely wear. Some turbine flow meters have grease fittings for use with non-lubricating fluids. In addition, turbine flow meters that are designed for a specific purpose, such as for natural gas service, can often be limited to an operate upper range of temperature, such as 60ºC. Operating above the upper temperature limit can cause damage to the flow meter. Smaller turbine flow meters can be installed directly in the piping, but the size and weight of larger turbine flow meters may require the installation of substantial concrete foundations and supports. The flow of corrosive liquids can be measured with proper attention to the materials of construction of all wetted parts, such as the body, rotor, bearings, and fittings. Applications for turbine flow meters are found in the water, petroleum, and chemical industries. Water applications include distribution systems within and between water districts. Petroleum applications include the custody transfer of hydrocarbons. Miscellaneous applications are found in the food and beverage, and chemical industries.

Application Cautions for Turbine Flow meters Turbine flowmeters are less accurate at low flow rates due to rotor/bearing drag that slows the rotor. Make sure to not operate these flowmeters above approximately 5% of maximum flow. Turbine flowmeters should not be operated at high velocity because premature bearing wear and/or damage can occur. Be careful when measuring fluids that are non-lubricating because bearing wear can cause the flowmeter become inaccurate and fail. In some applications, bearing replacement may need to be performed routinely and increase maintenance costs. Application in dirty fluids should generally be avoided so as to reduce the possibility of flowmeter wear and bearing damage. In summary, turbine flowmeters have moving parts that are subject to degradation with time and use. Abrupt transitions from gas flow to liquid flow should be avoided because they can mechanically stress the flowmeter, degrade accuracy, and/or damage the flowmeter. These conditions generally occur when filling the pipe and under slug flow conditions. Two-phase flow conditions can also cause turbine flowmeters to measure inaccurately.

Mass Flow Measurement with Turbine meters If the turbine flow meter has one rotor only, then it can only measure the velocity of the fluid. Temperature compensation will be need for accuracy in mass flow measurements, such as natural gas sales. Two rotor meters can be used to measure the angular momentum of the fluid for accurate mass flow measurements.

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Actual vs. Standard units of gas measure   

Turbine flow meters measure the actual volume of gas passing through the meter at the operating temperature and pressure. They are therefore sized in Actual Liters per Minute (ALPM) or Actual Cubic Feet (ACFM). Standard Liters per Minute (SLPM) or Standard Cubic Feet (SCFM) are the equivalent volume of gas referenced back to standard temperature and pressure as described previously in this section. The perfect gas law used to convert between ALPM and SLPM is:

T1  101.7 bar  ALPM = SLPM  *  P1 288.15 °K   P1 = Operating pressure in BarA T1 = Operating temperature in deg K

Standard air calibration The most common and economical calibration is in air at standard conditions. Data can be presented in actual units of measure or converted to standard units using the operating temperature and pressure. Actual air volume flow is often termed ACFM - Actual Cubic Feet per Minute. Unfortunately, in real life "actual conditions" are seldom "standard conditions." SCFM will change based on the flowing conditions:  pressure is applied a volume of air - it gets smaller  vacuum is applied to a volume of air - it expand Actual Cubic Feet per Minute - ACFM, depends on the following variables of the actual air.  pressure  temperature  humidity The conversion from SCFM to ACFM can be expressed as:

 Pstandard  Tactual  ACFM = SCFM     Pactual -Psaturation  Tstandard  Where: ACFM = actual cubic feet per minute SCFM = standard cubic feet per minute Pstd = standard absolute air pressure (psia) Pact = absolute pressure at the actual level (psia) Psat = saturation pressure at the actual temperature (psi) Φ = actual relative humidity o Tact = actual ambient air temperature ( R) o Tstd = standard temperature ( R)

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Turbine flow meter - worked example The basic equation for flow through a turbine meter is: V = KN Where: V = volume K = volume per pulse N = number of pulses The average flow rate ( Qavg ) is equal to the total volume divided by the time interval.

Qavg 

f 

V N K t t

N Number of pulses per unit time… t

Qavg  Kf Note: The turbine flow meter can measure the flow rate in units of cubic inches or gallons per pulse.

Sample problem: The turbine meter has a K value of 1.22 in3 per pulse. a) Determine the liquid volume transferred for a pulse count of 6,400. b) Determine the flow rate, if the 6,400 pulses are counted in duration of 40 seconds. c) What would be the totalized flow after 15 minutes at the current pulse rate of flow? d) What is the frequency ( f ) of the signal?

Answer: a) Liquid volume:

V  KN V  1.22in3   6400   7808in3

Gallons  7808in3 

1gal  33.8 gal 231in3

b) Flow Rate:

Q

V t

116

Q

7808in3 195.2in3  40sec sec

Q

195.2in3 60sec 1gal gal    50.7 3 sec 1min 231in min

c) Totalized flow after 15 minutes:

Q  50.7

gal 15min  760.5 gal min

d. Find the frequency Note: frequency in Hz is frequency per 60 seconds, so the Hz are: count(frequency)/sec = Hz

f 

N 6400 count 6400 count    160 Hz t 40sec 40sec

Sample problem: A Daniel size 2 turbine flow meter has a K value of 127 pulses per gallon. a) Determine the liquid volume in gallons transferred for a pulse count of 7,300. b) Determine the flow rate, if the flow meter sends a pulse count of 86,500 pulses in 6.8 minutes. c) What are the total gallons transferred in 8 hours for question (b.)? d) What is the frequency ( f ) of the signal for question (b.)?

Answer: a) Liquid volume:

V  KN  1 gallons  V    7300 pulses   57.5 gallons  127 pulses 

b) Flow Rate:

Q

V t

 1 gallons  V    86,500 pulses   681.1 gallons  127 pulses 

Q 117

681.1 gallons  100.16 gpm 6.8 min

c) Totalized flow after 8 hours for the flow rate in question (b.):

Q  681.1

gal 60 min * *8 hours  326,928 gallons min 1 hour

d) Find the frequency for the flow rate in question (b.): Note: frequency in Hz is frequency per 60 seconds, therefore the count(frequency)/sec = Hz

f 

N 86,500 count 1 min = * = 212 Hz Δt 6.8 min 60 sec

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Weight Measurement and Calibration Weight measurement devices and calibration Weight measurements are typically made with Load Cells (strain gauges attached to metal bars). The bending moment of the bar causes the strain gauge to elongate, resulting in an increase of resistance in the strain gauge. This variable resistance is connected to a bridge circuit and a voltage is measured across the bridge. The voltage is proportional to the weight applied to the measuring bar. This strain gauge technology is used in measuring the weight in tanks, the weight in screw conveyors and the weight on conveyor belts. The tare weight (tank weight) is nulled out and the voltage is set to zero or 0% in the bridge circuit. Then the maximum weight to be measured is applied. These weights are NIST (National Institute of Standards and Technology) certified. The span voltage is then calibrated to a maximum of 100%. This measurement is the net weight. Note: Remember all calibration processes should be repeated at least three times.

Load cells When outfitting a tank for batching, you must select a method for measuring the amounts of each ingredient added. A flow meter may be the first device that comes to mind. However, the load cell might actually be the better solution. A flow meter may come in many forms, but it is usually an in-line device that measures the rate or flow of a fluid, either in volume or mass. On the other hand, a load cell is a device that allows for the contents of a tank or vessel to be weighed. Because a flow meter is located in the tubing upstream from a tank, there is a difference between what the meter reads and what is truly in the tank. Programming changes can correct for the delays in measurement caused by this difference, but they can be imprecise and require frequent calibration. However, because a load cell measures the weight of the tank itself, delays are minimized. Load cells offer a particular benefit when dealing with products that don’t usually work well with flow meters. Liquids with entrained air or bubbles may give meters trouble, but they are no problem for load cells. Even dry ingredients like powders can be measured just like liquid mass and volumes using load cells.

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Load cells for (flow, level, force) applications in process

Mass Flow Meter

Batch Weighing

Weighbridge Measurements

Tank Dispensing

Silo Measurement

Automation Container Filling

Hydraulic/Pneumatic Press Force

Wire Tension Measurement

Robotic Tactile Sensing

(

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Process Analyzers Electrical conductivity and pH correction It is often useful to characterize an environment, such as a body of water, by measuring its pH and electrical conductivity (EC). pH is a measure of the acidity of the water or soil based on its hydrogen ion concentration and is mathematically defined as the negative logarithm of the hydrogen ion concentration: pH = -log[H+] The brackets around the H+ symbolize "concentration." The pH of a material ranges on a logarithmic scale from 1-14, where pH 1-6 are acidic, pH 7 is neutral, and pH 8-14 are basic. Lower pH corresponds with higher [H+], while higher pH is associated with lower [H+]. Electrical conductivity (EC) is a measurement of the dissolved material in an aqueous solution, which relates to the ability of the material to conduct electrical current through it. EC is measured in units called Siemens per unit area (e.g., mS/cm, or miliSiemens per centimeter), and the higher the dissolved material in a water or soil sample, the higher the EC will be in that material. See the section Chemical Process Technology and Equipment / Cooling Towers for more information on pH.

How are pH and electrical conductivity measured? A meter and probe or litmus paper can be used to measure the pH of a sample. The more accurate and t expensive of these methods, is the meter and probe. pH meters are calibrated using special solutions, or buffers with a known pH value. Electrical conductivity can be measured using a meter and probe as well. The probe consists of two metal electrodes spaced 1 cm apart (thus the unit of measurement is microSeimens or miliSiemens per centimeter). A constant voltage is applied across the electrodes resulting in an electrical current flowing through the aqueous sample. Since the current flowing through the water is proportional to the concentration of dissolved ions in the water, the electrical conductivity can be measured. The higher the dissolved salt/ion concentration, the more conductive the sample and hence the higher the conductivity reading.

Control of pH values in processes The process curve below shows the response of pH correction is not linear and cannot be controlled as such. Most pH "controllers" on the market are not truly pH controllers because they use simple on / off control or linear control algorithm by using a standard PID algorithm, which is far too simple to account for the ever changing control gain encountered with the logarithmic reaction of pH to control input. A true pH controller MUST have the ability to control a logarithmic and non-linear response, such as the typical pH process correction response curve shown below. The response of the process being corrected accelerates around a pH level equal to 7. Special pH controllers with adaptive gain and logarithmic algorithms are typically used. A window or hysteresis about the correction set point is typically used for control as shown below. This reduces hunting and allows the

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process to run continuously within acceptable tolerances. Chart recorders are typically used to document the pH correction before the process products are allowed to be discharged into rivers and sewage systems. Typical pH correction control scheme

Conventionally, in the controllers, 4 mA would correspond to 0 pH and 20 mA to 14 pH. When such a device is connected to a 1/4 DIN panel mounted chart recorder, the pH value can be constantly monitored. If the process requires a stringent control and is also operating within a narrow band of set points, say 1 pH; the recording on the chart paper will not be well resolved. This is due to the fact that in the conventional controller, the range of 14 pH is distributed over 16 mA. It can therefore be seen for a 1 pH variation, the current varies only by 1.15 mA approximately. See the section on The Application of Analog Circuits in Control Systems, for more information on 4 to 20 mA process signal current loops.

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Control of conductivity Electrical conductivity in water is a measure of the ion-facilitated electron flow through it. Water molecules dissociate into ions as a function of pH and temperature and result in a very predictable conductivity. Some gases, most notably carbon dioxide, readily dissolve in water and interact to form ions, which predictably affect conductivity as well as pH. For the purpose of this discussion, these ions and their resulting conductivity can be considered intrinsic to the water. Water conductivity is also affected by the presence of extraneous ions. The extraneous ions used in modeling conductivity are the chloride and sodium ions. A balancing quantity of cations, such as sodium ion, allows the impurity level to maintain electroneutrality. Extraneous ions such as these may have significant impact on the water's chemical purity and suitability for use in pharmaceutical applications. The combined conductivities of the intrinsic and extraneous ions vary as a function of pH and are the basis for the conductivity. Instrument specifications and operating parameters Water conductivity must be measured accurately using calibrated instrumentation. The conductivity cell constant, a factor used as a multiplier for the scale reading from the meter, must be known within ±2%. The cell constant can be verified directly by using a solution of known conductivity, or indirectly by comparing the instrument reading taken with the cell in question to readings from a cell of known or certified cell constant. Meter calibration is accomplished by replacing the conductivity cell with NIST-traceable precision resistors (accurate to ±0.1% of the stated value) or an equivalently accurate adjustable resistance device, such as a Wheatstone Bridge, to give a predicted instrument response. Each scale on the meter may require separate calibration prior to use. The frequency of recalibration is a function of instrument design, degree of use, etc.

Common Plant Analyzers There are many locations that should be measured and monitored with an analyzer to maximize product quality, combustion efficiency, safety, and emissions reductions including the following: 1. 2. 3. 4. 5.

Rotary Kiln gas outlet - O2, CO, NOx, CO2, SO2, CxHy, temperature Pre-Heater and Pre-Calciner - O2, CO, NOx, CO2, temperature Flue Gas Conditioning System (such as scrubber, SCR, SNCR) - CO, NOx, SO2, CO2 Electrostatic Precipitator (ESP) inlet - CO Main Stack (for CEM back-up) - O2, CO, NOx, CO2, SO2, CxHy

You may be asked some questions about the application of analyzers on the CSE exam Some possible applications of various analytical instruments in the crude distillation unit are as follows: Boiling Point Analyzers A Boiling Point or Distillation Analyzer would typically be used to control the 5% or 95% evaporated temperatures of the atmospheric tower side fraction products, the 95% evaporated temperature of the kerosene stream, and the 95% evaporated temperature of the diesel fraction. Depending on the individual refiner’s circumstance, boiling point analyzers might be profitably employed to monitor or control appropriate percent evaporated temperature for other streams in the crude distillation unit. Vacuum Distillation Analyzer This analyzer could be used to control appropriate percent evaporated temperatures on gas oil streams from the vacuum tower. Refiners will be more inclined to use this unit in refineries which have a hydrocracker or a lube oil manufacturing facility.

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Flash Point Analyzer This analyzer would most commonly be used to monitor or control the flash point of the kerosene products. In some instances, it might be installed on the naphtha or diesel stream. Cloud Point Analyzer This instrument would normally be used to monitor or control the diesel product from the crude distillation unit. Closer control of the cloud point would allow the refiners to reduce the amount of kerosene which must be used to product specification heating oil during the winter. Freeze Point Analyzer This instrument could monitor or control the freeze point of the naphtha or kerosene streams in refineries which produce jet fuel, thereby maximizing yields of these normally high-priced products. Pour Point Analyzer This analyzer would normally be used to monitor or control the pour point of the diesel stream from the crude distillation unit. This will decrease the amount of kerosene which must be added to produce specification product during the wintertime, and permit the kerosene to be added to the normally higherpriced jet fuel feeds. Color Analyzer Some refiners employ crude oil to cool and condense the crude tower overhead vapor stream. If a leak develops in this heat exchanger, crude oil can leak into the naphtha or light straight run product. This could have a serious effect on catalyst in the down-streaming processing units. A Color Analyzer installed on these streams can warn of leakage of crude oil into the light straight run or naphtha streams. A similar application could be made on the crude / pump-around reflux or crude/product exchangers. A Color Analyzer could also be installed on the atmospheric gas oil stream to warn unit operators if residual material is being entrained into the stream.

Combustion and Analyzers Combustion furnaces, such as heating furnaces and boilers in plants, include various sizes and types and serve as energy sources, that is, they are core components in all production activities. Because a large amount of fuel, such as gas or fuel oil, is consumed in plants, their combustion efficiency directly affects the performance and running cost of the plants. Since they generate large amounts of exhaust gas, in recent years it has become important to reduce various greenhouse gases including CO 2 in addition to coping with pollution caused by nitrogen oxide, sulfur oxide, etc. Consequently, not only is the proper measurement and control of O2 and CO important, but also solving of multi-faceted issues are required.

Relationship between Air-fuel Ratio and Heat Efficiency (Combustion)

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Combustion furnace and air-fuel ratio control Combustion requires fuel and air (oxygen), and insufficient air causes fuel residue, resulting in incomplete combustion with soot and smoke. On the other hand, excessive air causes problems, such as a larger amount of exhaust gas and heating of excessive air, resulting in lower fuel efficiency. The figure above shows the principle of the air-fuel ratio and state of combustion. The air-fuel ratio plotted on the horizontal axis shows the ratio of actual supply air to the theoretical amount of air required for fuel combustion (theoretical air amount). For combustion furnaces (such as heating furnaces and boilers in plants and factories), small-scale controllers (such as single loop controllers or PLCs) are employed to optimize the air-fuel control ratio for improving the combustion efficiency. In large combustion furnaces, distributed control systems (DCS) and advanced control (multivariable predictive control, etc.) are used. These mainly control the air-fuel ratio and internal pressure of the furnace to prevent CO, CO2 and NOx (nitrogen oxide) from being emitted and apply a cross limit circuit to prevent incomplete combustion while controlling combustion to maximize efficiency. See the section Chemical Process Technology and Equipment / Furnaces for more information on burner control. Air-Fuel ratio control utilizing CO and O2 concentrations According to Lyman F. Gilbert, the CO concentration in the optimum combustion zone (having the highest heat efficiency per unit amount of fuel) is around 200 ppm irrespective of fuel types and devices. However, CO increases rapidly once it has begun to increase. Thus, either a stable combustion must be kept with sufficient supply of air or a control system must monitor the CO concentration in real-time and keep it constant at a relatively low level. The amount of air supplied to a burner is controlled by two methods: using a forced draft fan (FDF) and damper as shown in the figure at the right, or using natural air intake by controlling the opening degree of the damper of an induced draft fan (IDF). The O2 and CO concentrations are measured by a concentration meter at the entrance of the flue and then supplied to the control system. The measured CO concentration can be used for combustion control by two methods: controlling O2 when the O2 concentration exceeds a prescribed value and overriding to CO control when the O2 concentration falls below the value, or giving a CO concentration bias (compensation) to the O2 concentration. BMS - Burner Management Safety A burner management system (BMS) safely controls the burner of the combustion furnace and includes an interlock mechanism and a safety shut-off mechanism to prevent explosion. The BMS must comply with safety standards based on risk assessment, such as the international standard (ISO12100) and the EU, USA and Japanese standards (EU standard: EN 746, USA standard: NFPA 86, Japanese standard: JIS B9700). Because the analyzer monitors the CO concentration in near real-time and detects the generation of toxic gas due to incomplete combustion, it increases the reliability of the safety system by inputting a signal of the detected CO concentration to the BMS. The CO concentration is expected for implementing the defined safety requirements. The figure to the right shows a typical combustion system in which CO (carbon monoxide) measurement capability is added to the BMS burner shut-off system.

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OSHA Requirements The Occupational Safety and Health Act of 1970: The employer must furnish a place of employment which is free from recognized hazards that could cause death or serious physical harm to employees if employees were exposed to fire and explosion hazards. 1) The burner management systems on boilers, furnaces, ovens and flare systems located within the facility must be in compliance with NFPA 85 Boiler and Combustion Systems Hazards Code 5.3.7.1 and 5.7.2, as well as manufacturer's and design specifications. 2) The Employer must perform a risk assessment to identify, evaluate and control the hazards involved with the process in accordance with ANSI/ISA S.84.001 and IEC-61511. Note: See the section Overview of Safety Instrumented Systems (SIS) for more CSE exam review material. Carbon dioxide (CO2) reading The CO2 level in the flue gas provides an indication of the efficiency of the combustion process. If the production of CO2 is as high as possible with slight excess air (complete combustion), the flue gas heat losses are at their lowest. The CO2 reading is calculated from the O2 reading by the analyzer. This maximum theoretical level is never reached in practice. Each fuel has a maximum possible CO 2 level (CO2 max), which is determined by the chemical composition of the fuel: • Light fuel oil - 15.4% by volume CO2 • Natural gas - 11.8% by volume CO2

Examples of Process Analyzers A Rosemount Analytical analyzer that is specifically designed for continuous emissions monitoring (CEMS) and process control. Often process gas cannot be taken directly from the process to the analyzer. Most systems demand a level of application specific sample handling.

Some Common Streams Measured:         

Sulfur Dioxide (SO2) Carbon Monoxide (CO) Nitrogen Monoxide (NO) Total Hydrocarbon (THC) Nitrogen Dioxide (NO2) Hydrogen Sulfide (H2S) Carbon Dioxide (CO2) Opacity Oxygen (O2)

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Select the appropriate analyzer and configuration

Off-line lab analysis • Manual sampling • Sample transport to the lab • Sample registration

At-line analysis • Manual sampling • Continuous manpower needed • Automated lab analysis close to sampling point inside plant • Ideal where multiple samples have to be taken at several sampling points along the process

On-line analysis • • • • • • •

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In-process measurement and response Automated sampling and registration Automated sample preconditioning Automated lab analysis Fast feedback of results Very limited manpower needed Close loop control

Typical Analyzer Piping and Control Schematic

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Process Control Valves and Actuators Process control valves A wide variety of valve types exist, the most widely used for process control systems and other industrial fluid applications are the valve types which have linear stem and rotary spindle movement:  

Linear stem movement type valves include globe valves and slide valves Rotary spindle type valves include ball valves, butterfly valves, plug valves and their variants

The first choice to be made is between two-port and three-port valves:  

Two-port valves 'throttle' (restrict) the fluid passing through them Three-port valves can be used to 'mix' or 'divert' liquid passing through them

Globe valves are frequently used for control applications because of their suitability for throttling flow and the ease with which they can be given a specific 'characteristic', relating valve opening to flow. For any given valve orifice size, the greater the differential pressure, the greater the flow rate. The maximum value of the valve flow coefficient Cv is defined as the number of U.S. gallons of water per minute (at standard pressure and temperature) that will flow through a wide open valve when there is 1 psig pressure drop across the valve. The flow rate can be determined by the following equation:

1 gpm  1 CV *

1 Ppsig

Control valve sizing will be discussed in detail for liquid, steam, gas, vapor and two phase applications in this section of the manual. We will also take a look at the accessories that are used on common valves and how valve sizing has limitation that must be considered. The style of the valve trim (internal makeup), the characteristics (the gain of the flow per signal) and the ΔP across the valve, all affect if the valve will function or not in the process piping loop. There may be limits of the maximum and minimum ΔP across the valve to adhere to. The ΔP can limit the flow through the valve and can cause excessive noise and even destruction of the valve.

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Considerations when sizing a control valve The following should be considered when sizing and selecting process control valves for a project.

1 gpm  1 CV *

1 Ppsig 1 S .G. flowing

Flow Coefficient Cv The use of the flow coefficient, Cv, first introduced by Masoneilan in 1944, quickly became accepted as the universal yardstick of valve capacity. So useful has Cv become, that practically all discussions of valve design and characteristics or flow behavior now employ this coefficient. By definition, the valve flow coefficient, Cv, is the number of U. S. gallons per minute of water that will pass through a given flow restriction with a pressure drop of one psi. For example, a control valve with a maximum flow coefficient of Cv = 12, has an effective port area in the full open position such that it passes 12 gpm of water with one psi pressure drop. Basically, it is a capacity index upon which the engineer can rapidly and accurately estimate the required size of a valve restriction for desired flow in any fluid system. The flow is dependent on other variables as well and there may be limitations of the maximum Δ P that can be applied across the valve. Specific Gravity In the flow formulas, the specific gravity is a square root function; therefore, small differences in gravity will have a minor effect on valve capacity. If the specific gravity is not known accurately, a reasonable assumption will suffice. The use of specific gravity equal to 0.9 for example, instead of specific gravity equal to 0.8, would cause an error of less than 5 % in valve capacity. Sqrt [1 / (0.9-0.8) ] = 3.16 % error in flow. Operating Conditions The selection of a correct valve size, as determined by formula, is always premised on the assumption of full knowledge of the actual flowing conditions. Frequently, one or more of these conditions is arbitrarily assumed. It is the evaluation of these arbitrary data that really determines the final valve size. No formulas, only good common sense combined with experience, can solve this problem. There is no substitute for good engineering judgement. Most errors in sizing are due to incorrect assumptions as to actual flowing conditions. Generally speaking, the tendency is to make the valve too large and to be on the "safe" side (commonly referred to as "oversizing"). A combination of several of these "safety factors" can result in a valve so greatly oversized it tends to be troublesome.

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ISA standard valve symbols

Valve (generic)

Globe valve

Butterfly valve

Ball valve

Gate valve

Saunders valve

Plug valve

Characterized ball valve

Pneumatic pinch valve

Pressure relief or safety valve

Angle valve

Three-way valve

Check valve (generic)

Pressure regulator valve

Ball check valve

Diaphragm valve

ISA standard pressure regulating valve symbols

Pressure reducing regulator self-contained with hand wheel

Pressure reducing regulator external pressure tap

Pressure reducing differential regulator external and internal pressure tap

Back pressure regulator self-contained

Back pressure regulator external pressure tap

Pressure reducing regulator with integral pressure relief valve and optional indicator

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Valve actuators The operation of a control valve involves positioning its movable part (the plug, ball or vane) relative to the stationary seat of the valve. The purpose of the valve actuator is to accurately locate the valve plug in a position dictated by the control signal. The actuator accepts a signal from the control system and, in response, moves the valve to a fully-open or fully-closed position, or a more open or a more closed position (depending on whether 'on/off' or 'continuous' control action is used). There are several ways of providing this actuation; the two major ways are by:  

Pneumatic Actuator Electric Actuator

Other significant actuators include the hydraulic and the direct acting types. It should be noted that pneumatic actuators do not operate on a standard 3 to 15 psig pressure output from a current to pneumatic convertor (I/P). This is a misconception. The standard pneumatic signal, 3 to 15 psig, is left over from the pneumatic controller days. The actuator operates on 0 to 15 psig or 0 to 30 psig or 0 to 60 psig. The (I/P) may be calibrated from 1.5 to 12.8 psig or 8 to 20 psig to close the valve and overcome the pressure in the pipe pushing up against the valve seat trying to open the valve, as well as any friction of the valve stem packing trying to stop the valve stem from moving. This is called the bench set calibration of the valve’s actuator. ISA standard actuator symbols

Diaphragm

Electric motor

Solenoid

Piston

Diaphragm with hand jack

Electric motor with hand jack

Hand manual

Piston with positioner

Diaphragm with positioner

Electro-hydraulic

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Limit switches on a valve - ISA standard symbol A typical application of a valve for a gas service is shown below. Limit switches are attached to the actuator to verify the valve position status. The limit switches send a full open signal (ZSO) or full closed signal (ZSC). If neither signal is received by the PLC or DCS within a reasonable time, the limit switches provide a valve stuck or malfunctioning indication (show proper ISA P&ID symbols, the “B” represents burner or combustion). The solenoid is a safety shutdown lockout type mechanism. The diamond symbol with the “R” indicates a manual reset of the solenoid valve in the field is necessary to provide instrument air to the gas valve for operation. This insures that personal inspect the furnace or heater before restoring the gas, to prevent explosions or fire.

Limit Switches

Position Transmitter Calculating the size of the actuator Reference the figure of the air to open (ATO) valve below. The process fluid flows through the valve from left to right, excerpting a force upward due to the process fluid’s pressure multiplied by the seating area on the valve trim, (the globe type “plug” against the valve seat). The actuator spring must be sized to not only hold the valve closed against the differential pressure excerpted upward on the plug by the process fluid’s pressure, but also to add extra seating force to the valve to prevent leakage of the process fluid between the valve’s plug and the seat. This leakage is measured in what is called bubbles per minute. Also extra force on the spring may be required to overcome the friction of the packing. The spring is usually oversized for the application, due to the fact that standard size springs are used for various applications and process fluid pressures. The actuator must be sized for the total forces needed to move the valve stem into position.     

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2

The force upward (Fp): Process fluid pressure (psig) * area of the plug (in ) in pounds force (lbf). The force downward by the spring (Fk): Force in (lbf) varies with spring size, Hook’s Constant The force upward of the diaphragm (Fd): The I/P supplied device pressure (psig) * area of the 2 valve diaphragm (in ) in pounds force (lbf). The force to overcome stem friction (Ff): To move valve against the friction of the stem packing. The force applied to the seat (Fs): The force applied to the plug to prevent leakage through the valve seat, in (lbf) per lineal inch of seat around the circumference.

For an air to open (ATO) valve, the diaphragm force (Fd) must be in the opposite direction of the spring force (Fk) and equal to the sum of the force excerpted by the spring (Fk) and the force excerpted by the stem packing (Ff), minus the force of the process fluid (Fp) pushing up on the valve seat, before the spring will start compressing and the valve plug will start moving open. For an air to close (ATC) valve, the diaphragm force (Fd) must be in the opposite direction of the spring force (Fk) and equal to the sum of the force excerpted by the spring (Fk) and the force excerpted by the stem packing (Ff), before the spring will start compressing and the valve stem will start moving closed. Once it starts closing, the diaphragm force (Fd) must be increased to equal of the compressed spring force (Fk) and equal to the process fluid force (Fp) pushing up on the seat and the force excerpted by the stem packing (Ff) and the extra seating force (Fs) needed to meet bubble leakage specification (say 150 lbf per linear inch of seat), before the diaphragm force will fully seat the valve plug. This force (Fd) may equal 8 2 pisg * 100 in for the diaphragm, to equal 800 lbf excerpted downward by the actuator diaphragm. The diaphragm pressure must be increased to force the stem downward more. The spring is already forcing up against the diaphragm plate and must be compressed more (see Hook’s Constant); the process fluid (Fp) is forcing up against the seat trying to open the valve; plus we must add the force for seating (Fs) the valve and the still required added resisting force of the packing friction (F f), will all add up to the required force that must be generated by the diaphragm and diaphragm plate connected to the plug stem. 2

The I/P supplied device pressure (psig) * area of the valve diaphragm (in ) in pounds force (lbf), will produce the minimum diaphragm force (Fd) needed to overcome the total resistive forces against the diaphragm. The spring will start compressing and the valve will start moving toward the fully closed position. If the I/P (current to pressure convertor) excerpts 15 psig to the diaphragm, the diaphragm force 2 downward (Fd) will be 15 psig * 100 in which equals 1,500 lbf. A force of 1,500 excerpted by the diaphragm is the force needed to compress the spring all the way and allow the valve trim plug to move to the fully closed and seated position and provide safe and effective operation. It can be seen that all valve I/Ps are not calibrated 3 to 15 psig. When a large pressure exists in process piping system, the valve’s actuator will be calibrated to a range to produce sufficient force to overcome the force of the process fluid and seat the plug. In our example, the I/P was calibrated 8 to 15 psig. Example actuator sizing

Sample problem: We will now size a reverse acting valve actuator (ATO) for a process having the following data: Single seated globe valve with flow under the plug (air to open). Delta pressure across the valve: 25 psig Stem travel: 1.5 inches 2 Actuator area: 78.5 inches Port diameter: 2-5/16 inches Plug seating class: II (20 lbf per lineal inch) Stem friction: Ff =125 lbf (graphite packing) Spring force: Fk = 500 lbf

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First calculate the force excerpted by the process fluid (F p): 25 psig * area of plug:

FP  25*

 2.31252 4

 105.0 lbf

Find Seating force for plug for a class II shutoff:

FS   * D * 20lbf per inch   * 2.375* 20  149.23 lbf To unseat the valve and start movement of the stem toward open, we add the stem friction force to the spring force and subtract the process fluid force pushing upward:

FD(min)  FK  Ff  FP  500  125  105.0  520.0 lbf Find the LRV of the I/P pressure:

P

F 520.0   6.63 psi A 78.5

The force of the spring compressed when the valve is fully open:

FX  FK * x(inches of travel) FX  500lbf *1.5inches  750lbf To open the valve fully, we add the stem friction force to the spring force pushing down: Note: The valve plug is already unseated, so there will no longer be a force Fp helping the spring to fully open, due to the fact that there is practically no delta pressure being excerpted upon the plug.

FD(max)  FX  Ff  750  125  875 lbf Find the URV of the I/P pressure:

P

F 875   11.15 psi A 78.5

The I/P transducer will be calibrated: 6.63 to 11.15 psig

Split ranging control valves In a split range control loop, output of the controller is split and sent to two or more control valves. The splitter defines how each valve is sequenced as the controller output changes from 0 to 100%. In most split range applications, the controller adjusts the opening of one of the valves when its output is in the range of 0 to 50% (4 to 12 mA) and the other valve when its output is in the range of 50% to 100% (12 to 20 mA). When split ranging valves to handle flow rates varying from very large to very small, a 10% overlap in the valve signal is recommended. This allows the valves to have a smoother transition, due to the difference in the Cv ranges of the two valves. The overlap provides a more linear process gain for the system.

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In this example when the gas pressure exceeds the pressure that the compressors can handle, the extra gas is sent to the flare to burn, this relieves the pressure on the vessel.

In this example the reactor needs to maintain at a specific temperature range. This requires heating and cooling the jacket to regulate the temperature for the reaction.

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Valve positioner applications A valve positioner takes an input signal from the DCS or PLC and positions the valve plug using a feedback signal from the position of the valve stem. The positioner will provide air pressure to the pneumatic actuator’s diagram. The air pressure output signal to the actuator will be a percentage of the full scale calibrated air output of the positioner. The percentage of full scale air output will be proportional to the percentage of the full scale input signal. There may be a gain in the percentage of air output; this will be due to the amplifier setting being greater or less than 1. The actuator moves the valve stem to a percentage of full stroke that is equal to the percentage of the input signal, say 50% open. The positioner receives a feedback signal from a lever arm connected to the valve plug stem. The positioner may also apply additional corrective pressure to the actuator diaphragm. This extra compensated pressure is proportional to the error of the position of the plug stem and will try to move the valve plug into the exact position being called for by the signal from the DCS or PLC. The positioner is being used as a cascade controller for the flow loop. It provides tighter and faster control of the valve stem position. When a positioner is fitted to an 'air-to-open' valve with an actuator, the spring range of the actuator may be increased to increase the closing (seating) force of the plug in the valve. A positioner can compensate for the extra required pressure required to properly position the valve. The positioner will allow for an increase in the maximum differential pressure a particular valve can tolerate across the plug. Pulsations in this differential pressure across the plug will cause upward forces on the valve plug and can cause the valve to fluctuate in position. The positioner will compensate for these fluctuations with a feedback signal from the lever arm and send a proportional air signal to the diaphragm of the actuator to compensate for the error in position of the plug and move the valve plug to the true desired position. The positioner also sends additional air pressure to the actuator when an error is measured in position, allowing the actuator to overcome the friction of the stem packing and reduce hysteresis effects. It should be noted that a positioner is a proportional device, and in the same way that a proportional controller will always give an offset, so does a positioner. On a typical positioner, the proportional band may be between 3 and 6%. The positioner sensitivity can usually be adjusted.

ISA standard valve positioner symbols A typical positioner on a valve

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SIS System application with solenoid Interlock

Summary of positioners 1. A positioner ensures that there is a linear relationship between the input signal from the control system and the position of the control valve. This means that for a given input signal, the valve will always attempt to maintain the same position regardless of changes in valve differential pressure, stem friction, diaphragm hysteresis and so on. 2. A positioner can also sometimes modify the input signal to characterize the action of the valve trim. This is especially true of a digital valve positioner. 3. A positioner may be used as a signal amplifier or booster. It accepts an input signal in the form of a low pressure air control signal (3-15 psig). Using the positioner amplifier to add gain to the input position signal, the positioner provides an amplified pressure output air signal to the actuator diaphragm to position the valve plug. This ensures that the valve reaches the desired position. 4. Some positioners incorporate an electro-pneumatic converter so that an electrical input (typically 4 - 20 mA) can be used to control a pneumatic valve. 5. Some positioners can also act as basic controllers, accepting input from sensors.

When should a positioner be used? A positioner should be considered in the following circumstances: 1. When accurate valve positioning is required. 2. To speed up the valve response. The positioner uses higher pressure and greater air flow to adjust the valve position. 3. To increase the pressure that a particular actuator and valve can close against. (To act as an amplifier). 4. Where friction in the valve (especially the packing) would cause unacceptable hysteresis. 5. To linearize a non-linear actuator. 6. Where varying differential pressures within the fluid would cause the plug position to vary. Note: Positioners should not be used on fast responding loops, such as a flow loop with a lot of noise. The loop is much harder to stabilize and cyclic oscillations may be continuous. To ensure that the full differential pressure across the valve can be accepted, it is important to adjust the positioner zero setting so that no air pressure opposes the spring force when the valve is in its normal zero percent state or off-the-shelf position.

Electrical positioners Electric valve positioners send and receive electrical signals. These signals are typically a 4-20 mA positioning control signal and digital or discrete on/off position indication signals from limits switches inside the valve. There are three electric actuation types: single-phase and three-phase alternating current (AC), and direct current (DC) voltage. Electrical actuators are fairly responsive and can develop large torques for high pressure applications. Most actuators offer compatibility with a wide range of communication and process control systems. Network control of the actuator may be available using PROFIBUS, FOUNDATION Fieldbus, Modbus, DeviceNet, HART, and Rotork's Pakscan. More recent innovations of these actuators include the option of advanced display, Bluetooth® communications interface and absolute encoders.

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Control valve application comparison chart

Valve Type

Globe body with characterized plug or cage Sizes from needle up to 24 inches Ball valve availability up to 42 inches

Butterfly valve availability up to 150 inches

Characteristic and Rangeability

Uses on Slurries, Dirty Solid Bearing Fluids

Equal percentage or linear Max 50:1 Approx. 35:1 for needle

Very poor, can be constructed of corrosion resistant materials

Equal percentage Approx. 50:1 Ball can be characterized

Reasonably good, can be constructed of corrosion resistance materials

Equal percentage or linear Approx. 30:1 (some can characterized for quick opening)

Saunders valve availability up to 20 inches

Approx. Linear 3:1 conventional 15:1 dual range

Pinch valve availability up to 24 inches

Approx. Linear 3:1 to 15:1, depending on type

Poor, a variety of material for construction available

Very good, available with liner to resist corrosion

Excellent, several materials available to resist corrosion

Relative Cost

High, very high in larger sizes

Excellent; any desired characteristic can be designed into this type valve

Medium

Excellent, if characteristic is suitable

Lowest cost for large size valves

Good, if characteristic is suitable

Medium

Conventional is poor; dual range is fair. Use only when ability is needed to handle dirty flow

Low

Poor to fair. Use only when ability is needed to handle dirty flow

Note: See appendix for more tables on valve sizing applications and material section. This may be asked on the CSE exam When valves are mounted in a position or orientation other than the vertical position, the actuator must be supported so the stem does not bind. This may prevent the valve from opening or closing properly due to stiction of the valve. Valve stiction is one of the largest stand-alone reasons for oscillatory behavior in process industry. It is a problem that is hard to detect and time consuming for oil and gas plants. When stems are in a binding position they may be subject to stem packing wear and leakage. The ISA standard and most EPA rules only allow 500 ppm leakage from packing seal of the stem and joints. Read on LDAR (leakage detection and repair) in the code review section.

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Rating as Control Valve

Understanding flow with valve characteristics When controlling a process fluid flow rate, the full capacity of the valve (100%) cannot be used. All processes have upsets due to disturbances and changing load demands on the process system. The valve needs to throttle the process fluid to control the process, not just regulate a fix amount of flow. Due to the nature of the valve and piping systems, the differential pressure (ΔP) across the valve is always changing. This leads to choked flow, cavitation and even flashing of the liquid into vapor. We will now discuss how a valve really works when installed in a process piping system. What is the ΔP for valve sizing? As it has already been stated, you cannot arbitrarily just pick a ΔP for sizing the process control valve. It is not a made-up or magical number. It is the extra pressure head in the piping system. The Cv verses valve stem stroke chart in the valve sizing book is based on a fixed pressure drop across the valve. This is called the inherent characteristic of the valve. But when the valve is installed in a real piping system, the pressure across the valve is constantly changing as the flow rate changes. This is called the installed characteristics of the valve. This is why the valve starts choking at about 70% of the maximum flow rate of the valve. As the flow increases, the pressure drops in the piping system become greater across the other elements in the piping system; they need more energy to do more work. So the pressure drop across the valve becomes lower, hence less flow rate per percent of valve stem stroke for the valves percent Cv rating in the catalog. Therefore, there is less flow through the valve at the maximum opening than assumed by the percent of stroke in the catalog. 100% valve opening is not equal to 100% flow when installed in the piping system, unless the valve is sized at the lowest pressure drop in the system for the maximum flow rate. As the flow becomes less or slower, the pressure drops in the system become less and the pressure drop across the valve becomes greater, therefore, there is more flow thought the valve at less stroke of the valve stem.

1 gpm = 1 CV * 1 ΔPpsig This installed characteristic makes the equal percentage valve look more like a linear valve and a linear valve look more like a quick opening valve. Also keep in mind that when sizing the valve, we need to control system upsets. This requires more or less flow than the normal demand for flow. The pump needs to provide about 15 to 40% more head than is required to pump through the piping system, to provide the extra ΔP across the valve to ensure higher flow rates and even that the valve will operate. Without this extra ΔP in the system, the valve will not function properly and there will be hardly any flow through the valve until it is almost fully open. Also the valve Cv will have to be larger than the demand flow (normal conditions) to handle 10% to 15% more flow for process upsets. The industrial standard is to size the valve Cv for 200% of demand flow or throttle the valve at 50% of the valve’s Cv rating. System piping ΔP pressure drops Look at the figure below. In the section on fluid mechanics we discussed the pump head, pressure head, kinetic head and static head in a piping system. We showed how the pressure head changed to kinetic head to accelerate the fluid through the piping system and that work was done on the pipe, fittings and elements. The figure below on the right side shows, the pump head equals the pressure head at no flow. When the system is at minimum flow (the green low flow line) the available pressure head produced by the pump is much less. This reduction in pressure head is the difference of the pump head minus the kinetic head, to accelerate the fluid and do work on the piping system. The reduction in head will be constant for this flow rate. As we increase the flow rate to maximum flow (the blue high flow line) the pressure head drops even

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more to add more kinetic energy to the pipline system to do even more work on the piping system. Moving from left to right on the graph, we see there is additional drop in pressure for each section of the pipe and the elements in the piping system. At the end of the graph you will see there is still pressure head above zero. This is the head pressure of the tank level in feet of head. Notice the ΔP across the valve in the middle of the graph. At low flow it is very large, just the opposite of the orifice element in our studies previously. The orifice or a head device consumes energy to do work passing the fluid through the orifice. The control valve absorbs the left over energy of the system, the difference of pump head minus the kinetic head and minus the work done on the system (the energy consumed in the form of heat and vibration). The control valve has to consume or burn up the extra head energy in the system or the fluid would accelerate far too fast. ΔP * A (area) = F (force), there is a ΔF across the piping system. Work = ΔF * D (distance) also ΔF/m (mass) = g (acceleration). The valve has to burn up the extra ΔP in the system or the fluid would be accelerating far too fast for the demand of flow. By burning up some of the pressure head across the valve the fluid decelerates. This allows us to control the flow rate of the process fluid. Notice there is less ΔP across the valve at the higher flow rate. This is because we need a greater differential pressure across the piping system to accelerate the fluid faster and to do more work. Note that the hand valves typically do not change, so they act just like an orifice or head device and consume a fixed amount of energy proportional to the flow rate of the process fluid. Control valve ΔP pressure drop The varying ΔP across the valve in the piping system discussed above is shown in the figure to the right. The graph shows the total energy put into the system and how it is divided up into its head energy components. Let’s do a breakdown of flow rates for a 2” linear valve, max Cv = 39.2

gpm  CV * Flow Cv rate required GPM for flow

Ppsig

ΔP Valve ft / psi

%Stem stroke (open)

35.0

5.66

88 ft/ 14.54% 38.26 psi

50.0

10.72

50 ft/ 27.35% 21.74psi

70.0

20.43

27 ft/ 52.12% 11.74 psi

80.5

29.62

17 ft/ 7.39 psi

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75.54%

Graph of the Inherent valve characteristics (off the shelf) The control valve characteristics refers to the relationship between the volumetric flowrate C v or GPM (Yaxis) through the valve AND the valve travel or stem opening position m (X-axis), as the valve is opened from its closed position to various degree of opening. (Note that the symbol m or Z is used here to represent the valve travel or opening position, in %). The control valve manufacturer can only state the inherent valve characteristics, which refer to the flowrate (Cv) versus the valve travel position (% open) relationship, at a constant pressure drop across the control valve (ΔPv). Note that the pressure drop across the control valve (ΔPv) can be almost constant only if the piping system pressure drops (ΔPs) is concentrated at the control valve and not distributed along the pipeline. This means that the pipeline must be of very short length with minimum pressure reducing devices or equipment in series with the control valve. Such a condition rarely exists in actual installation except in the control valve manufacturer testing facilities, where the control valve characteristics are obtained using very short lengths of piping.

Cage valves are shown to the left Globe valves are shown below left Valve characteristics chart is below

Which valve characteristic trim to use? Since it is desirable to achieve and maintain process stability, the proper inherent valve characteristic must be selected to compensate for process changes. The first step is to determine the controlled process variable. There are four main classes: liquid level, pressure, flow, and temperature.

Controlled Variable: Liquid Level If the valve pressure drop is constant, the inherent valve characteristic should be linear. This is because the process gain does not change. For varying pressure drops, the following guidelines are recommended: use equal-percentage if the drop at maximum flow is less than 20% of the drop at minimum flow and a quick-opening if the drop at minimum flow is greater than twice the drop at minimum

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flow. The equal-percentage is selected because as the load changes, the variation in valve gain is minimized. The quick-opening is selected to negate the effects of the large pressure drop at high flows. Controlled Variable: Pressure Processes that control pressure are a function of the process time constant. These processes can be “slow” (e.g., large volumes, receivers, or long distribution lines) or “fast” (e.g., liquid flowing in a pipe). For the same reasons as liquid level, a linear characteristic is recommended for a slow process with a constant pressure drop. If the pressure drop at maximum flow is less than 20% of the drop at minimum flow in a slow process, then an equal-percentage is used. For fast processes under any pressure drop, an equal-percentage is again recommended. Controlled Variable: Flow Controlling flow as the process variable offers additional challenges since the flow does not vary with the load. A load change in a flow loop does not change the flow rate, but results usually in a change in pressure. The flow is controlled by the set point. An additional aspect is that transmitters are not always linear. Some are proportional to flow and some are proportional to the square of the flow rate. The selection of the valve characteristic then becomes a function of the type of signal sent to the controller. Whether the valve is used in series or a bypass also makes a difference. Controlled Variable: Temperature In temperature control loops, the time constants are generally large and the characteristic frequency of the system changes as the load varies. Numerous temperature control loops exist in chemical plants and refineries, and experience has shown the best inherent characteristic is equal-percentage. Valve Selection for Liquid Level

Valve Selection for Pressure

Valve ΔP Approximately Constant

Characteristic Linear

ΔPQmax < 0.20 ΔPQmin

Equal-Percentage

ΔPQmax > 2.0 ΔPQmin

Quick-Opening

Process Fast Slow

Valve ΔP Any Constant or ΔPQmax > 2.0 ΔPQmin ΔPQmax < 0.20 ΔPQmin

Characteristic Equal-Percentage Linear Quick-Opening

Valve Selection for Flow Signal Proportional to Q (% flow) 2 Proportional to Q (% flow squared)

Valve Location Series Bypass Series Bypass

Characteristic If set point varies Linear Linear Linear Equal-Percentage

Characteristic If load varies Equal-Percentage Equal-Percentage Equal-Percentage Equal-Percentage

Characteristic distortion in valves Flow distortion in valve characteristics (Cv verse % stem position) Most control systems give the best performance when they behave in a linear manner. So you might ask the question, “Why would you use an equal percentage valve which is not at all linear?” The answer is because of the installed characteristic. The installed characteristic is the relationship between valve position and flow in the specific system being considered, taking into account any changes in the

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pressure differential available to the control valve, due to the flow squared relationship between flow and the piping pressure losses and/or the behavior of a centrifugal pump’s head curve. The majority of fluid process systems include a significant amount of pipe and other pressure consuming elements (elbows, pipe reducers, isolation valves, heat exchangers, pumps whose pressure decreases with increasing flow, etc.). This results in a relationship between system flow and pressure differential available to the control valve as it was just explained earlier with the curves in the figures under this section. See the sections: What is the ΔP for valve sizing? and System piping ΔP pressure drops and Control valve ΔP pressure drop. When the control valve is installed into the piping in a process plant, its flow characteristics are no longer independent (inherent) of the rest of the system. This is because the flow through the valve will be subject to the frictional resistance, which is in series with the valve. The consequence is this type of distortion is illustrated in figures below. From the figures below for a linear and an equal percentage valve, you can understand that the pressure drops in different piping installations, will have a very substantial effect on both the characteristics and rangeability of the valve. Under conditions of excessive distortion, the equal percentage valve characteristics can be distorted toward linear or even quick opening. The distortion can be approximated from the formula to the right: Where: ΔP = pressure drop across the valve ΔPt = pressure of the pump head ΔPs= pressure drop across the pipe plus the fittings It should be emphasized that the figure of the piping installation above assumes the use of a constant speed pump. In variable-speed pumping systems, you can adjust the pump speed to keep the ΔP across the valve pretty much at a constant, and, therefore, in a VFD pump controlled system, the theoretical (inherent) valve characteristics and the real (installed) valve characteristics are pretty much similar, and less distortion will occur.

Naturally, in variable-speed pumping systems you can completely eliminate the valve and just throttle the pump speed. The predictability of installed valve behavior is reduced, not only because the inherent valve characteristics deviates but the ΔP across the valve and the ΔP across the pipe are constantly changing at different rates.

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Gain and Rangeability (turndown ratio in valves) Turndown is the ratio of maximum to minimum controllable flow. For a pinch valve, 10:1 is typical, so if you have a maximum flow of 5,000 scfm, you can expect to maintain stable control down to 500 scfm. Of course, the valve can close or drop tight to zero flow, but it’s difficult to maintain stable control between zero and your minimum controllable flow. Turndown says nothing about the response, speed of valve, undershoot, overshoot or duty cycle. The conventional definition of rangeability is the ratio between the maximum and minimum “controllable” flows through the valve. Minimum controllable flow (F min) is not the leakage flow (which occurs when the valve is closed), but the minimum flow that is still controllable, and can be changed up or down as the valve is throttled. Using this definition, manufacturers usually claim a 50:1 rangeability for equal-percentage valves, 33:1 for linear valves, and about 20:1 for quick-opening valves. These claims suggest that the flow through these valves can be controlled down to 2%, 3%, and 5% of maximum. However, these percentages are often exaggerated. Also it can be seen in figure above that the minimum controllable flow (Fmin) rises as the distortion coefficient (Dc) drops. Therefore, at a Dc of 0.1, the 50:1 rangeability of an equal-percentage valve drops to about 10:1. Consequently, the rangeability should be defined as the flow range over which the actual installed valve gain stays within ±25% of the theoretical valve gain. To illustrate the importance of this limitation, the figures below show that the actual gain of an equal percentage valve starts to deviate from its theoretical gain by more than 25%, when the flow reaches about 65%. Therefore, in determining the rangeability of such a valve, the maximum allowable flow should be 65%. Actually, if you use this definition, the rangeability of an equal-percentage (=%) valve is seldom more than 10:1. In such cases, the rangeability of a linear valve can be greater than that of an equal-percentage (=%) valve. Also, the rangeability of some rotary valves can be higher because their clearance flow tends to be lower, and their body losses near the wide open position also tend to be lower than those of other valve designs.

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To stay within ±25% of the theoretical valve’s gain, the maximum flow should not exceed 60% of maximum Cv in a linear valve or 70% of maximum Cv in an equal-percentage (=%) valve. In terms of valve lift, these flow limits correspond to 85% of maximum lift for an equal-percentage (=%) and 70% for linear valves.

Proper control valve sizing The symptom of a misapplied control valve flow characteristic is a control loop that only gives good control at one end of its operating range and is either sluggish or becomes unstable at the other end of its operating range. An example of a misapplied valve inherent flow characteristic would be an equal percentage valve in a system with very little piping. The left-hand graph in the figure to the right shows the unstable oscillations as results of a short run. The flow characteristic is due to the fact there is not enough non-linear flow pressure drop that would normally be created by long runs of piping that would greatly reduce the ΔP across the valve at maximum flow. Looking at the previous figure above, the gain for an equal-percentage valve is very high near 100% of stroke, so when there is an upset and the valve opens, the flow rate accelerates very quickly, overshooting the desired flow for correction. The control system (controller) has to hunt and as the valve starts to close down the process loop gain becomes less, allowing the loop to stabilize. Upon startup of this system, if it was running at a low process load and the valve was around 25% open (Point 1), after going through the process of tuning a PID controller you can see that the slope of the valve’s installed characteristic curve is quite shallow. This means that the valve’s gain (or the sensitivity of flow to changes in valve position) is quite low. To make up for this, the proportional gain of the controller would need to be set fairly high. As expected, when you make a step change in the set point, there is a quick and stable response. Later, when the process load increases, the valve might be around 50% open (Point 2). At this point, the slope of the valve’s installed characteristic curve (its gain) is higher meaning that the value of controller proportional gain previously selected is higher than it should be when the valve is 50% open. When the set point is stepped up from the current 50% position there is an oscillatory response. When the process load increases to where the valve is around 75% open (Point 3) the slope of the valve’s installed characteristic curve is quite steep, meaning that the valve’s flow gain is quite high.

The value of controller gain originally selected when the valve was 25% open is now much too high, and when the set point again is stepped up there is a very unstable response. If the loop were instead tuned when the control valve was 75% open, a lower value of proportional gain in the controller had been used, there would be a fast, stable response to a step change in set point. However, if operated at lower loads, the response would be very sluggish. If you had misapplied a linear valve in a system with a lot of pipe, the situation would be the opposite of what is shown in figure above right. Just as the system with a lot of pipe pushes the equal percentage inherent characteristic upward into a linear installed characteristic, it would push a linear inherent characteristic upward into a quick-opening characteristic. With a quick-opening characteristic, a small increment of valve position at small openings results in a large increase in flow capacity, while the same increment of valve position at large openings results in a small increase in flow capacity. This system would be very sensitive at low valve openings (high gain) and very insensitive at large openings (low gain). The system would still be very difficult or impossible to tune to get a fast stable response throughout the flow range.

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On the other hand, a properly applied control valve inherent characteristic (an equal percentage valve in a system with a lot of pipe, or a linear valve in a system with little pipe) results in a linear, or at least nearly linear installed characteristic, as shown in the left-hand graph of the figure to the right. A linear installed characteristic gives responsive and stable control throughout the entire flow range. This properly applied valve’s installed flow characteristic has a slope that is quite constant throughout the entire flow range and the sensitivity of flow to changes in valve position is a nearly a linear flow gain. Regardless of what the operating point was during the controller tuning process, the PID tuning parameters selected would be appropriate at all points in the operating range. In simplicity the above learning can be summarized just by looking a heat exchanger application which has a significate amount of pressure drop, using an equal-percentage control valve as shown below for flow control. When more heat or BTU per (lbm * °F) is called for, the flow must greatly increase so the gain of the heat exchanger drastically drops off near the top of the design flow rate. The pipe friction creates a greater non-linear pressure drop as shown below. The equal-percentage valve has a gain that is the inverse of the heat exchanger, so when there is an increase in flow, the heat exchanger gain is dropping and the equal-percentage valve gain is increasing, creating a fairly linear gain over the flow range and temperature control range of the process loop. This will be discussed further in the section in this manual Process Control Theory and Controller Tuning.

Equal percentage valves provide linear gain in flow applications

Oversized valves present problems Next, it’s important to understand the importance of proper control valve sizing. If the right size valve is not selected, there are two possibilities: 1) The valve may too small. If it is, it won’t be able to pass the required flow. In actual practice, undersized valves are fairly uncommon 2) The valve may be too large, which turns out to be all too common. An oversized control valve will cost more than is necessary, but it is only a minor point compared to the real problem they present. The real problem with an oversized valve is that it will be very sensitive; meaning small changes in valve position will cause large changes in flow. This will make it difficult, or even impossible, for the valve to adjust exactly to the required flow. The figure below shows graphs of the installed characteristics of two different valves in the same system. These are both segment ball valves, which have equal percentage inherent characteristics, and the system has a lot of pipe. Note that up to the specified maximum flow rate of 550 GPM both have reasonable linear installed characteristics. The 3” valve is a properly sized valve and the 6” valve is an

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oversized valve. The reason that the 3” valve is a properly sized valve is because it meets the criterion of the rule of thumb of being between 60% and 80% open at the maximum required flow of 550 GPM. This rule of thumb has served valve users well because it gives a good balance between using as much of the valve’s control range as possible, giving good flow resolution, while providing adequate safety factor. (The 3” valve can increase flow about 20% above 550 GPM which should be adequate, while the 6” valve can increase the flow about 60% above 550 GPM, which is more than should ever be required. Starting at 550 GPM, if the properly sized valve opens by 1 percentage point the flow will increase by 8 GPM. If the oversized valve opens by 1 percentage point the flow will increase by 20 GPM. All valves exhibit a certain amount of stickiness. After a valve has been in service for a long time, especially if someone has been a little overzealous in adjusting the packing, it is not unusual to find that the smallest increment that the valve can move is 1%. If the best each of these valves can do is position themselves in 1% increments, the 3” valve will be able to control flow within 8 GPM increments, and the 6” valve will only be able to control flow within 20 GPM increments. In general, the more oversized a control valve is, the poorer the accuracy of control will be. Note: For problems with stiction in valves, review the previous lesson on the application of valve positioners. But remember they should not be used with fast responding process flow loops. Although not always possible, it is also preferable to have the minimum opening no less than 20% to provide some safety factor at the low end. Normally, the control valve manufacturers publish Cv values in 10% increments beginning at 10% open, so it’s impossible to know what is happening to the Cv below that point. It is also not uncommon for the inherent characteristic to start deviating from the ideal Cv curve somewhere below 20% open. It is not unusual to find properly sized full-ball, segment-ball and high-performance butterfly valves that are two sizes smaller than the line and properly sized globe valves that are one size smaller than the line. This is not a rule, but just the way things often turn out. If a valve is sized, and it turns out to be different than these, it is a good idea to check the work. A mistake may have been made. Additionally, the person who sized the pipe may have made a mistake. Most people consider it poor piping practice to use a control valve that is less than one half the pipe line size or larger than the line size.

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Experiment and understand Installed valve characteristics The top row shows the Cv verses stroke for an equal percentage and a linear valve as in the sizing catalog. The second row shows the actual or installed characteristic flow rate in gpm verses the percent signal for stem stroke from the DCS or PLC. The third row shows the ideal (off the self) flow rate in gpm verses the percent signal for stem stroke from the DCS or PLC, for a constant pressure differential. Remember a constant ΔP across the valve cannot be achieved in a real flow control system. Remember the valve starts choking at about 70% of its rated catalog Cv verses stem stroke.

Go to the Learn Control Systems web site for a free Excel Spreadsheet which will demonstrate how the valve works in an installed piping system with real-time graphs of the real installed characteristics of the valve. Download this free excel spreadsheet I have created and play with different flow rates and percent extra pump head for the operation of an installed valve and a flow meter orifice application. Liquid System Sizer - version 2.7 (Size Pump, Valve, Orifice, Transmitter and Piping System) http://www.learncontrolsystems.com/studymaterials/System-Sizer.htm

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Summary of control valve characteristics Here are some points to remember: 

If a set of loop-tuning parameters only works at one end of the control range and not the other, the valve’s flow characteristic is most likely the wrong one.



If a system has a lot of pipe and/or other pressure consuming elements, or a pressure source that decreases with increasing flow, an equal percentage valve will usually be the best choice.



If a system has very little pipe and/or other pressure-consuming elements and has a pressure source that doesn’t decrease with increasing flow, a linear valve will usually be the best choice.



A control valve that is sized to operate around 60% to 80% open at the maximum required flow and not much less than 20% open at the minimum required flow will give the best control.



The valve will start choking at about 70% of its rated Cv when installed in a system with long pipe runs.



The maximum flow should not exceed 60% of maximum Cv in a linear valve or 70% of maximum Cv in an equal-percentage valve.

This chapter has laid the foundation for a solid understanding of loop response and tuning of control loops. This subject and it applications will be further expanded on in these sections of the manual: Process Control Theory and Controller Tuning and Chemical Process Technology and Equipment

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Control Valve Sizing As demonstrated in the previous studies of the section, it is important to understand that you cannot just pick a differential pressure (ΔP) to be across the valve and size the valve for a flow control system. It is a system and all the elements interact as a system. The pressure drops across the elements in the system are constantly changing as the flow rate changes. The piping system can be thought of as being similar to an electrical circuit. There is a battery (the pump) and fixed resistors in series to make up the system (the pipe, the fittings, the orifice plate or measuring restriction). The valve is a variable resistor in the system and is constantly changing resistance. From electrical physics, you will remember Kirchhoff’s voltage law. The sum of the voltage drops (pressure drops) equals the sum of the source (pressure produced by the pump). Unless we are pumping into a pressurized vessel or tank maintaining a level head, all the pressure is dropped as we exit the pipe and the fluid’s pressure equals the atmosphere upon exiting the pipe. All the pressure has been used up. Remember that the pressure drop is “head pressure” and it is a component of the total head energy produced by the pump. The head pressure does not just drop off as it goes down the pipe; it is consumed to do work. This can be seen by looking at the pump motor. It absorbs a constant wattage to produce a constant horsepower (HP) which in turn produced the hydraulic head. The wattage or energy does not change with a constant pump rpm. Energy cannot be created or destroyed, so it just changes to heat and vibration to be dissipated into the environment. There will be other advanced consideration when sizing the valve based on the ΔP across the valve, such as choking, cavitation and flashing. We will discuss these concerns in detail at the end of this section after we are familiar with control valve sizing for different applications. For more information on these and other subjects of process plant design, visit my web site to gain extensive insight into design applications with the online study course at http://learncontrolsystems.com.

The Valve Sizing Equations The Basic equation for liquid flow

q   N1 Fp Cv 

p Gf

Note: N1 = always equal to 1 for psia

The basic equation for gas flow

q   N1 N 7 Fp Cv PY 1 

x G f T1Z

Note: N1 = always equal to 1 for psia, N7 = 1360

The basic equation for steam flow

w   N1 N6 FpCvY  xP1 1

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Note: N1 = always equal to 1 for psia, N6 = 63.3

Where:

G f  Specific gravity, for gas

 molecular weight of gas  28.967  is the M.W. of air 

Cv  Valve sizing coefficient Fk  Ratio of specific heat factors

Fp  Piping geometric factor K1  Inlet velocity head loss coefficient K 2  Outlet velocity head loss coefficient K i  Inlet head loss coefficient; K1  K B1 K B1  Inlet Bernoulli coefficient K B 2  Outlet Bernoulli coefficient K  K1  K 2  K B1  K B 2 N1  1.00 (for psia; equation constant see Table A13. in appendix) N 6  63.3 (for lb / h; equation constant see Table A13. in appendix) N 7  1360 (for scfh; equation constant see Table A13. in appendix) N 9  7320 (for scfh; equation constant see Table A13. in appendix) p  Pressure in psid across the valve

P1  Inlet pressure  psi absolute  P2  Outlet pressure  psi absolute 

q  Volumetric Flow  in gpm for liquid or scfh for gas 

T1  Fluid operating temperature  psi absolute ;  reference temp in  F + 460

w  Volumetric flow (in pounds per hour) x  Ratio of delta pressure to inlet pressure absolute Z  Fluid compressibility

 f  Specific weight of the steam or vapor in pounds per cubic foot  operating cond . Note: for SI (metric) calculations K v  0.856(Cv ) Note: The Fisher Control Valve Handbook, the Fisher Control Valve Catalog or Table A11 and Table A12 of the guide can be used for CV, FL and XT references for problems in this guide and on the CSE exam. All variables are discussed in detail. We will keep the equations simple and to the point for sizing. We will size for the correct size valve to be installed. On the CSE examination, only obtaining the C V of the valve may be of interest, and not sizing for actual applications. The other factors—such as the piping geometry factor (Fp) for reducers in the piping, the expansion factor (Y) of gas and vapors, and the Bernoulli factors (Kb)—will probably not be used in the CSE exam. There may be questions of temperature limits and hardness of the materials that make up the valve for given applications. ISA offers video tape training (The Control Valves and Actuators Series) and Integrated Systems offers online training on control valve sizing and selection, http://learncontrolsystems.com.

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Sizing valves for liquid - worked example The basic equation for liquid flow through a control valve is:

p Gf

q   N1 Fp Cv 

Note: N1 = always equal to 1 for psia

Solving for Cv we get:

Cv 

q

N F  1

Note: N1 = always equal to 1 for psia

p Gf

p

  K  Cv  2  Fp  1   2   890  d  

1

2

Note: FP = piping geometric factor

The piping geometry factor covers reducing fittings attached to each side of the valve body. See Table A11 - Properties and Sizing Coefficients of Globe Valves and Table A12 - Properties and Sizing Coefficients of Rotary Valves in the appendix of this guide, for use of C V, XT and FL. Now the equation becomes:

q

Cv 

N1 Fp

p Gf

LIQUID WORKED EXAMPLE

Sample problem: We will now assume an 8-inch pipe connected to a Globe Valve, with the following service, Liquid Propane. Size the equal percentage valve for the following criteria.

q = 800 gpm

T1 = 70⁰F

P1 = 300 psig

P2 = 275 psig

Gf = 0.5

∆P = 25 psi

Find the approximate CV. The CV is needed to find FP (for now set to FP = 1).

q

Cv  Fp

p Gf



800 25 0.5

 113.13

Note: If piping were the same size as the valve, we’re done.

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From Table A11 - Properties and Sizing Coefficients of Globe Valves, we find a 3” Globe Valve (equal percentage) has a maximum CV of 136 at full open. But we want to throttle at 50%, so pick a 4” with a CV of 224. Now we will plug this CV into the piping geometry equation to get the installed valve CV.

K  K1 (the entry factor )  K 2 (the exit factor ) 2

2

K  K1 2

 d2   1.5 1  2   D 

 d2  Note: K1  K 2,  (0.5  1) 1  2  same size piping  D 

K  K1 2

 42   1.5 1  2   0.844  8 

2

  K  Cv  2  Fp  1   890  d 2   

1

 0.844  224  2  Fp  1     890  42   

Note: 4 = valve size, 8=pipe size

2

Note: Fp = piping geometry factor.

1

2

 1.1859

1

2

 0.918

Find the corrected CV for the installed valve.

q

Cv  Fp

Cv 

p Gf

800

 0.918

25 0.5



800  123.24 or 124 6.238

This shows a 3” valve is too small; it will require the 4” with the maximum CV = 224.

%

124  55.4% of maximum Cv and about 75% open 224

In Table A11 - Properties and Sizing Coefficients of Globe Valves, a Fisher type ED (equal percentage) valve is used. A 3”valve would be correct with a CV of 136, but it is too small. The valve would be (124/136) or 91% of maximum CV, and you might not get the required flow through the valve for throttling. Remember, valves start choking at about 75% throttle, so size your CV to fit at about 50% maximum CV. The industrial standard is to size your valves for 200% CV.

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Sizing valves for gas - worked example The basic equation for gas or vapor flow through a control valve is:

q   N1 N 7 Fp Cv PY 1 

Cv 

x G f T1Z

q (in scfh)

Note: N1 = always equal to 1 for psia, N7 = 1360

Note: for volumetric flow units

x 1360 Fp PY 1 G f T1Z

Where:

 x  Y 1    3Fk xTP 

Note: the expansion factor

Note: The expansion factor must be between 1.0 and 0.667. The velocity downstream will always be greater than upstream velocity.

Fk 

k 1.4

Note: ratio of specific heat factor

k = ratio of specific heats x

P P1

Note: pressure drop ratio of ΔP to inlet P1

xT  pressure drop ratio required to produce maximum flow through the valve when Fk =1.0. ( xT can be found in valve coefficients table) 2 xT  xT Ki  Cv   xTP  2 1+  Fp  N5  d 2  

-1

Note: pressure drop ratio factor with installed fittings attached

Where:

  K  Cv  2  Fp  1   2   890  d   K i  K1  K b1

Note: piping geometric factor

2

2

d K B1 or K B 2  1    D

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2

Note: inlet head loss coefficient

 d2  K1  0.5 1  2   D 

 d2  K 2  1 1  2  D  

1

4

Note: Bernoulli coefficients

GAS WORKED EXAMPLE

Sample problem: We will now assume a 6” inch pipe connected to a Globe Valve, with the following service, Natural Gas. Size the equal percentage valve for the following criteria.

q = 800,000 scfh

T1 = 60⁰F = 520⁰R

Gf = 0.60

P1 = 400 psig

P2 = 250 psig

Mw = 17.38

∆P = 150 psi k = 1.32

The molecular weight, Mw of gas/ Mw of air (17.38 /28.96) gives the specific gravity, Gf = 0.60. We will use specific gravity and N7 = 1360.

Cv 

q (in scfh) x 1360 Fp PY 1 G f T1Z

Note : for volumetric flow units

First find the approximate valve size and CV for formulas. Set Fp = 1, Y = 1, Z = 1.

x

P 150  1.32    0.362; Fk xT    0.68  0.641 P1  400  14.7   1.4 

Use the lesser value of the two equations above for “x” in the valve sizing formula.

Cv 

q (in scfh) x 1360P1 G f T1



800,000 0.362 1360(400  14.7)  0.60 60  460

 41.64 or 42

Note: If piping were the same size as the valve in the CSE exam, we’re done. When the pressure differential ratio x reaches a value of FK xT. The limiting value of x is defined as the critical differential pressure ratio. The value of x used in any of the sizing equations and in the relationship for Y, shall be held to this limit, even if the actual pressure differential ratio is greater. Thus, the numerical value of Y may range from 0.667, when x = FK xT, to a value of 1.0 for very low differential pressures. The xT comes from the valve coefficient tables in the appendix. (Calculate the valve for 200% CV for throttling applications). From Table A11, we want to throttle at about 50% of maximum Cv, so double the Cv of the initial equation. In the globe valve coefficients table, we see a 3” valve with the CV = 136. Calculate for piping geometric factors. Inlet = 6” and Outlet = 6” schedule 40 pipe.

K  K1  K 2  K B1  K B 2

156

2

  3  d2  K1  0.5 1  2   0.5 1  2   0.281  D   6 

Note: 3 = valve size, 6 = pipe size

2

  3  d2  K 2  11  2   11  2   0.5625  D   6  2

 d2   3 K B1   2      0.0625  D  6 2

4

 d2   3 K B 2   2      0.0625  D  6 4

Sum resistance coefficients and Bernoulli coefficients and get the piping geometry factor:

K  0.281  0.5625  0.0625  0.0625  0.8435  K  Cv 2  Fp  1   2  890  d  

1

2

1

 1

0.8435  136   890  32 

2

 0.9067

Find the pressure drop ratio for the installed fitting attached to the 3” valve.

K i  K1  K B1  0.281  0.0625  0.3435 From Table A11 and Table A13 in the appendix we find: N5 =1000 and xT = 0.68 2 xT  xT Ki  Cv   xTP  2 1+ Fp  N5  d 2  

xTP 

-1

 x K C 2 Fp2 1+ T i  2v N5  d   

0.68   0.68  0.3435   136 2 0.9067 1+ 2   1000  3  

 0.7853

2

Find the expansion factor Y, it must be between 0.667 and 1.0

Fk 

1.32  0.943 Note: ratio of specific heats factors 1.4

 x Y 1   3Fk xTP

157

  0.362   0.837  1    3  0.943 0.7853 

Cv 

q (in scfh) x 1360 Fp PY 1 G f T1

800,000



1360  0.9067  414.7  0.837 

0.362  0.60 520 

 54.872 or 55

We want to throttle at around 50% so; a 3 inch valve has a CV of 136. Using a 2-inch valve, the calculation would have required a CV of 55.89 and the 2-inch valve only has a CV of 50.7 at 100% open.

%

55  41% of maximum Cv and about 64% open 136

C g  40 Cv xT ; if needed to convert Cv to C g as in the FCVH

Sizing valves for vapor and steam - worked example The basic equation for vapor or steam flow through a control valve is:

w   N6 FpCvY  xP1 1

Cv 

w(lb / h) 63.3FpY xP1 1

Note: N6 = 63.3

Note: for mass flow units in pounds per hour

STEAM WORKED EXAMPLE

Sample problem: We will now assume 6-inch pipe inlet and 8-inch pipe outlet of schedule 40, is connected to a type ED Globe (equal percentage) Valve, with the following service: Process Steam. Size the valve for the following criteria. Note: 1/ (  1 ) can be found in Table A9 - Saturated Steam Tables in the appendix of this guide.

q = 125,000 lb/h

T1 = 470⁰F

Gf = 0.60

∆P = 250 psi

P1 = 500 psig

P2 = 250 psig

 1 = 1.089

k = 1.31

Answer: First find the approximate valve size and CV for the formulas. Set Fp = 1, Y = 1. Find  1 :

 1 =Specific weight is the reciprocal of specific volume

1 lb  3  ft / lb  ft 3

From Table A9 - Properties of Saturated Steam, we can find the specific volume of the steam at a

158

3

pressure of 514.7 psia equals 0.9182 ft /lb

  ft 3 ft 3  P desired - P lower value   ft 3 ft 3 upper value lower value low value      lb  P upper value - P lower value  lb lb   lb  ft 3  514.7  500  ft 3   0.9278  0.8915  0.8915  0.9182     lb  520  500  lb   1 =Specific weight is the reciprocal of specific volume

Fk 

 ft

1 3

/ lb





1 0.9182

 1.089

lb ft 3

1.31  0.936 Note: Ratio of specific heat factors 1.4

 x  P

P1  0.486   x  Fk xT   0.936  0.69   0.646 

Pressure ratio is smaller than critical limits, so we will use x = 0.486. Find the CV:

Cv 

w (in lb / h) 63.3FpY xP1 1



125,000 63.311

 0.486 514.7 1.089

 119.65 or 120

Note: If piping were the same size as the valve in the CSE exam, we’re done. When the pressure differential ratio x reaches a value of FkxT. The limiting value of x is defined as the critical differential pressure ratio. The value of x used in any of the sizing equations, and in the relationship for Y, shall be held to this limit, even if the actual pressure differential ratio is greater. Thus, the numerical value of Y may range from 0.667, when x = FkxT, to a value of 1.0 for very low differential pressures. The xT comes from Table A11 - Properties and Sizing Coefficients for Globe Valves. The Table shows a 3-inch valve with a CV of 136, but we want to throttle around 50% (200% of 120 = 240), so a 4-inch valve with the CV of 224 is too small. Doing the calculation with a 4-inch valve will prove we are already at 71% CV at normal flow and will probably be choking already. You should select a 6-inch pipe with the CV of 394. B: Calculate for piping geometric factors. Inlet = 6-inch and Outlet = 8-inch schedule 40 pipe. 2

2

  62  d2  K1  0.5 1  2   0.5 1  2   0.0  D   6  2

2

  62  d2  K 2  11  2   11  2   0.1914  D   8  2

 d2   6  K B1   2      1.0  D  6

159

4

2

 d2   6  K B 2   2      0.3164  D  8 4

Sum resistance coefficients and Bernoulli coefficients and get piping geometry factor:

K  K1  K 2  K B1  K B 2

K  0.0  0.1914  1.0  0.3164  0.875  K  Cv  2  Fp  1   2   890  d  

1

2

1

 1

0.875  394    890  62 

2

 0.9459

C: Find the pressure drop ratio for the installed fitting attached to the valve.

K i  K1  K B1  0.0  1.0  1.0 From the Table A13 - Numerical Constants for Valve Sizing Formulas and Table A11 - Sizing Coefficients for Globe Valves , in the appendix shows : N5 = 1000 and xT = 0.78

x xTP  T2 Fp

xTP 

 xT Ki  Cv 2  1+ N5  d 2   

-1

 x K C 2 Fp2 1+ T i  2v N5  d   

0.78   0.78 1.0   394  2  0.94592 1+    1000  62   

 0.9783

D: Find the expansion factor Y, it must be between 0.667 and 1.0

   x  0.486 Y 1    0.823   1    3Fk xTP   3  0.936  0.9783  Note: Replace xTP with xT if pipe size, inlet and outlet, are the same size as the valve

Cv 

w (in lb / h) 63.3FpY xP1  1



125,000 63.3 0.9459 0.823

 0.486 514.71.089

 153.69 or 154

This shows a 6” valve is the correct size.

%

154  39% of maximum C v and about 63% open 394

Note: This valve is a 6 inch valve with a CV = 394 and should be used for this application.

C g  40 Cv xT ; if needed to convert Cv to C g as in the FCVH

160

Sizing valves for two phase flow - worked example Two phase flow is a flow which is comprised of liquid and vapor or liquid and gas in part ratios of mass. The quality of the gas or vapor and liquid must be known to size the valve. Recall the quality of gas or vapor is Quality (vapor) = Vapor mass / Total mass and Quality (liquid) = Liquid mass / Total mass.

Some Types of Two Phase Flow

161

The basic equations for two phase flow through a control valve are:

w   N6 FpCvY  xP1 1 Note: N 6 = 63.3

w   N6 FpCvY  ( P1  P2 ) 1 Note: N 6 = 63.3 Note: Y 2 only applies to the gas portion and not the liquid portion of the mass flow

w(lb / h)

Fp Cv 

N6 P 1Y 2

1   1Y 2 ve

Note: specific volume is the reciprocal of density

ve  f g vg / Y 2  f f v f

Fp Cv 

w(lb / h) ve N6 P

Y 1

x 3Fk xt

x

Note: Y 2 is in the coefficient ve

P P1

Fk 

k 1.40

Note: v g is the specific volume of the gas and M is the molecular weight of air

vg 

RT M  P1  conversion factor in2 to ft 2 

ft * lbf   1545   deg R  ft 3 lb * mol * R   vg   lbm lbm  lbf   in 2    28.97  P1 2  144 2  lb * mol  in   ft  

162

Two Phase Flow Worked Example

Sample problem: The goal in this example is to find the required valve capacity (FpCv) for the conditions listed below:

Air flow rate: 600 lb/hr Water flow rate: 26,000 lb/hr Upstream pressure, P1: 150 psia

Pressure drop, ∆p: 50 psi Temperature: 90°F (550°R) Line size: 3 in. schedule 40

Answer: Step 1: Determine the relative mass fractions of gas and liquid, fg and ff. The total mass flow rate is w = 600 + 26,000 = 26,600 lb/hr. The fraction of gas:

fg 

600  0.0226 26,600

The fraction of fluid:

ff 

26,000  0.9774 26,600

Step 2: Make a preliminary selection of valve type and determine the critical pressure drop ratio factor (xT) for expansion factor (Y ) of the valve. Assume a single-seated globe valve with a contoured plug with flow under the plug (to open).

Cv 

gpm P



26,000lb 1gpm 1min 52 gpm 52 gpm   7.35 * * = 1 8.33lb 60sec P 50

Double the Cv for an approximation of the vapor through the valve. Approx. Cv = 14.7 Using the manufacture’s catalog tables, for valves ranging from 0.75” to 1-1/2” we obtain an average estimate of xT = 0.68. Find the expansion factor (Y):

Y 1

x 0.334 1  0.8454 3Fk xt 3 1 0.72 

Step 2: Calculate the pressure drop ratio, (x):

x

163

50  0.334 150

Because x < xT, and the gas flow is not choked. Find the ratio of specific heat factor (FK):

Fk 

1.40  1.0 1.40

Step 4: Determine the effective specific volume of the mixture at upstream conditions. The specific volume of the air can be calculated from the gas law equation:

ft * lbf   1545   550  R  ft 3 lb * mol * R   vg   1.358 lbm lbm  lbf   in 2    28.97 150 2  144 2  lb * mol  in   ft   From Table A7 - Properties of Water Specific Volume and Density at 90°F, The liquid specific volume is:

v f  0.01610

ft 3 lbm

The mixture effective specific volume ve :

ve 

f g vg Y

2

 f f vf 

(0.0226)(1.358) ft 3   0.9774  0.01610   0.0587 2 0.8454 lbm

Step 5: Calculate valve capacity from Equation:

Fp Cv 

w(lb / h) ve 26,600 0.0587  =14.39 N6 P 63.3 50

If the piping geometric factor (Fp) is equal to 1, then the Cv of the valve would be: 14.39 If the piping geometric factor (Fp) is equal to 0.98, then the Cv of the valve would be: (0.98)(14.39)=14.1 We want to throttle at 50%, so size the valve Cv for 200%. 14.1 * 2.00 = 28.2 Cv Choose a 1-1/2” valve with a Cv = 35.8 and xT = 0.68 (The xT matches our calculation, so no recalculation is necessary)

%

14.1  39.4% of maximum Cv and about 63% open 35.8

Note: This valve is a 1-1/2 inch valve with a CV = 35.8 and should be used for this application.

164

ΔP Valve Limitations - Very Important! On a simple back pressure or pressure reducing application, the drop across the valve may be calculated quite accurately. This may also be true on a liquid level control installation, where the liquid is passing from one vessel at a constant pressure to another vessel at a lower constant pressure. If the pressure difference is relatively small, some allowance may be necessary for line friction. On the other hand, in a large percentage of control applications, the pressure drop across the valve will be chosen arbitrarily as a percent of piping pressure drop. Any attempt to state a specific numerical rule for such a choice becomes too complex to be practical. The design drop across the valve is sometimes expressed as a percentage of the friction drop in the system, exclusive of the valve. A good working rule is that 15% to 40% of this friction drop (piping pressure drop) should be available as drop across the valve. With a pressure drop of 40% you should be very safe, but 15% to 30% is usually all you need. With 30% drop, in other words, one-third of the total system drop, including all heat exchangers, mixing nozzles, piping etc., is assumed to be absorbed by the control valve. This may sound excessive, but if the control valve were completely eliminated from such a system, the flow increase would only be about 23%. In pump discharge systems, the head characteristic of the pump becomes a major factor. For valves installed in extremely long or high-pressure drop lines, the percentage of drop across the valve may be somewhat lower, but at least 15% (up to 25% where possible) of the system drop should be taken. Remember one important fact, the pressure differential absorbed by the control valve in actual operation will be the difference between the total available head and that required to maintain the desired flow through the valve. It is determined by the system characteristics rather than by the theoretical assumptions of the engineer. In the interest of economy, the engineer tries to keep the control valve pressure drop as low as possible. However, a valve can only regulate flow by absorbing and giving up pressure drop to the system. As the proportion of the system pressure drop across the valve is reduced, its ability to further increase flow rapidly disappears. Valves work in the same way as orifice plates and head meters, using Bernoulli’s Principal. In some cases, it may be necessary to make an arbitrary choice of the pressure drop across the valve because there is not enough process data are available at the time of design. For instance, if the valve is in a pump discharge line, having a discharge pressure of 100 psi (7 bars), a drop of 10 to 25 psi (0.7 to 1.7 bar) may be assumed sufficient. This is true if the pump discharge line is not extremely long or complicated by large drops through heat exchangers or other equipment. The tendency should be to use the higher figure. On more complicated systems, consideration should be given to both maximum and minimum operating conditions. Masoneilan Valve or Fisher Valve product companies offer engineering assistance for analysis of such applications. Both companies also offer free valve sizing software for selection and engineering of valve applications.

Flowing Quantity (the turndown ratio of a valve) The selection of a control valve is based on the required flowing quantity of the process. The control valve must be selected to operate under several different conditions. The maximum quantity that a valve should be required to pass is 10 to 15 % above the specified maximum of normal flow (this is compensating for process upsets). The normal flow and maximum flow used in sizing calculations should be based on actual operating conditions, whenever possible, without any factors having been applied.

165

On many systems, a reduction in flow means an increase in pressure drop, and the Cv ratio may be much greater than would be suspected. If, for example the maximum operating conditions for a valve are: 200 gpm at 25 psi drop, and the minimum conditions are 25 gpm at 100 psi drop, the Cv ratio is 16 to 1, not 8 to 1 as it would first seem. The required change in valve Cv is the product of the ratio of maximum to minimum flow and the square root of the ratio of maximum to minimum pressure drop, example:

200 gpm  25 psi

Same Energy Head =

200 gpm 25 psi



25 gpm

Rearranging

100 psi

200 gpm 100 psi 25 gpm 25 psi



16 1

Flashing If the downstream pressure is equal to or less than the vapor pressure, then vapor bubbles created at the vena contracta do not collapse, resulting in a liquid-gas mixture downstream of the valve. This is commonly called flashing. When flashing of a liquid occurs, the inlet fluid is 100% liquid which experiences pressures at the inlet and downstream of the control valve which are at or below the vapor pressure. The result is a two phase mixture (vapor and liquid) at the valve outlet and in the downstream piping. Velocity of this two phase flow is usually very high and results in the possibility for erosion of the valve and piping components

Joule-Thomson Effect (J-T) – auto refrigeration in valves The throttling process is commonly exploited in thermal expansion processes, such as refrigerators, air conditioners, heat pumps, and liquefiers. To minimize or prevent the gas from liquefying and the valve from freezing, often a two-stage pressure reduction scheme is used to minimize the J-T Effect. By taking the pressure drop in two stages, the total cooling effect is split between the two pressure reducing valves, each of which may be able to absorb enough heat from the atmosphere to prevent the gas from liquefying. Also heat can be applied to the piping before the first and second stage reducing valves, raising the gas temperature enough to prevent the gas from liquefying. For details on the J-T Effect, read about it in the section later in this guide under Chemical Process Technology and Equipment.

Choked Flow Choked flow occurs in gases and vapors when the fluid velocity reaches sonic values at any point in the valve body, trim, or pipe. As the pressure in the valve or pipe is lowered, the specific volume increases to the point where sonic velocity is reached. In liquids, vapor is formed as the result of cavitation or flashing and increases the specific volume of the fluid at a faster rate than the increase in flow due to pressure differential. Lowering the downstream pressure beyond this point in either case will not increase the flow rate for a constant upstream pressure. The velocity at any point in the valve or downstream piping is limited to sonic (Mach = 1). As a result, the flow rate will be limited to an amount which yields a sonic velocity in the valve trim or the pipe under the specified pressure conditions. Under choked conditions, ΔPmax (the Allowable Sizing Pressure Drop), is the choked pressure drop.

See the section in this manual Chemical Process Technology and Equipment / Vapor Pressure, Boiling and Cavitation in Equipment on the subject of vapor pressure and cavitation. There is a simple, very insightful and excellent video that demonstrates this phenomenon.

166

Maximum ΔP and Maximum Flow (qmax) in Valves Applications You must be aware of the maximum delta pressure to be absorbed across the valve. If the ΔP is too large the valve will choke the flow and cavitation or flashing may occur. Determining qmax or ΔPmax

qmax (the Maximum Flow Rate) or ΔPmax (the Allowable Sizing Pressure Drop). Calculate either qmax or ΔPmax to determine if it is possible for choked flow to develop within the control valve that is to be sized. The values can be determined by using the following procedures. Determining qmax (Maximum Flow Rate)

qmax  N1 FL CV

P1 - FF PV Gf

Values for the coefficient FF (liquid critical pressure ratio) factor used in the formula can be obtained from figure below, or from the equation:

FF  0.96  0.28

PV PC

Use the FF curve to the right for liquids other than water. Determine the vapor pressure/critical pressure ratio by dividing the liquid vapor pressure at the valve inlet by the critical pressure of the liquid. Enter on the abscissa at the ratio just calculated and proceed vertically to intersect the curve. Move horizontally to the left and read the critical pressure ratio, FF. on the ordinate. Values of FL, the recovery factor for valves installed without fittings attached, can be found in the flow coefficient tables (Table A11 and Table A12). If the given valve is to be installed with fittings (such as a reducer) attached to it, FL in the equation must be replaced by the quotient FLP/Fp, where:

 K1  CV  2 1  FLP    2   2   N 2  d  FL  K1 = K1 + K B1 Where: K1 = Resistance coefficient of upstream fittings

KB1 = Inlet Bernoulli coefficient

(See the procedure for Determining Fp, the Piping Geometry Factor, for definitions of the other constants and coefficients used in the above equations.)

167

Determining ΔPmax (the Allowable Sizing Pressure Drop) The maximum value for differential pressure (ΔPmax) at which the flow rate is achieved due to cavitation, is obtained with the FL value from above and the equation ΔPmax (the allowable sizing pressure drop). We can now determine the following relationships: For valves installed without fittings:

For valves installed with fittings attached:

Recovery factor valves:

2

Pmax( L )  FL2  P1  FF PV 

F  Pmax( LP )   LP   P1  FF PV   FP 

FL2 

Pmax PVC

Where: P1 = upstream absolute static pressure P2 = downstream absolute static pressure Pv = absolute vapor pressure at inlet temperature Pvc = absolute vapor pressure at vena contracta FF = value of the liquid critical pressure ratio factor, can be calculated as previously shown above FLP = combined liquid pressure recovery factor and piping geometry factor with attached fittings FL = value of the recovery factor for valves Note: FL for valves installed without fittings attached, can be found in (Table A11 and Table A12) An explanation of how to calculate values of FLP, the recovery factor for valves installed with fittings attached, is presented in the procedure for determining qmax (the Maximum Flow Rate). Once the ΔP max value has been obtained from the appropriate equation, it should be compared with the actual service pressure differential (ΔP = P1 − P2). If ΔPmax is less than ΔP, this is an indication that choked flow conditions will exist under the service conditions specified. If choked flow conditions do exist (ΔPmax < P1 − P2), then the procedure for sizing valves for liquids must be modified by replacing the actual service delta pressure ΔP = (P1 − P2) in the valve sizing equation with the calculated ΔPmax value.

Important Note: Once it is known that choked flow conditions will develop within the specified valve design (ΔP max is calculated to be less than ΔP), a further distinction can be made to determine whether the choked flow is caused by cavitation or flashing. The choked flow conditions are caused by flashing if the outlet pressure of the given valve is less than the vapor pressure of the flowing liquid. The choked flow conditions are caused by cavitation if the outlet pressure of the valve is greater than the vapor pressure of the flowing liquid.

168

Cavitation in valves In liquids, when the pressure anywhere in the liquid drops below the vapor pressure of the fluid, vapor bubbles begin to form in the fluid stream. As the fluid decelerates there is a resultant increase in pressure. If this pressure is higher than the vapor pressure, the bubbles collapse or (implode) as the vapor returns to the liquid phase. Cavitation occurs in two steps and produces noise, vibration, and causes erosion damage to the valve and downstream piping. The onset of cavitation, known as incipient cavitation, is the point when the bubbles first begin to form and collapse. Advanced cavitation can affect capacity and valve performance, which begins at a ΔP(cavitation) determined from the factor Kc.

KC 

P P1  PV

The point at which full or choked cavitation occurs (severe damage, vibration, and noise) can be determined by the equation:

P(cavitation )  KC  P1  PV 

KC  FL2 Where: Kc = liquid cavitation factor or valve recovery coefficient. P1 = upstream pressure, psia PV = vapor pressure of the liquid, psia FL = liquid pressure recovery factor (as referred to by most control valve manufacturers) ΔP(cavitation) = maximum allowable pressure drop across the valve (psig) The valve recovery coefficient, Kc, depends on the design of the valve. It is always less than 1. As the values of FL and Kc of the different valve designs become smaller, the probability of cavitation increases. Cavitation damage always occurs downstream of the vena contracta when pressure recovery in the valve causes the temporary voids to collapse. Destruction is due to the implosions that generate the extremely high-pressure shock waves in the substantially non-compressible stream. When these waves strike the solid metal surface of the valve or downstream piping, the damage gives a cinder-like appearance. Cavitation is usually coupled with vibration and a sound resembling rock fragments or gravel flowing through the valve. For typical valves, such as globe and control ball valves, a valve recovery factor of Kc = 0.5 to 0.6 can be expected. If Kc is not known, a conservative estimate of Kc = 0.5 should be used. The cavitation formula can be rearranged as follows: ΔP allowed = 0.5 * (P1 – Pv) Flowserve uses the following formula to check for the severity of cavitation in a valve:



P1  PV P

• σ > 2.0 No cavitation is occurring. • 1.7 < σ < 2.0 No cavitation control required. Hardened trim provides protection. • 1.5 < σ < 1.7 Some cavitation control required. Mutual impingement trim may work. • 1.0 < σ < 1.5 Potential for severe cavitation. Use staged pressure drop trim.

• σ < 1.0 Flashing is occurring.

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Check for cavitation and choked flow in a control valves - worked examples

The thermodynamic effects of velocity and pressure through the valve port are shown above as a result of ΔP applied across the valve body to induce flow through the valve in a process piping system. Let’s work some problems dealing with choking, cavitation and flashing in process control valves. Sample problem: Check for cavitation and choked flow in this HVAC hydronic valve installation Example1: ΔP(actual) = 10 psid (69 kPa) P1 = 20 psig = 34.7 psia (239 kPa) Pv = 9.3 psia (64 kPa) for 190°F (88°C) water. ΔP allowed = 0.5 (34.7 – 9.3) = 12.7 psid (88 kPa) The operating pressure drop for this valve would probably be 4 to 10 psid (28 to 69 kPa). Cavitation would not be a problem in this application. Example 2: ΔP(actual) = 10 psid (69 kPa) P1 = 10 psig = 24.7 psia (170 kPa) Pv = 9.3 psia (64 kPa) for 190°F (88°C) water. ΔP allowed = 0.5 (24.7 – 9.3) = 7.7 psid (53 kPa) The ΔP pressure drop across the valve must not be greater than 7.7 psi (53 kPa) or cavitation will occur. The alternative is to increase the pump pressure by at least 2.3 psia (10 - 7.7) / 0.5 = 4.6 to use a ΔP of 10 psig or psid across the valve for operation without cavitation. 10 psig + 4.6 psig + 14.7 psia = 29.3 psia ΔP allowed = 0.5 (29.3 – 9.3) = 10 psid (69 kPa)

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Sample problem: Check for cavitation, choked flow, ΔPmax and qmax for this valve in a process plant piping installation.

Liquid .................................. Water Critical Pressure (PC) ..........3206.2 psia Temperature........................ 250° F Upstream Pressure (P1) ......314.7 psia Downstream Pressure (P2) ..104.7 psia Specific Gravity ...................0.94

Valve Action .......................... Flow-to-open Line Size ................................ 4-inch (Class600) Flow Rate Maximum............... 500 gpm Vapor Pressure (PV) .............. 30 psia Kinematic Viscosity (n) ...........0.014 centistokes Flow Characteristic .................Equal Percentage

Answer: Step 1) Calculate actual pressure drop across the valve ΔP(actual): ΔP(actual) = 314.7 psia - 104.7 psia = 210 psid Step 2) Find initial valve size using the ISA standard liquid equation:

q   N1 Fp Cv 

p Gf

->

Cv  q

Gf P

-> 33.45  500 gpm

0.94 210

We will size the valve for 50% operating capacity or 200% Cv: From the appendix Table A11: A Fisher 2” equal percentage valve has a maximum Cv of 59.7. This will be close enough to check the size.

Step 3) Check for choked flow: Find FL, it can be found in the appendix Table A11: Looking under the column for globe valve, 2 inch, equal percentage, we find FL equals 0.85. Next, estimate FF using Equation:

FF  0.96  0.28

PV PC

FF = 0.96 - 0.28(0.097) = 0.93 Insert FL and FF into the ΔPmax equation:

Pmax( L )  FL2  P1  FF PV 

Pmax( L )  0.852 [314.7 - (0.93)(30)] = 207.2 psi If this were a straight pipe run with no reducing fittings the flow would be choked. Since the calculated ΔPmax is less than ΔP(actual), the flow is choked; therefore, use the smaller ΔPmax to size the valve. This is the maximum ΔP that the valve can absorb and produce increasing flow. Any increase in ΔP greater than ΔPmax will not deliver any increase in flow rate. Note: But we are using reducer fittings so we need to use the equation F LP with ΔPmax(LP) :

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K LP1  K1  K B1 Note: Find FLP for a Class 600 (600 psi rating) Fisher ED 2” equal percentage valve. It has a port diameter of 2.3125” The Fisher ED valve is rated for service up to Class 900 (900 psi). 2

2

  2.31252  d2  K1  0.5 1  2   0.5 1    0.2245 4.0262   D   4

K B1 or K B 2

4

d  2.3125  1   = 1    0.8911 D  4.026 

K LP1  0.2245  0.8911  1.1156

 K  C  2 1  1.1156  59.7  2 1  FLP   LP1  V2   2      1.54  2  2   N 2  d  FL   890  2.3125  0.85  Sum resistance coefficients and Bernoulli coefficients and get piping geometry factor: We will use K2 to find ΣK for FP 2

2

 d 2   2.31252  K 2  1  2   1    0.449 4.0262   D   K  K1  K 2 2

2

  2.31252  d2  K  1.5 1  2   1.5 1    6.735 4.0262   D  

  K  Cv  2  Fp  1   2   890  d  

1

2

 0.6735  59.7  2  = 1     890  2.31252   

2

1

2

 0.9559

F   1.54  Pmax( LP )   LP   P1  FF PV     314.7   0.93 30   744.38 psi  0.9559   FP  2

Since the calculated ΔPmax is greater than ΔP(actual) the valve will work, it is not choking. Step 4) Check for cavitation using the cavitation equation:

P(cavitation)  KC  P1  PV 

KC  FL2 P(cavitation )  0.852 (314.7-30) = 187 psi

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Flowserve uses the following formula to check for the severity of cavitation in a valve:



P1  PV 314.7  30   1.36 P 210

What the sigma means to cavitation in the valve: • σ > 2.0 No cavitation is occurring. • 1.7 < σ < 2.0 No cavitation control required. Hardened trim provides protection. • 1.5 < σ < 1.7 Some cavitation control required. Mutual impingement trim may work. • 1.0 < σ < 1.5 Potential for severe cavitation. Use staged pressure drop trim. • σ < 1.0 Flashing is occurring Since ΔP(actual) and ΔPmax exceeds ΔP(cavitation), substantial cavitation will occur when the ΔP exceeds 187 psid across the valve and if the ΔP across the valve exceeds 285 psid there will be flashing of the fluid. The piping system needs to be redesigned for a lower (smaller) ΔP (actual) or if you need 187 psid across the valve, special attention should be paid to the material and trim selection.

Step 5) Check for check for maximum flow rate through the valve qmax: Estimate FF using Equation:

PV PC

FF  0.96  0.28

FF  0.96 - 0.28(0.097)  0.93

qmax  N1 FL CV

314.7 -  0.93 30  P1 - FF PV  1 0.85  59.7   886.38 gpm 0.94 Gf

Step 6) Check for check for maximum flow rate through piping systems:

  K  Cv  2  Fp  1   2   890  d  

q   N1 Fp Cv 

1

2

 0.6735  59.7  2  = 1     890  2.31252   

1

2

 0.9559

p 210  1 0.9559  59.7   852.96 gpm Gf 0.94

Step 7) Calculate exit velocity through valve: The following Equation is used to calculate entrance or exit velocities for liquids:

V

0.321 q actual  AV



 0.321 500 2.31252

 30 ft sec

Where: V = velocity, ft/sec q (actual) = liquid flow rate, gpm 2 Av = applicable flow area, in of body port

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The speed of sound is 1125.33 ft/sec The exit velocity of the fluid is: 30/1125.33 = Mach 0.023 The inlet velocity is:

velocity( ft / sec) 

gpm *0.4085 500*0.4085   12.6 ft / sec ID2 (inches) 4.262

Since q(actual) is less than q(max) we will not have any problems except the cavitation. You might consider a 3” valve to reduce the effect of cavitation by operating at a lower ΔP(actual) and reduced velocity through the valve body.

Fluid Velocities through Control Valves

The recommended (maximum inlet flow velocities) applied to control valves are shown below Globe Valves Size mm inch 15 - 25 1/2 - 1 40 - 50 1 1/2 - 2 65 - 100 2 1/2 - 4 150 - 200 6-8 250 – 400 10 – 16

m/s 9 7.5 6 6 4.5

Angle Valves Size mm inch 15 - 25 1/2 - 1 40 - 50 1 1/2 - 2 65 - 100 2 1/2 - 4 150 - 200 6-8 250 – 400 10 – 16

Liquid m/s 13.5 12 10.5 9 7.5

Liquid ft/s 30 25 20 20 15 ft/s 45 40 35 30 25

m/s 120 90 75 70 55

Steam or Gas ft/s 400 300 250 225 175

Steam or Gas m/s 135 105 90 85 70

ft/s 450 350 300 275 225

The recommended (maximum outlet flow velocities) recommended by Fisher Valve are below Liquids Gases Mixed Gases and Liquids

50 feet per second Approaching Mach 1.0 500 feet per second

(limit to Mach 0.3 or less to reduce noise)

Note: Not only is the table of maximum inlet flow velocities into a control valve important, the characteristics and size of the control valve port opening and trim (valve interior mechanical makeup) is also very important for the smooth function of the entire control loop. The exit velocity of the fluid through the valve orifice (port opening) should be less than Mach 0.3 to reduce noise in the environment. Velocities between Mach 0.3 and Mach 0.7 are acceptable for short periods of time. With velocities above Mach 0.7 there will be no difference in the sound between a standard valve and one with a sound reducing valve design. Flow will start to choke at Mach 0.7 and should be fully choked at Mach 0.8 to Mach 1.0.

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Viscosity Correction for Sizing Valves There are a few methods available for calculating the flow through a control valve under non-turbulent conditions. The two receiving the stamp of official international recognition are those described in the IEC standard 60534-1-2 and the ISA/ANSI standard 75.01 (refs 1 and 2). Similar to the reducer correction factor Fp, we have to increase the C V from that calculated with the standard sizing equations in order to make up for the additional friction caused by the stickiness of the of a laminar fluid passing through the valve. This is expressed by the "valve Reynolds number factor," F r. The corrected valve CV you need is the CV originally calculated divided by Fr. Using the CV determined by the basic liquid sizing equation and the flow and viscosity conditions, a fluid Reynolds number can be found by using the nomograph in the Fisher Control Valve Handbook. The graph of Reynolds number vs. viscosity correction factor (Fv) is used to determine the correction factor needed. (If the Reynolds number is greater than 3,500, the correction will be 10% or less.) The actual required CV (Cvr) is found by the equation: Cvr = FvCv. From the valve manufacturer's published liquid capacity information, select a valve having a C v equal to or higher than the required coefficient (Cvr) found by the equation above. The valve size correction factor using the Reynolds number is only needed if:  

The fluid has a viscosity exceeding 40 centistokes (or = 40 centipoises for liquids) A valve is needed with a Cv of less than 0.1

See the attached files on control valve sizing for more detailed information and procedures for sizing valves for different processes.

First blowout and unpredicted plant shutdown at Total refinery in Spergau located in Europe. Cavitation damage occurred in a rotary plug valve as a result of “quick and dirty” sizing.

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Modular wiring of skid control valves using wire trays. Visit the Turck and Belden cable web sites for more information.

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Pressure Relief Valves and Rupture Disks Pressure Relief Valves (PRV) and Pressure Safety Valves (PSV)

Gases and steams can be compressed, when gas reaches the disk in a valve it compresses and builds up pressure before escaping through the valve (F=P*A). This compression can cause system pressure to build up rapidly. A liquid type relief valve doesn’t open fast enough to relief gas or steam pressure. A gas system requires a valve that can open wide open under excess pressure or a ‘Pressure Safety Valve’. 'Pressure Safety Valve' and 'Pressure Relief Valve' are commonly used terms to identify pressure relief devices on a vessel. Frequently these terms are used interchangeably and it may entirely depend on a particular project or company standards to identify all the pressure relief devices either as 'safety valves' or as 'relief valves' or sometimes even as 'safety relief valves'. Although used freely and interchangeably, these terms differ in the following aspect: Pressure Relief Valve - is the term used to describe a relief device on a liquid filled vessel. For such a valve the opening is proportional to the increase in the vessel pressure. Therefore, the opening of the valve is not sudden but gradual, if the pressure is increased gradually. Pressure Safety Valve - is the term used to describe a relief device on a compressible fluid or gas filled vessel. For this type of valve, the opening is sudden. When the set pressure of the valve is reached, the valve opens almost fully. Safety valve performance summary

Important Note: (Do Not Throttle Pressure Relief Valves) A pressure relief valve should not be used to control the pressure out of a pump. The pressure relief valve will chatter and the hammering action due to the pulsations will destroy the valve no time. A proportional control valve needs to be used for this application. Contact your manufacturer for more information about this application.

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EPA regulations Many environmental protection agencies worldwide have been tightening regulations on hazardous material emissions. In the U.S., for example, the EPA has been issuing new and tighter regulations for several types of industries, ranging from food and beverage to nuclear power plants. There are regulations for refineries, with specific sections for each type of plant unit, such as fluid catalytic cracking units, catalytic reforming units, utilities, storage, and water treatment. The requirements for refineries and other types of industries are similar, with the main difference being the tolerated amounts for each type of pollutant released. The more stringent rules established by the new EPA regulations, issued in September 2015 and other environmental agencies can be generalized with three simple requirements: 1. Provide indication and location where a PRD (pressure relief device) event occurs through electronic monitoring. 2. Measure the time and duration of the PRD event for recording and reporting of emissions releases. A. Protected vessel B. Rupture disc C. Relief valve D. Bypass valve 3. Notify the operator of the event so corrective action can occur. Also, the EPA expects “flare operation at all times during the process of gas being sent to the flare,” so quick identification of a PRD (pressure relief device) release is not optional. In general, newer and more stringent rules apply not only to normal operation, but now also to startup/shutdown periods, where there have historically been more leniencies. These startup/shutdown periods are often when process upsets are most likely to occur, so compliance with these new regulations can be very demanding. Plants must comply with environmental regulations by law. Failing to do so can cause serious damage to the environment and personnel. It can also cause serious damage to plant equipment and explosions. In addition, lack of compliance can result in expensive fines, production disruptions, and bad publicity. But there is another very compelling reason to monitor and curb fugitive emissions: leakages caused by PRD malfunctions can waste large amounts of valuable product, along with the energy required to produce these products. Regulation details Every national and international government has its own rules to control and monitor emissions of pollutants. In the U.S., the Clean Air Act (CAA) is the key federal law regulating air emissions from stationary and mobile sources. Among other things, this law authorizes the EPA to establish national ambient air quality standards to protect public health and public welfare by regulating emissions of hazardous air pollutants (HAPs). CAA section 111(b) requires the EPA to set and periodically review emission standards for new sources of Criteria Air Pollutants (CAP), Volatile Organic Compounds (VOC) and other pollutants. CAA section 112 requires the EPA to set emission standards for toxic air pollutants from stationary sources reflecting the new Maximum Achievable Control Technology (MACT II) based on the best performing facilities in an industry. The EPA created or tightened regulations for several types of industries, going so far as to issue detailed requirements for specific units in a plant. For refineries, for example, the EPA issued a revised Code of Federal Regulations 40 (CFR) Parts 60 and 63: Petroleum Refinery Sector Risk and Technology Review and New Source Performance Standards. These regulations establish tighter emission control requirements for a refinery. The document addresses, among other things: Petroleum Refinery Sector Risk and Technology Review and New Source Performance Standards, EPA, Code of Federal Regulations 40 (CFR), Parts 60 and 63. More stringent operating requirements for flare control to ensure good combustion. This is achieved, but not restricted, by:   

Measuring and monitoring the flow of waste gas going to the flare Measuring and monitoring the content of the waste gas going to the flare Measuring and monitoring any air or steam added into the flare

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2. Emission control requirements for storage tanks, flares and delayed coking units at petroleum refineries 3. Pollutant monitoring around the plant fence line as a development in practices for managing emissions of toxic pollutants from fugitive sources 4. Elimination of exemptions during periods of startup, shutdown and malfunction Most importantly, CFR 40 parts 60 and 63 establish that bypasses and discharges through PRDs are a violation of these laws. The law now requires plants to monitor discharges of individual PRDs. PRD bypass Safety relief devices require shutoff valves and a bypass valve as shown in the figure below. These valves are used for device maintenance and special process conditions. If a rupture disc diaphragm has to be replaced, for example, the device has to be isolated using these valves. In some cases (such as during startup, shutdowns, tests or load changes) it may be necessary to bypass the PRD. It is not uncommon for plant personnel to forget and leave these valves in the open position or not close them properly, causing process fluid losses and emissions that can go undetected for a very long period of time. Monitoring bypass valve position enables quick response to human error or defective equipment. Also releases can be monitored with a pressure transmitter. It can detect pressure changes and an acoustic monitor can indicate flow of fugitive emissions from the PRD on the tank or process line. Many times, when the process pressure returns to normal operating conditions, the PRV does not close completely. There are several reasons for this:  Pressure increase on the discharge side  Valve seat damaged after repeated actuations  Deposition or formation of solids between the disc and the seat  Altered process fluid  Corrosion  Mechanical malfunction Rupture discs, see figure to the right, are safety devices for one-time use. They consist of a membrane that bursts when the differential pressure between its two sides exceeds a set value. These devices are used alone or in combination with a PRV, providing a physical isolation layer between the process and the relief valve, especially on processes containing highly corrosive fluid. Some models are equipped with a sensor that indicates when the diaphragm is broken. Rupture discs are very simple devices, with no moving parts. Unlike pressure relief or safety valves, the rupture disc will remain open until the ruptured diaphragm is replaced. Diaphragms are less susceptible to causing fugitive emissions, but there is always the possibility of pitting corrosion which creates pinholes, leading to undetectable leakage.

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Pilot operated safety valve This type of safety valve uses the flowing medium itself, through a pilot valve, to apply the closing force on the safety valve disc. The pilot valve is itself a small safety valve. There are two basic types of pilot operated safety valve, namely, the diaphragm and piston type. The diaphragm type is typically only available for low pressure applications and it produces a proportional type action, characteristic of relief valves used in liquid systems. They are therefore of little use in steam systems. The piston type valve consists of a main valve, which uses a piston shaped closing device (or obturator), and an external pilot valve. The figure below shows a diagram of a typical piston type, pilot operated safety valve.

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Bellow or balanced bellow and diaphragm Some safety valves, most commonly those used for water applications, incorporate a flexible diaphragm or bellows to isolate the safety valve spring and upper chamber from dirty process fluid and contaminates. Balanced bellows relief valves are typically used where the relief valves are piped to a closed flare system and the back-pressure exceeds 10% of the set pressure which can’t be handled by conventional relief valves. The balanced bellows relief valves also used in flow lines, multiphase lines, or for paraffinic or asphaltic crude which may plug the pilot-operated valves. When superimposed back pressure is variable, a balanced bellows or balanced piston design is recommended. The bellows or piston is designed with an effective pressure area equal to the seat area of the disc. The Bonnet is vented to ensure that the pressure area of the bellows or piston will always be exposed to atmospheric pressure and to provide a telltale sign should the bellows or piston begin to leak. Variations in back pressure, therefore, will have no effect on set pressure. Back pressure may, however, affect flow.

Standard Relief Valve Guided Stem

Balanced Bellow Relief Valve

Weight loaded PRV operation The weight loaded PRV (Pressure Relief Valve) is one of the simplest and least complex type of any PRV. It is a direct acting valve. Because the dead weight pushing down on the valve’s internal moving parts, the valve is held closed until the tank pressure equals the dead weight. These valves are often called weighted pallet valves because the set pressure can be varied by adding or removing weights on the top of a trim part called a pallet.

These weighted pallet valves are also known as conservation vents or breather vents. This is because one of the primary uses of these devices is to protect low pressure storage tanks that have fixed roofs. These storage tanks are often designed per API Standard 620 or 650 and have very low design pressures in the inches of water column [mbar] range. Since the design pressures are very low, the simple pumping in of product or increased ambient temperatures can raise vapor pressures in the tank and cause these weight loaded valves to “breathe” and discharge the pressure.

181

The sizing and selection of these weight loaded valves is often done per API 2000 or ISO 28300.

Side by Side – Weighted Pressure/ Vacuum Vent

Large Weight Loaded Emergency Vent

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Blowdown is defined as the difference between opening and closing pressure. This pressure difference is expressed as pressure or as a percent of the set pressure. Typical blowdowns are 0% to 7%. A vent valve with 0% blowdown is known as a throttling vent valve. A throttling vent valve is similar to a direct-acting vent valve because it begins to open and close at almost the same pressure; however, unlike in a directacting vent valve, full lift of the seat in a throttling vent valve is obtained at or below 10% overpressure (see figure C-5 chart below). Where tank operating pressures are very close to the maximum allowable tank pressure, this lift characteristic permits overpressure protection to be accomplished with smaller or fewer venting devices. One weighted PRV device may pass the same flow rate as two or more PRD in parallel, such as a standard PRV and a rupture disk. Figure C-5

Venting Atmospheric and Low-Pressure Storage Tanks Sizing and installing pressure relief valves on low pressure tanks is required by law per federal regulation 49 CFR 195.264 – API 2000 Venting Atmospheric and Low-Pressure Storage Tanks. (Click red link to view code) § 195.264 Impoundment, protection against entry, normal/emergency venting or pressure/vacuum relief for aboveground breakout tanks. (a) A means must be provided for containing hazardous liquids in the event of spillage or failure of an above ground breakout tank. (b) After October 2, 2000, compliance with paragraph (a) of this section requires the following for the above ground breakout tanks specified: (1) For tanks built to API Specification 12F, API Standard 620, and others (such as API Standard 650 or its predecessor Standard 12C), the installation of impoundment must be in accordance with the following sections of NFPA 30: (i) Impoundment around a breakout tank must be installed in accordance with section 4.3.2.3.2; and (ii) Impoundment by drainage to a remote impounding area must be installed in accordance with section 4.3.2.3.1.

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(2) For tanks built to API 2510, the installation of impoundment must be in accordance with section 5 or 11 of API 2510 (incorporated by reference, see§ 195.3). (c) Aboveground breakout tank areas must be adequately protected against unauthorized entry. (d) Normal/emergency relief venting must be provided for each atmospheric pressure breakout tank. Pressure/vacuum-relieving devices must be provided for each low-pressure and high-pressure breakout tank. (e) For normal/emergency relief venting and pressure/vacuum-relieving devices installed on aboveground breakout tanks after October 2, 2000, compliance with paragraph (d) of this section requires the following for the tanks specified: (1) Normal/emergency relief venting installed on atmospheric pressure tanks built to API Specification 12F (incorporated by reference, see§ 195.3) must be in accordance with Section 4, and Appendices B and C, of API Specification 12F (incorporated by reference, see§ 195.3). (2) Normal/emergency relief venting installed on atmospheric pressure tanks (such as those built to API Standard 650 or its predecessor Standard 12C) must be in accordance with API Standard 2000 (incorporated by reference, see§ 195.3). (3) Pressure-relieving and emergency vacuum-relieving devices installed on low pressure tanks built to API Standard 620 (incorporated by reference, see§ 195.3) must be in accordance with section 9 of API Standard 620 (incorporated by reference, see§ 195.3) and its references to the normal and emergency venting requirements in API Standard 2000 (incorporated by reference, see§ 195.3).

(4) Pressure and vacuum-relieving devices installed on high pressure tanks built to API Standard 2510 (incorporated by reference, see§ 195.3) must be in accordance with sections 7 or 11 of API Standard 2510 (incorporated by reference, see§ 195.3). API STANDARD 2000 Table C-1-0perating Characteristics of Venting Devices Characteristic

Type of Venting Device Direct Acting

Pilot Operated

Seat Tightness

Leakage rate increases with increasing pressure. Leakage may begin at 75% of set.

Leakage rate decreases with increasing pressure. Typically, no leakage above 30% of set. A small amount of leakage at pilot may begin at 90% of set.

Capacity/Overpressure (Refer to Figure C-5)

Rated capacity normally obtained at 200% of set, for pressure or vacuum.

Rated capacity obtained at 110% of set for pressure or vacuum.

Set Pressure Range (Typical)

Pressure-Weight Loaded 1/2 oz/in2 to 16 oz/in2 (0.865" we to 27.7" WC) (2 mbarg to 69 mbarg)

Pressure2" WC to 15.0 psig (5 mbarg to 1.034 barg)

Pressure-Spring Loaded 1.0 psig to 15.0 psig (69 mbarg to 1.034 barg)

Vacuum-2" WC to -14.7 psig (-5 mbarg to -1.013 barg)

Vacuum-Weight Loaded -1/2 oz/in to -10 oz/in (-0.865" to -17.3" WC) (-2 mbarg to -43 mbarg) Vacuum-Spring Loaded -10 oz/in2 to -7 psig (-43 mbarg to 0.48 barg) Typical Blowdown

0%

0% to 7%

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The Weighted Relief Valve is typically available either 0.5 PSI incremental weights or 1.0 PSI increment weights. To adjust add or remove weight plates. Below is a typical Republic blower pressure relief valve.

Manway Covers (PRVs) by Pentair shown below provide quick, easy access for tank inspection and maintenance. When the tank is exposed to abnormal internal pressure beyond the capability of the breather vent, the manway helps protect the tank against costly rupture. The most common cause of excessive internal pressure is fire exposure. Emergency venting capacity requirements depend on the wetted surface area of the tank. The venting requirements can be calculated using API Standard 2000.

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API Standards for pressure relieving systems Standard

Title

Description

API 520 Part I

Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries—Part I, Sizing and Selection

Guide for sizing and selection of pressure relief devices used in petroleum related industries for equipment with maximum allowable working pressure of 15 psig greater. The document is intended for protection of unfired pressure vessels and equipment against overpressure from operation or fire. Pressure relief valves or rupture disks may be used independently or in combination with each other to provide the required protection against excessive pressure accumulation

API 520 Part II

Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries—Part II, Installation

Guide for installation of pressure relief devices used in petroleum related industries for equipment with maximum allowable working pressure of 15 psig greater.

API 521

Guide for Pressure-relieving and Depressuring Systems Petroleum petrochemical and natural gas industries, Pressure relieving and depressuring systems

This API standard specifies requirements and gives guidelines for determining overpressure causes, relieving rates for pressure relieving and vapor depressurizing systems in petroleum related industries. The standard also discusses selection and design of disposal systems, including such component parts as piping, vessels, flares, and vent stacks.

API 526

Flanged Steel Pressure-relief Valves

The standard covers specifications for flanged steel pressure relief valves (PRVs) by presenting basic requirements, such as orifice designation and area, valve size, pressure rating, and materials, for direct spring-loaded pressure relief valves and pilot-operated pressure relief valves

API 527

Seat Tightness of Pressure Relief Valves

Describes methods of determining the seat tightness of metal and soft-seated pressure relief valves (PRVs), including those of conventional, bellows, and pilotoperated designs.

API 576

Inspection of Pressure-relieving Devices

Describes the inspection and repair practices for automatic pressure relieving devices commonly used in the oil and petrochemical industries. This API standard covers pressure relief valves, pilot-operated pressure relief valves, rupture disks, and weight-loaded pressurevacuum vents, with regards to inspection and repair.

API- 000

Venting Atmospheric and Lowpressure Storage Tanks Petroleum, petrochemical and natural gas industries—Venting of atmospheric and low-pressure storage tanks

Guide for normal and emergency vapor venting requirements for above ground petroleum and petroleum product storage tanks, above ground and underground refrigerated storage tanks. The tanks discussed in the document are designed for low pressures ranging from full vacuum through 15 psig. This API standard discusses causes of overpressure and vacuum, venting requirements, means of venting, and breathing selection, and installation of venting devices and testing and marking of relief devices etc. for storage tanks.

186

CFR Standards for pressure relief required by federal law Standard

Title

Description

API 2003

Protection against ignitions arising out of static, lightning, and stray currents

The prevention of ignition of hydrocarbons by the release of energy charge generated by static electricity and stray currents, which can cause extreme pressures on tanks.

API 2350

Overfill protection for storage tanks in petroleum facilities

This standard is referenced by API 2000 and NFPA 30 applies to storage tanks associated with marketing, refining, pipeline, and terminals operations.

API 2510

Design and construction of LPG installations

This standard covers the design, construction, and location of liquefied petroleum gas (LPG) installations at marine and pipeline terminals, natural gas processing plants, refineries, petrochemical plants, or tank farms. This standard covers storage vessels, loading and unloading systems, piping, or and related equipment.

NFPA 30

Flammable and combustible liquids code

Enforceable under OSHA and many state and local regulations, NFPA 30 reduces the hazards associated with the storage, handling, and use of flammable and combustible liquids. Topics covered are explosion prevention and risk control, storage of liquids in containers, storage of liquids in tanks, piping systems, processing facilities, bulk loading-unloading, wharves.

ASME VIII

Boiler and Pressure Vessel Code Section VIII – Unfired pressure vessels

Division 1 - Provides requirements applicable to the design, fabrication, inspection, testing, and certification of pressure vessels operating at either internal or external pressures exceeding 15 psig. Division 2 - Alternative rules, provides requirements to the design, fabrication, inspection, testing, and certification of pressure vessels operating at either internal or external pressures exceeding 15 psig. Division 3 - Alternative rules for Construction of High Pressure Vessels, provides requirements applicable to the design, fabrication, inspection, testing, and certification of pressure vessels operating at either internal or external pressures above 10,000 psi.

API Standard 2000 – Venting atmospheric and low-pressure storage tanks (API 2000 Click red link to view code)

4.3 DETERMINATION OF VENTING REQUIREMENTS 4.3.1 General Venting requirements are given for the following conditions: a. Inbreathing resulting from maximum outflow of liquid from the tank. b. Inbreathing resulting from contraction or condensation of vapors caused by maximum decrease in vapor space temperature (thermal breathing). c. Outbreathing resulting from maximum inflow of liquid into the tank and maximum vaporization caused by such inflow. 187

d. Outbreathing resulting from expansion and vaporization that result from maximum increase in vapor space temperature (thermal breathing). e. Outbreathing resulting from fire exposure. Although design guidelines are not presented in this standard for other circumstances discussed in Section 4.2.5, they should be considered. *** See Chapter 4 of the API 2000 for venting and breathing flow rate requirements API Standard 2003 – Protection against ignitions from static, lightning, and stray currents (API 2003 Click red link to view code)

This standard is referenced by API 2000 and NFPA 30. The prevention of ignition of hydrocarbons by the release of energy charge generated by static electricity and stray currents, which can cause extreme pressures on tanks. (Also see NFPA 77 Static Electricity and NFPA 780 Lightning Protection). The principles discussed in this recommended practice are applicable to other operations where ignitable liquids and gases are handled.

API Standard 2350 – Overfill protection for storage tanks in petroleum facilities (API 2350 Click red link to view code)

This standard is referenced by API 2000 and NFPA 30. Applies to storage tanks associated with marketing, refining, pipeline, and terminals operations. This standard addresses overfill protection for petroleum storage tanks. It recognizes that prevention provides the most basic level of protection, thus while using both terms “protection” and “prevention,” the document emphasizes prevention. (CSE Note: Overfilling will over-pressure the vessel, hence this is a form of over-pressure control) The standard's scope covers overfill (and damage) as well as requirements for alarming and shutdown systems. The goal is to receive product into the intended storage tank without overfill or loss of containment. This standard does not apply to: underground storage tanks; aboveground tanks of 1320 U.S. gallons (5000 liters) or less; aboveground tanks which comply with PEI 600; pressure vessels; tanks containing non-petroleum liquids; tanks storing LPG and LNG; tanks at service stations; tanks filled exclusively from wheeled vehicles (i.e., tank trucks or railroad tank cars); and tanks covered by OSHA 29 CFR 1910.119 and EPA 40 CFR 68, or similar regulations.

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API 2350 categorizes storage tanks by the extent to which personnel are in attendance during receiving operations. The overfill prevention methodology is based upon the tank category.

API Standard 2510 – Design and construction of LPG installations (API 2510 Click red link to view code)

API Standard 2510 provides minimum requirements for the design and construction of installations for the storage and handling of LPG at marine and pipeline terminals, natural gas processing plants, refineries, petrochemical plants, and tank farms. This standard covers storage vessels, loading and unloading systems, piping and related equipment.

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NFPA 30 – Flammable and combustible liquids code

(NFPA 30 Click red link to view code) is required also by federal regulation 49 CFR 192.735 as of May 17, 2004 and is required by 49 CFR 195.264 (API 2000 Standard) for the sizing of pressure relief valves. It provides the minimum NFPA 30

requirements for the design and construction of installations for the storage and handling at marine and pipeline terminals, natural gas processing plants, refineries, petrochemical plants, and tank farms. This standard covers storage vessels, loading and unloading systems, piping and related equipment. The purpose of this code shall be to provide reasonable requirements for the safe storage and handling of flammable and combustible liquids. Chapter 4 and Chapter 5 shall apply to bulk storage of liquids in tanks and similar vessels. Chapter 6 shall apply to storage of liquids in containers and portable tanks in storage areas and in warehouses. Chapter 7 shall apply to handling of liquids in manufacturing and related operations and processes. Chapter 8 shall apply to electrical systems. Important excerpts from NFPA 30 code: I have added important references to these code excerpts as ‘CSE Note:’ in italics and parenthesis.

Chapter 4: Tanks Storage 4.3.4.3.4* Storage tanks shall be separated from other occupancies within the building by construction having at least a 2-hour fire resistance rating. As a minimum, each opening shall be protected by either a listed, self-closing fire door or a listed fire damper having a minimum I-hour fire protection rating. The fire door or fire damper shall be installed in accordance with NFPA 80, Standard for Fire Doors and Fire Windows; NFPA 90A, Standard for the Installation of Air-Conditioning and Ventilating Systems; or NFPA 91, Standard for Exhaust Systems for Air Conveying of Vapors, Gases, Mists, and Noncombustible Particulate Solids; whichever is applicable. (CSE Note: Fire detection system required, such as IR and UV sensors and interlocking to door closers, damper and or building fire detection system) Table 4.3.4.2.1 Location of Storage Tank Buildings with Respect to Property Lines, Public Ways, and the Nearest Important Building on the same property. (CSE Note: Minimum distances must be maintained from nearest important building to the pressure relief valve discharge.) 4.3.4.4.5 For storage tank buildings with the interior grade more than 300 mm (1 ft) below the average exterior grade, continuous mechanical ventilation in accordance with 4.3.4.4.2(3) shall be provided or a vapor detection system shall be provided and set to give a warning alarm at 25% of the lower flammable limit and to start the mechanical ventilation system. The alarm shall sound at a constantly attended location. (CSE Note: LEL, lower explosive limit, sensor and detection system required.)

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Chapter 5: Piping Systems 5.5.6 Valves. Piping systems shall contain a sufficient number of valves to operate the system properly and to protect the equipment. Piping systems in connection with pumps shall contain a sufficient number of valves to properly control the flow of liquid both in normal operation and in the event of physical damage. Each connection to a piping system by which equipment, such as tank cars, tank vehicles, or marine vessels, discharges liquids into storage tanks shall be provided with a check valve for automatic protection against backflow if the piping arrangement is such that back-flow from the system is possible. (See also 4.3.2.5.1.) (CSE Note: Be sure there are enough valves to handle abnormal conditions. Excessive pressure can build up in the piping system.) 5.5.7 Common Loading and Unloading Piping. If loading and unloading is done through a common pipe system, a check valve shall not be required. However, an isolation valve shall be provided. This valve shall be located so that it is readily accessible or shall be remotely operable. (CSE Note: Possible remote control of required isolation valve). 5.7.2.6 Where tank vent piping is manifold, pipe sizes shall be such as to discharge, within the pressure limitations of the system, the vapors they can be required to handle when manifold tanks are filled simultaneously. Float-type check valves installed in tank openings connected to manifold vent piping to prevent product contamination shall be permitted to be used provided that the tank pressure will not exceed that permitted by 4.3.3.2.3 when the valves close (CSE Note: In buried tanks the bottom tank pressure cannot exceed 10 psig maximum.)

Chapter 6: Container and Portable Storage Tanks 6.2.2 Each portable tank or intermediate bulk container shall be provided with one or more devices installed in the top with sufficient emergency venting capacity to limit internal pressure under fire exposure conditions to a gauge pressure of 70 kPa (10 psig) or 30% of the bursting pressure of the portable tank, whichever is greater. The total venting capacity shall be not less than that specified in 4.2.5.2.3 or 4.2.5.2.5. At least one pressure-actuated vent having a minimum capacity of 170 m3 (6000 ft3) of free air per hour at 1 bar (14.7 psia) and 15.6°C (60°F) shall be used. It shall be set to open at not less than a gauge pressure of 35 kPa (5 psig). If fusible vents are used, they shall be actuated by elements that operate at a temperature not exceeding 150°C (300°F). Where plugging of a pressureactuated vent can occur (such as when used for paints, drying oils, and similar materials), fusible plugs or venting devices that soften to failure at a maximum of 150°C (300°F) under fire exposure shall be permitted to be used for the entire emergency venting requirement. (CSE Note: These requirements must be followed!) 6.8.1.3* For the purpose of Section 6.8, a relieving-style container shall mean a metal container, a metal intermediate bulk container, or a metal portable tank that is equipped with at least one pressure-relieving mechanism at its top that is designed, sized, and arranged to relieve the internal pressure generated due to exposure to fire so that violent rupture is prevented. 6.8.1.3.1 The pressure-relieving mechanism for containers shall be listed and labeled in accordance with Factory Mutual Research Corporation Class 6083, Examination Program for Fusible Closures for Steel Drums, or equivalent. The pressure relieving mechanism shall not be painted. (CSE Note: These pressure relief devices must have a factory mutual rating!)

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Chapter 7: Operations 7.7.1 Section 7.7 shall apply to all wharves as defined in 3.3.50 whose primary purpose is the bulk transfer of liquids. General purpose wharves that handle bulk transfer of liquids and other commodities shall meet the requirements of NFPA 307, Standard for the Construction and Fire Protection of Marine Terminals, Piers, and Wharves. (CSE Note: Unloading and loading of vessels to and from petrochemical plant or distribution center.) 7.10.2 Overpressure/Vacuum Protection. Tanks and equipment shall have independent venting for overpressure or vacuum conditions that could occur from malfunction of the vapor recovery or vapor processing system. Exception: For tanks, venting shall comply with 4.2.5. (CSE Note: Vapor recovery can be used to obtain product left in the tank or vessel of the delivery system, such as a rail car, truck, or ship. As with anhydrous ammonia, recovering the vapor in a shipment tank can add up to thousands of dollars that would otherwise be lost. But pressure relief must be used as to not collapse the tank or vessel under the vacuum of the recovery system. The recovery system creates a lower pressure to atmosphere. This atmospheric pressure in inches of water pushing against the outside of the tank, times the enormous area of the tank, can add up to thousands of pounds of force on the tank, causing it to collapse. This also applies to drainage of the tank or vessel.) 7.6.6* Loading and unloading facilities ...shall consist of a metallic bond wire that is permanently electrically connected to the fill pipe assembly or to some part of the rack structure that is in electrical contact with the fill pipe assembly... shall form a continuous electrically conductive path.7.6.7 Tank car facilities where flammable and combustible liquids are loaded. (CSE Note: Although not directly related to pressure relief valves, this is to prevent fire from explosions due to electro-static discharge. This subject is covered in detail in the code review section of NFPA 79 – Static Electricity.) 7.6.7 Tank car facilities where flammable and combustible liquids are loaded or unloaded through open domes shall be protected against stray currents by permanently bonding the fill pipe to at least one rail and to the facility structure, if of metal. Multiple pipelines that enter the area shall be permanently bonded together. In addition, in areas where excessive stray currents are known to exist, all pipelines entering the area shall be provided with insulating sections to electrically isolate them from the facility piping. (CSE Note: Although not directly related to pressure relief valves, this is to prevent fire from explosions due to electro-static discharge. Note that both side of the system isolator are grounded to earth. The isolator will be a dielectric insulator and could store a large charge. By grounding both sides, the charge is drained to earth.) 7.7. 7 Loading pumps capable of building up pressures that exceed the safe working pressure of cargo hose or loading arms shall be provided with bypasses, relief valves, or other 2003 Edition 30-68 FLAMMABLE AND COMBUSTIBLE LIQUIDS CODE arrangements to protect the loading facilities against excessive pressure. Relief devices shall be tested at least annually to determine that they function satisfactorily at their set pressure. (CSE Note: These requirements must be met for wharf loading and unloading stations!) 7.10.2 Overpressure/Vacuum Protection. Tanks and equipment shall have independent venting for overpressure or vacuum conditions that could occur from malfunction of the vapor recovery or vapor processing system. Exception: For tanks, venting shall comply with 4.2.5. (CSE Note: These requirements must be followed for vapor recovery systems!) 7.10.5* Liquid Level Monitoring 7.10.5.1 A liquid knock-out vessel used in the vapor collection system shall have means to verify the liquid level and a high liquid level sensor that activates an alarm.

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7.10.5.2 For unmanned facilities, the high liquid level sensor shall initiate shutdown of liquid transfer into the vessel and shutdown of vapor recovery or vapor processing systems. (CSE Note: Prevents excessive pressure on the top and bottom of the vessel.) 7.10.6 Overfill Protection 7.10.6.1 Storage tanks served by vapor processing or vapor recovery systems shall be equipped with overfill protection in accordance with 4.6.1. 7.10.6.2 Overfill protection of tank vehicles shall be in accordance with 7.6.10.5 through 7.6.10.7. (CSE Note: Overfill protection prevents excessive pressure on the top and bottom of the vessel. This especially applies to low pressure tanks and vessels as in the API 2000 Standard, typically 5 psi or less. If the tank fills to the top, the flow stops and the full head pressure of the pump is applied to the top and bottom of the tank. If the pump has 30 psi then, 30 psi * 10 ft diameter area = 340,000 pound of force on the roof and bottom of the tank. Pressure relief is necessary.)

ASME VIII code for sizing relief valves and rupture disks

(ASME boiler and pressure vessel code) ASME VIII is required by federal law and Home Land Security now, not just state and city code. Visit site Cornel University Law School Federal Regulation 73 FR 65164. (Click the blue links for documents)

46 CFR 54.01-2 - Adoption of division 1 of section VIII of the ASME Boiler and Pressure Vessel Code. § 54.01-2 Adoption of division 1 of section VIII of the ASME Boiler and Pressure Vessel Code. (a) Pressure vessels shall be designed, constructed, and inspected in accordance with section VIII of the ASME Boiler and Pressure Vessel Code (incorporated by reference, see 46 CFR 54.01-1), as limited, modified, or replaced by specific requirements in this part. The provisions in the appendices to section VIII of the ASME Boiler and Pressure Vessel Code are adopted and shall be followed when the requirements in section VIII make them mandatory. For general information, Table 54.01-2(a) lists the various paragraphs in section VIII of the ASME Boiler and Pressure Vessel Code that are limited, modified, or replaced by regulations in this part. (b) (b) References to the ASME Boiler and Pressure Vessel Code, such as paragraph UG-125, indicate:

(c) U = Division 1 of section VIII of the ASME Boiler and Pressure Vessel Code. G = Part containing general requirements. 125 = Paragraph within part. (d) (e) (c) When a paragraph or a section of the regulations in this part relates to material in section VIII of the ASME Boiler and Pressure Vessel Code, the relationship with the code will be shown immediately following the heading of the section or at the beginning of the paragraph, as follows: (f) (1) (Modifies U___.) This indicates that the material in U___ is generally applicable but is being altered, amplified or augmented. (g) (2) (Replaces U___.) This indicates that U___ does not apply. (h) (3) (Reproduces U___.) This indicates that U___ is being identically reproduced for convenience, not for emphasis.

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Table 54.01-2(a)—Limitations and Modifications in the Adoption of Section VIII of the ASME Boiler and Pressure Vessel Code The references to specific provisions in section VIII of the ASME Boiler and Pressure Vessel Code are coded. The first letter, such as “U,” refers to division 1 of section VIII. The second letter, such as “G,” refers to a subsection within section VIII. The number refers to the paragraph within the subsection. Paragraphs in section VIII of the ASME Boiler and Pressure Vessel Code1 and disposition

U-1 and U-2 modified by U-1(c) replaced by U-1(d) replaced by U-1(g) modified by U-1(c)(2) modified by UG-11 modified by UG-22 modified by UG-25 modified by UG-28 modified by UG-84 replaced by UG-90 and UG-91 replaced by UG-92 through UG-103 modified by UG-98 reproduced by UG-115 through UG-120 modified by UG-116, except (k), replaced by UG-116(k) replaced by UG-117 replaced by UG-118 replaced by UG-119 modified by UG-120 modified by UG-125 through UG-137 modified by UW-1 through UW-65 modified by UW-2(a) replaced by UW-2(b) replaced by UW-9, UW-11(a), UW-13, and UW-16 modified by UW-11(a) modified by UW-26, UW-27, UW-28, UW-29, UW-47, and UW-48 modified by UB-1 modified by UB-2 modified by UCS-6 modified by UCS-56 modified by UCS-57, UNF-57, UHA-33, and UHT-57 modified by UCS-65 through UCS-67 replaced by UHA-23(b) and UHA-51 modified by UHT-5(c), UHT-6, and UHT-23 modified by UHT-82 modified by Appendix 3 modified by

Unit of this part

54.01-5 through 54.01-15. 54.01-5. 54.01-5(a) and 54.01-15. 54.01-10. 54.01-15. 54.01-25. 54.01-30. 54.01-35. 54.01-40. 54.05-1. 54.10-3. 54.10-1 through 54.10-15. 54.10-5. 54.10-1. 54.10-20(a). 54.10-20(b). 54.10-20(c). 54.10-20(a). 54.10-20(d). 54.10-25. 54.15-1 through 54.15-15. 54.20-1. 54.01-5(b) and 54.20-2. 54.01-5(b) and 54.20-2. 54.20-3. 54.25-8. 54.20-5. 54.23-1 52.01-95(d) and 56.30-30(b)(1). 54.25-3. 54.25-7. 54.25-8. 54.25-10. 54.25-15. 54.25-20. 54.25-20 and 54.25-25. 54.15-3.

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Introduction to ASME VIII

ASME and installing pressure relief valves on unfired pressure vessels is required by law per federal regulation 49 CFR 173.32 (c)(4). The User is responsible for overpressure protection of the vessel, not the designer or manufacturer. Therefore, the User must explicitly state the type of overpressure protection that will be provided once the vessel is installed. Finally, the User must state whether jurisdictional acceptance of the vessel is required prior to operation of the vessel per the AHJ (authority having jurisdiction) Note: The ASME VIII and API 2000 Standard can be retroactive if determined by AHJ that after evaluation, the system could possibly endanger the life and property of the public.

Overview Section VIII - Pressure Vessels Division 1 provides requirements applicable to the design, fabrication, inspection, testing, and certification of pressure vessels operating at either internal or external pressures exceeding 15 psig. Such vessels may be fired or unfired. This pressure may be obtained from an external source or by the application of heat from a direct or indirect source, or any combination thereof. Specific requirements apply to several classes of material used in pressure vessel construction, and also to fabrication methods, such as welding, forging, and brazing. Division 1 contains mandatory and non-mandatory appendices detailing supplementary design criteria, nondestructive examination and inspection acceptance standards. Rules pertaining to the use of the single ASME certification mark with the U, UM and UV designators are also included. Division 2 requirements on materials, design, and nondestructive examination are more rigorous than in Division 1; however, higher design stress intensify values are permitted. These rules may also apply to human occupancy pressure vessels typically in the diving industry. Rules pertaining to the use of the single ASME certification mark with the U2 and UV designators are also included. Division 3 requirements are applicable to pressure vessels operating at either internal or external pressures generally above 10,000 psi. It does not establish maximum pressure limits for Section VIII, Divisions 1 or 2, nor minimum pressure limits for this Division. Rules pertaining to the use of the single ASME certification mark with the U3 and UV3 designator are also included. ASME VIII – Pressure relief requirements UG-125 (a) — All pressure vessels within the Scope of this Division, irrespective of size or pressure, shall be provided with pressure relief devices in accordance with the requirements of UG-125 through UG137. (1) It is the responsibility of the user to ensure that the required pressure relief devices are properly installed prior to initial operation. Excerpts from ASME Unfired Pressure Vessel Code UG-125 (c) — All pressure vessels other than unfired steam boilers shall be protected by a pressure relief device that shall prevent the pressure from rising more than 10% or 3 psi (20 kPa), whichever is greater, above the maximum allowable working pressure except as permitted in (1) and (2) below. (See UG-134 for pressure settings.) (1) When multiple pressure relief devices are provided and set in accordance with UG-134(a), they shall prevent the pressure from rising more than 16% or 4 psi (30 kPa), whichever is greater, above the maximum allowable working pressure. (2) When a pressure vessel can be exposed to fire or other unexpected sources of external heat, the pressure relief device(s) shall be capable of preventing the pressure from rising more than 21% above the maximum allowable working pressure. Supplemental pressure relief devices shall be installed to protect against this source of excessive pressure if the pressure relief devices used to satisfy the capacity requirements of UG-125(c) and UG- 125(c)(1) have insufficient capacity to provide the required protection.

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UG-125(d) — Where an additional hazard can be created by exposure of a pressure vessel to fire or other unexpected sources of external heat (for example, vessels used to store liquefied flammable gases), supplemental pressure-relieving devices shall be installed to protect against excessive pressure. Such supplemental pressure-relieving devices shall be capable of preventing the pressure from rising more than 20% above the maximum allowable working pressure of the vessel. A single pressure-relieving device may be used to satisfy the requirements of this paragraph and (c), provided it meets the requirements of both paragraphs. UG-133(f) — The set pressure tolerances, plus or minus, of safety or relief valves, shall not exceed 2 PSI (13.8 kPA) for pressures up to and including 70 PSIG (483 kPa), and 3% for pressures above 70 PSIG (483 kPa).

ASME VIII - Pressure limits in sizing The ASME Code requires that when a rupture disk or pressure relief valve is used as the primary relief device, it must be sized to prevent the pressure from rising above 110% of the MAWP (UG-125(c)). If used as a secondary relief device or as multiple relief devices, the size must prevent the pressure from rising above 116% of the MAWP (UG-125(c)(1)). If used as a supplementary relief device for hazards external to the protected vessel or system, the size must prevent the pressure from rising above 121% of the MAWP (UG-125(c)(2)).

Table 5 - ASME standard nozzle orifice data

RELIEF VALVE NOZZLE ORIFICE AREAS Size Designation

Orifice Area, in2

D

0.110

E

0.196

F

0.307

G

0.503

H

0.785

J

1.280

K

1.840

L

2.850

M

3.600

N

4.340

P

6.380

Q

11.050

R

16.000

T

26.000

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ISA pressure relief valve and rupture disc symbols

Pressure Relief Valve

Pressure Rupture Disk

Vacuum Relief Valve

Vacuum Rupture Disc

Breathing Valve or Pressure / Vacuum Relief Valve

A. Rupture Disk B. Disk Holder C. Sensor

A Typical Rupture Disk and Holder

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Operation of Breather / Vacuum Relief Valve

Sizing equations for relief valves and rupture disks ASME VIII code equations USCS units The user should understand the symbols used in the sizing and capacity calculation formulas. The basic equation for flow through a pressure relief valve or rupture disk is:

VAPOR OR GASES

VAPOR OR GASES

Mass Flow Rate Sizing (W = lb/hr)

Volumetric Flow Rate Sizing 3 (Q=Standard ft /Min Flow Rate at 14.7 psia and 60⁰F)

A

W T Z A

CKP1 Kb M w

60Q  T Z CKP1 Kb M w

STEAM

AIR

Mass Flow Rate Sizing (W = lb/hr)

Volumetric Flow Rate Sizing 3 (Q = Standard ft /Min Flow Rate at 14.7 psia and 60⁰F)

A

W 51.5KPK 1 b

A

60Q  0.0763 T Z 356 KPK 1 b  5.3824 

LIQUIDS

Critical Pressure Ratio ( rc )

Certified Volumetric Flow Rate Sizing (If Q = U.S. Gallons per minute, Ku=38) (If Q = Cubic feet per hour, Ku=5.2143)

 2  k 1 rc     k  1

A

k

Q Gf Ku KK v P1  P2

Gas Constant ( C ) sonic flow (typically 15 psig and above)

If (P2/P1) is less than rc the flow will be sonic. Use this formula:

 2  C  520 k    k 1

k 1 k 1

Gas Constant ( C ) subsonic flow (low pressure flow) If (P2/P1) is greater than rc the flow will be subsonic. Use this formula: 2 k 1   k  P2  k  P2  k  C  735      k  1  P1   P1    

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A Note about sonic or choked flow The critical flow which also referred to as sonic flow, choked flow or Mach 1 is the limitation point of a compressible fluid flow through an orifice. The critical flow can occur on a relief valve orifice or a choke. A choke is a condition where piping goes from a small branch into a larger header, where pipe size increases, or at the vent tip. The maximum flow occurs at sonic velocity, which exists as long as the pressure drop through the orifice is greater than the critical pressure drop. The maximum chocked flow can be less than the desired flow. Calculations are necessary to determine if the flow is choked below the desired or required flow rate that is needed for control of the process.

Variables for PRV and PSV sizing equations A = actual nozzle area of valve, square inches C = gas constant (C = 315 if ratio of specific heats is unknown) Gf = (s.g.) specific gravity of flowing fluids (liquid/water) or (gas/air) k = specific heats ratio K = coefficient of discharge (Kd * 0.9), (0.8775 for Vapor, Gas or Steam), (0.67 for Liquid) Kb = back-pressure correction factor, dimensionless (See Table 4 - Calculate Kb) Kc = combination factor for installations with a rupture disc upstream of the valve. Use a 0.9 value for any rupture disc/pressure relief valve combination. Use a 1.0 value when a rupture disc is not installed Kd = dimensionless value relating the actual vs. theoretical safety relief valve flow rate, (0.975 for Vapor, Gas or Steam), (0.744 for Liquid) Kp = overpressure correction for liquid (0.60 at 110%) Ku = dimensionless factor used to adjust for the type of units used in the sizing equation. (See liquid equation for value of Ku for gpm or cfh applications) Kw = variable or constant back-pressure factor for bellows sealed valves only Kv = viscosity correction factor (use Kv = 1 except for very high viscous fluids) Mw = molecular weight P1 = relieving pressure (psia). This is the set pressure (psig) + overpressure (psig) + atmospheric pressure (14.7 psia) – inlet pressure piping loss (psig) P2 = the pressure at the outlet of the valve in absolute pressure units (psia)

ρ = Density of gas or vapor: for vapors = (s.g.) x (Density of Air) for liquids = (s.g.) x (Density of Water) Density of Air = 0.0763 lb/ft3 at 14.7 psia, and 60°F (USCS) Density of Water = 62.305 lb/ft3 at 70°F (USCS) Q = capacity in volume per time units. T = relieving temperature, absolute ⁰R (⁰F + 460) W = required relieving rate, mass flow Z = compressibility factor (Z = 1 for ideal gases)

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Table 4 – Calculate Kb

200

Sizing rupture disks - worked examples The function of a rupture disk is to protect pressure vessels, piping systems, and other equipment from pressures exceeding their design pressure by more than a fixed predetermined amount. The permissible amount of overpressure is covered by various codes and is a function of the type of equipment and the conditions causing the overpressure. The aim of safety systems in processing plants is to prevent damage to equipment, avoid injury to personnel and to eliminate any risks of compromising the welfare of the community at large and the environment. Proper sizing, selection, manufacture, assembly, test, installation, and maintenance of a pressure relief valve are critical to obtaining maximum protection. Note: Where rupture disks are installed upstream of a relief valve, the rupture disc is normally the same size as the relief valve inlet nozzle.

Rupture Disk Sizing Example 1

Sample problem: We will size a rupture disk for the following service, LIQUID. Size the rupture disk for the following criteria. Application: (Primary Relief).

Q = 1500 gpm (required)

Vessel MAWP = 45 psig

Gf = 0.85

P2 (Back Pressure) = 5 psig Use 10% over-pressure as permitted by ASME code. P1 = (1.10)MAWP + 14.7 K = 0.67 Kv = 1 (except for very viscous applications) Ku = 38 for gpm application P1 = (1.1)(45) + 14.7 = 64.2 P2 = 5 + 14.7 = 19.7

A

Q Gf Ku KKv P1  P2



1500 0.85 (38)  0.67 1 64.2  19.7

 8.14in2

Use manufacturer’s catalog for the actual disk size to order for your application.

Rupture Disk Sizing Example 2

Sample problem: We will size a rupture disk for the following service, GAS (Air). Size the rupture disk for the following criteria. Application: (Primary Relief). Q = 5000 scfm (required)

Vessel MAWP = 150 psig

P2 (Back Pressure) = 20 psig

Flow temperature = 250⁰F

Use 10% over-pressure as permitted by ASME code. P1 = (1.1)(MAWP) + 14.7 = 179.7 P2 = 20 + 14.7 = 34.7

201

Mw = 28.9

k = 1.40 Z=1

Flow pressure ratio:

P2 20  14.7   0.193 P1 (1.1)(150)  14.7 Critical pressure ratio: k

1.40

 2  k 1  2  1.40 1 rc    0.528   1.40  1   k  1   If (P2/P1) is less than rc , use this formula k 1

1.40 1

 2  k 1  2  1.40 1 C  520 k   520 1.40  356  1.40  1   k  1   From Table 4 - Calculate Kb, we find that the value of Kb =1 K = 0.8775 Given the required flow in actual cubic feet per minute:

A

60Q  0.0763 T Z 356 KP1  5.3824  K b



 60  5000  0.0763  250  460  1  2.02in 2  356  0.8775179.7  5.38241

Use manufacturer’s catalog for the actual disk to order your application.

Rupture Disk Sizing Example 3

Sample problem: We will size a rupture disk for the following service, GAS (some process). Size the rupture disk for the following criteria. Application: (Primary Relief).

Q = 2000 scfm (required)

Vessel MAWP = 15 psig

Gf = 0.72

k = 1.26

P2 (Back Pressure) = 5 psig

Flow temperature = -40⁰F

Mw = 20.808

Z = 0.95

In this case 10% of gauge pressure is less than 3 psi, therefore, 3 psi over-pressure is permitted by ASME code. P1 = 3+ MAWP + 14.7 = 32.7 Flow pressure ratio:

P2 5  14.7   0.602 P1 3  15  14.7 Critical pressure ratio:

202

1.26

k

 2  k 1  2  1.26 1 rc    0.553   1.26  1   k  1   P2/P1 is greater than rc, use the low pressure subsonic formula: 2 k 1   2 1.26 1 k  P2  k  P2  k  1.26   C  735   735 0.602 1.26   0.602  1.26   115.68         k  1  P1   P1  1.26  1    

Find the constants for the equation: Multiply Mw and  by specific gravity Mw (gas) = Mw (air)(0.72)=20.808 3

Density of Air = 0.0763 lb/ft at 14.7 psia, and 60°F (USCS)

 = (0.0763 lb/ft3)(0.72) = 0.054936 From Table 4 - Calculate Kb, we find that the value of Kb =0.99 K =0.8775

A

60Q T Z CKPK 1 b Mw



 60 2000 0.054936  40  460 1  9.01in2 115.68 0.8775 32.7  0.99 20.808

Use manufacturer’s catalog for the actual disk size to order for your application.

Sizing pressure relief valves - worked examples The function of a pressure relief valve is to protect pressure vessels, piping systems, and other equipment from pressures exceeding their design pressure by more than a fixed predetermined amount. The permissible amount of overpressure is covered by various codes and is a function of the type of equipment and the conditions causing the overpressure. It is not the purpose of a pressure relief valve to control or regulate the pressure in the vessel or system that the valve protects, and it does not take the place of a control, proportional, or regulating valve. There are modulating type proportional valves available for the purpose of regulating over pressure, such as in the application of positive displacement pumps, but the backpressure will have to be known for proper sizing. The aim of safety systems in processing plants is to prevent damage to equipment, avoid injury to personnel and to eliminate any risks of compromising the welfare of the community at large and the environment. Proper sizing, selection, manufacture, assembly, test, installation, and maintenance of a pressure relief valve are critical to obtaining maximum protection.

203

EXAMPLE 1 (Atmospheric Back Pressure Application)

Sample problem: We will size a Pressure Relief Valve for the following service, Natural GAS. Size the Pressure Relief Valve for the following criteria. Application: (Primary Relief). Q = 5900 lb/hr

Set Pressure = 210 psig

P2 (Back Pressure) = 14.7 psia

Relieving temperature = 120⁰F

Mw = 19

k = 1.27 Z=1

Use 10% over-pressure as permitted by ASME code. P1 = Set Pressure + (0.10)Set Pressure + 14.7 P1 = (1.1)(210) + 14.7 = 245.7(psia). P2 = 14.7 (psia) Flow pressure ratio:

P2 14.7   0.0598 P1 (1.1)(210)  14.7 Critical pressure ratio: Note: the value of “k” can be found in Table A20 – Typical properties of gases. k

1.27

 2  k 1  2  1.27 1 rc    0.55   1.27  1   k  1   P2/P1 is less than rc , use this formula k 1

1.27 1

 2  k 1  2  1.27 1 C  520 k   520 1.27  344.13  1.27  1   k  1   From Table 4 – For atmospheric pressure Kb = 1 Use formula: VAPOR OR GASES Mass Flow Rate Sizing (W = lb/hr)

A

W T Z CKP1 K b M w



(5900) (120  460) 1

 344.13 0.8775  245.7 1 19 

 0.439in 2

Use Table 5 – ASME Standard nozzle orifice data to find the orifice size for the relief valve. 2

F = 0.307 in 2 G = 0.503 in So we will select an orifice size of “G”

204

EXAMPLE 2 (Gas/Vapor with Back Pressure Application)

Sample problem: We will size a Pressure Relief Valve for the following service, NH3 (ammonia). Size the Pressure Relief Valve for the following criteria. Application: (Primary Relief).

Q = 15,000 lb/hr

Set Pressure = 325 psig

P2 (Back Pressure) = 15 psig

Relieving temperature = 138⁰F

Mw = 17

k = 1.30 Z=1

Use 10% over-pressure as permitted by ASME code. P1 = Set Pressure + (0.10)Set Pressure + 14.7 P1 = (1.1)(325) + 14.7 = 372.2(psia). P2 = 15 + 14.7 = 29.7 (psia) Flow pressure ratio:

P2 15  14.7   0.0798 P1 (1.1)(325)  14.7 Critical pressure ratio: Note: the value of “k” can be found in Table A20 – Typical properties of gases. k

1.30

 2  k 1  2  1.30 1 rc    0.546   1.30  1   k  1   P2/P1 is less than rc , use this formula k 1

1.30 1

 2  k 1  2  1.30 1 C  520 k   520 1.30   346.98    k  1 1.30  1  From Table 4 – For atmospheric pressure Kb = 1 Use formula: VAPOR OR GASES Mass Flow Rate Sizing (W = lb/hr)

A

W T Z CKP1 K b M w



(15,000) (138  460) 1

 346.98 0.8775 372.2 1 17 

 0.785in 2

Use Table 5 – ASME Standard nozzle orifice data to find the orifice size for the relief valve. 2

H = 0.785 in

So we will select an orifice size of “H”.

205

EXAMPLE 3 (Air SCFH Application) Sample problem: We will size a Pressure Relief Valve for the following service, AIR. Size the Pressure Relief Valve for the following criteria. Application: (Primary Relief).

Q = 6,000 scfh

Set Pressure = 100 psig

P2 (Back Pressure) = 15 psig

Relieving temperature = 138⁰F

Mw = 28.97

k = 1.40 Z=1

Use 10% over-pressure as permitted by ASME code. P1 = Set Pressure + (0.10)Set Pressure + 14.7 P1 = (1.1)(100) + 14.7 = 124.7(psia). P2 = 15 + 14.7 = 29.7 (psia) Flow pressure ratio:

P2 15  14.7   0.238 P1 (1.1)(100)  14.7 Critical pressure ratio: Note: the value of “k” can be found in Table A20 – Typical properties of gases. k

1.40

 2  k 1  2  1.40 1 rc    0.528   1.40  1   k  1   P2/P1 is less than rc , use this formula k 1

1.40 1

 2  k 1  2  1.401 C  520 k   520 1.40   356    k  1 1.40  1  C=356, We will use the AIR formula instead of the VAPOR / GAS formula. From Table 4 – For atmospheric pressure Kb = 1 Use formula: AIR Volumetric Flow Rate Sizing 3

(Q = Standard ft /Min Flow Rate at 14.7 psia and 60⁰F)

A

60Q  0.0763 T Z 356 KP1 K b  5.3824 



 60  6,000  0.0763 138  460  1  3.2in 2  356  0.8775124.7 1 5.3824

Use Table 5 – ASME Standard nozzle orifice data to find the orifice size for the relief valve. 2

L = 2.850 in 2 M = 3.600 in So we will select an orifice size of “M”.

206

EXAMPLE 4 (Saturated Steam Application) Sample problem: We will size a Pressure Relief Valve for the following service, Saturated Steam. Size the Pressure Relief Valve for the following criteria. Application: (Primary Relief).

Q = 40,000 lb/hr

Set Pressure = 140 psig

MW = 18

P2(Back Pressure) = 14.7 psia Use 10% over-pressure as permitted by ASME code. P1 = Set Pressure + (0.10)Set Pressure + 14.7 P1 = (1.1)(140) + 14.7 = 168.7(psia). P2 = 14.7 (psia) Flow pressure ratio:

P2 14.7   0.087 P1 (1.1)(140)  14.7 From Table 4 – For atmospheric pressure Kb = 1 Use formula: STEAM Mass Flow Rate Sizing (W = lb/hr)

A

W (40,000)   5.247in2 51.5KP1 Kb  51.5 (.8775) 168.7 1

Use Table 5 – ASME Standard nozzle orifice data to find the orifice size for the relief valve. 2

N = 4.340 in 2 P = 6.380 in So we will select an orifice size of “P”.

207

208

Review of Feedback Control Fundamentals Compare Open Loop Control to Closed Loop Control Open Loop Example – A Mathematical Analysis Most industries today use closed loop control. It offers a faster and tighter response. That is, it can maintain the desired set point of a process almost exactly. Its output is almost perfect, (exactly what is desired). Let us examine an everyday application, speed control of an automobile. Look at the figure C-1 below. There is a desired speed (R); a controller, mechanical accelerator pedal mechanism or microprocessor controller and electronics, which provides a signal to the engine and transmission (u); there is a disturbance, the slope of the road (w); and a desired output, the actual speed of the automobile (Y).

Figure C-1

First let us examine open loop control and its drawbacks. Open loop control is cheap and can work in a circumstance where the output can vary, that is the output can be in a range of speeds and does not have to be exact for the conditions of the process. This may not always be desirable. Look at the figure C-2 below. Here we have variable (R), desired speed and variable (Yol), output speed of the open loop. The automobile uses a mechanical linkage with an accelerator pedal to send a signal to the engine and transmission, which will control the speed of the automobile. The mechanical linkage combined with the accelerator pedal has a gain of 1/10. The accelerator pedal and mechanical linkage gain of 1/10 adds to the automobile’s output speed. The road has a slope. This slope subtracts from the automobile’s response of desired set point speed (R), with a gain of 0.5. When the slope of the road is zero, (for a level surface), the disturbance does not affect the output speed. When the slope is greater than zero (e.g., 1% or 10% grade) the automobile’s actual speed is less than the desired speed. This can be seen driving down a road and holding the accelerator pedal at a constant position. You will slow down going up a hill or slope (the rise verses the run or Y/X).

209

Figure C-2 Where: R = desired or reference speed (mph) u = throttle angle in degrees (sets engine speed) Yol = actual open loop speed of the automobile (mph) w = road grade in % The set point (desired speed) is multiplied by the gain of the controller (1/10). The output of the controller is called the manipulated variable (u). Then the system disturbance (multiplied by a gain of 0.5) is subtracted from the manipulated variable (u). The manipulated variable (u), which is the throttle angle of the carburetor, sets the engine speed. The process final correction control device or element is the engine and transmission, which has a gain of 10. The manipulated variable (u), minus the system disturbance multiplied by a gain of 0.5, is then multiplied by the final control device or element gain of 10, to set the value of the final output, which is the actual speed of the process or plant (Yol). In this case the process or plant is the automobile. Let us look at the math to prove what is happing in the system. The open loop output speed is given by:

 1 u  R   10  Yol   u  0.5w 10 R  Yol    0.5w 10  10  Yol  R  5w

210

So it can be seen for a slope of 0%, if the set point is 55 mph, the output of the process is the actual automotive speed of 55 mph. This is only true if there is no disturbance.

55 mph  55  5(0);

(a slope of 0%)

If the slope is 1% the output is 50 mph:

50 mph  55  5(1);

(a slope of 1%)

If the slope is 10% the output is 5 mph:

5 mph  55  5(10);

(a slope of 10%)

Closed Loop Example – A Mathematical Analysis It can be seen for a large disturbance, open loop control is not desirable. Let us look at the automobile with closed loop control used, the speed control setting. Refer to figure C-3 below. Now the controller uses a microprocessor combined with electronics to set the throttle angle setting of the engine’s carburetor. This will set the speed of the engine to maintain the output of the process or plant, the actual speed of the automobile. The desired speed is reached and the speed control button is pushed. This is called the set point (R), the desired speed of the automobile. The closed loop controller has a gain of 100. We will now illustrate the tight control of the final output of the process (Ycl). The set point or desired speed variable (R) is entered. Then the feedback signal, the process variable (Ycl), is subtracted from the set point variable (R). This is called the error or set point error signal (e). The set point error (e) is multiplied by the controller gain of 100. This output is called the manipulated variable (u). The manipulated variable (u), which is the throttle angle of the carburetor, sets the engine speed. The process final correction control device or element is the engine and transmission, which has a gain of 10. The manipulated variable (u), minus the system disturbance multiplied by a gain of 0.5, is then multiplied by the final control device or element gain of 10, to set the value of the final output, which is the actual speed of the process or plant (Ycl). In this case the process or plant is the automobile.

Figure C-3

211

Where: R = desired or reference speed (mph) e = set point error u = throttle angle in degrees (sets engine speed) Ycl = actual closed loop speed of the automobile (mph) w = road grade in % Let us look at the math to prove what is happing to the system. The closed loop output speed is given by:

e  R  Ycl u   e  100 u   R  Ycl  100 Ycl   u  0.5w  10 Ycl  100R  100Ycl   0.5w  10 Ycl  1000R  1000Ycl  5w 1000Ycl  Ycl  1000R  5w 1001Ycl  1000R  5w Ycl 

1000R  5w 1001

Ycl  0.999R  0.005w So it can be seen for a slope of 0%, if the set point is 55 mph, the output of the process is the actual automotive speed of 54.945 mph. This is only true if there is no disturbance.

54.945 mph  0.999(55)  0.005(0);

(a slope of 0%)

If the slope is 1% the output is 54.94 mph:

54.94 mph  0.999(55)  0.005(1);

(a slope of 1%)

If the slope is 5% the output is 54.92 mph:

54.92 mph  0.999(55)  0.005(5);

(a slope of 5%)

If the slope is 10% the output is 54.90 mph:

54.90 mph  0.999(55)  0.005(10);

(a slope of 10%)

212

The Transfer Function for the Automobile See the block diagram in figure C-4 below for the process of deriving the transfer function for the automobile.

Figure C-4 By using a more complex controller with additional modes of control, the process error can be removed completely and the process (plant) can respond very quickly. We have just seen how proportional control has an offset from the set point. Proportional control will stop the upset or process error and try to return the process back to the set point. The proportional controller can have a significant error in the process output, if the disturbance is large. By using the integral mode in a controller, the offset can be completely removed. This is sometimes called “reset action,” due to the fact in the old days; the operator would make a manual change in the set point (reset the set point), to achieve the proper process output. With integral mode, or reset action, the proportional output is increased (or repeated) every few seconds or minutes, depending on the controller design, until the process output equals the set point of the system. By using derivative mode, the controller can respond very quickly to a fast changing process error or upset. The derivative mode or “rate action,” subtracts from the controller output to slow down a process that is increasing too quickly, such a chemical reaction where the heat may increase so quickly it may explode.

213

214

Review of Frequency Response Fundamentals Electrical Application – A First Order System Frequency response is a way to analyze what the output of the process or plant will be. We can calculate the output (e.g., volts or watts in power), for a given system gain and input (e.g., volts) at some frequency. Remember the capacitance reactance is varying with the change in frequency (Xc = 1/2πfC). First we will take a look at where the transfer function comes from. See figure T-1 below.

Figure T-1

We will now derive the transfer function for this first order system, where R(S) is the input signal at some frequency and Y(S) is the output voltage with some phase angle and amplitude. Current equals the voltage drop across the resistor divided by the resistor value:

I

VR R

I

Vin  Vout R

Current also equals the voltage out of the capacitor:

I C

dVout dt

Substitute voltage drop divided by resistance for amps (I) and set the two equations equal to each other:

Vin  Vout dVout C R dt Vin  Vout  RC S

dVout dt

d dt

Vin  Vout  RCS Vout  215

Vin  Vout  RCS Vout  Vin  1  RCS Vout Vin  Vout 1  RCS 1 Vout  1  RCS Vin t  RC The transfer function is equal to the gain of the system:

1 Vout  1  St Vin Use the transfer function to calculate the voltage out of the system:

 1  Vin    Vout  1  St  We have now derived the transfer function for this first order system. We can now plug in an input voltage and an angular frequency and calculate the attenuation of the output signal and the phase angle of the output signal.

Bode Plot of First Order System Make a Bode plot for a circuit with the following components. Where: Resistor = 100Ω Capacitor = 2.65µF Volts in =10v

f C = 60 Hz (corner or cutoff frequency)

t sec  

1  RC 2 fC

t (time constant) = 1000 (Ω) x 0.00000265 (F) = 0.00265 seconds

 1 Vin  2  12   S  t  

   Vout   

S    2 f dB  20 log

 Vout     Vin 

216

Calculate the data for the Bode Plot

Freq.

Rads /sec

1

6.28

Volts Out Phase Angle

 1  10v  2  12  6.28  0.00265   

Signal Attenuation

    9.9986v  

 9.9986v     10v 

20 log

= -0.0012 dB

 6.28  0.00265   TAN 1    0.95  1  

5

12.56

 1  10v  2  12  12.56  0.00265   

    9.9889v  

 9.9889v   10v 

20 log

= -0.0096 dB

 12.56  0.00265   TAN 1    1.9  1  

10

62.8

 1  10v  2  12  62.8  0.00265   

    9.8643v  

 62.8  0.00265   TAN 1    9.5  1  

217

 9.8643v   10v 

20 log

= -0.1187 dB

Calculate data for the Bode Plot Continued:

Freq.

Rads /sec

50

314

Volts Out Phase Angle

 1  10v  2  12  314  0.00265   

Signal Attenuation

    7.69v  

 7.69v     10v 

20 log

= -2.28 dB

 314  0.00265   TAN 1    40  1  

60

377

 1  10v  2  12  377  0.00265   

    7.07v  

 7.07v     10v 

20 log

= -3.0 dB

 377  0.00265   TAN 1    45  1  

100

628

 1  10v  2  12  628  0.00265   

    5.15v  

 5.15v     10v 

20 log

= -5.76 dB

 628  0.00265   TAN 1    59  1  

200

1256

 1  10v  2  12  1256  0.00265   

    2.88v  

 2.88v   10v 

20 log

= -10.8 dB

 1256  0.00265   TAN 1    73.3  1  

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Calculate data for the Bode Plot Continued:

Freq.

Rads /sec

10000 62800

Volts Out Phase Angle

Signal Attenuation

 1  10v  2  12  62800  0.00265   

    0.006v  

 0.006v   10v 

20 log

= -64.44 dB

 62800  0.00265   TAN 1    89.7  1  

100000 628000

 1  10v  2  12  628000  0.00265   

 0.0006009     20 log 10v  = -84.424 dB    0.0006009v  

 628000  0.00265   TAN 1    89.97  1  

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Creating a Bode Plot – First Order System using Frequency

Voltage Signal Attenuation

Phase Angle

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Hydraulic Application – A First Order System Frequency response is a way to analyze what the output of the process or plant will be. We can calculate the output (e.g., flow as volume out), for a given system gain and input (e.g., flow as volume in) at some low frequency (the rate of change of head in the tank with respect to time) and a varying time constant RC (the resistance of the valve relating to a changing corrective position, multiplied by the capacitance of the tank). First we will take a look at where the transfer function comes from. See figure T-2 below.

Figure T-2 We will now derive the transfer function for this first order system, where R(S) is the input signal at some flow rate with the tank volume changing at some frequency and Y(S) is the output flow rate with some phase angle and amplitude. The accumulated volume in the tank equals the flow in (Fin) – the flow out (Fout):

Fin-Fout = Accumulated Volume in Tank The accumulated volume in the tank also equals the head (H) multiplied by the area of tank (C):

Accumulated Volume in Tank  C

dH dt

Set the equations equal to each other:

Fin  Fout  C

dH dt

The valve resistance opposes flow out of the tank:

H  R( Fout )

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Substitute the head equation in to the formula:

Fin  Fout  C

S

d  RFout  dt

d dt

Fin  Fout  RCS  Fout  Fin  Fout  RCS  Fout  Fin  1  RCS  Fout Fin  Fout 1  RCS 1 Fout  1  RCS Fin t  RC The transfer function is equal to the gain of the system:

1 Fout  1  St Fin Remember the accumulated flow (tank volume) equals the flow in minus the flow out of the system. Use the transfer function to calculate the flow out of the system:

 1  Fin    Fout  1  St  We have now derived the transfer function for this first order system. At steady state there is no charging of the tank and, therefore, no frequency (S). The transfer function is now 1/(1 +0) and we have a gain of 1 or DC steady state. The flow in equals the flow out and the head in the system (tank) does not vary.

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Process Control Theory and Controller Tuning The process control industry covers a wide variety of applications: petrochemical; pharmaceutical; pulp and paper; food processing; material handling; even commercial applications. Process control in a plant can include discrete logic, such as relay logic or a PLC; analog control, such as single loop control or a DCS (distributed control system); as well as pneumatic, hydraulic, and electrical systems as well. The Control Systems Engineer must be versatile and understand a broad range of control subjects as applied to controller applications, configuration, and tuning, as well as analysis and understanding of loop gain and stability. This section will review the foundations of process control theory and its applications. Some of this material may be on the CSE examination. I have tried to keep the studies to a minimum and reduce the math for the problem to a form in which you can just plug in the values and get the answer you need for the exam. We will cover degrees of freedom, process loop gain and applications, filtering of noise in process variable signals, open and closed loop tuning, damping of the system, time constants, overshoot of process set points and check for stability of a system transfer function.

Degrees of Freedom in Process Control Systems In an unconstrained dynamic or other system, the number of independent variables required to specify completely the state of the system at a given moment, must be defined. If the system has constraints, that is, kinematic or geometric relations between the variables, each such relation reduces by one the number of degrees of freedom (DOF) of the system. Process Variables - (Equations + Constants) = Degrees of Freedom Degrees of Freedom = The Minimum Number of Process Controllers Required

Example 1: An Airplane Variables Altitude Latitude Longitude

1 1 1 3 Minus Constants 0 Minus Equations 0 Degrees of freedom = 3 DOF = 3 – (0+0) = 3 Three (3) controllers are needed. One (1) for each variable.

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Example 2: A Train Variables Altitude Latitude Longitude Minus Constants Altitude Latitude Minus Equations Degrees of freedom =

1 1 1 3 1 1 0 1

DOF = 3 – (2+0) = 1 One (1) controller is needed. One (1) for Longitude only.

Example 3: A Hot Water Heat Exchanger Variables Ws (flow rate of steam) Wcw (flow rate of cold water) Whw (flow rate of hot water) Q (quantity of steam in cubic feet) Ps (supply pressure of steam) Tcw (temperature of cold water) Thw (temperature of hot water) Minus Constants Q (quantity of steam) Ps (supply pressure of steam) Tcw (temperature of cold water) Minus Equations Material Balance (conservation of mass) Energy Balance (conservation of energy)

1 1 1 1 1 1 1 7 1 1 1 3 1 1 2

DOF = 7 – (3+2) = 2 Two (2) controllers are needed. 1. One (1) controller for steam flow. 2. One (1) controller for the energy equation (mass*Cp*deltaT). The controller type will be a temperature controller, and it will be on the outlet water temperature. It will provide a remote set point to the steam flow controller.

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Controllers and control strategies (models-modes) In general terms, a control loop is a group of components working together as a system to achieve and maintain the desired value of a system variable by manipulating the value of another variable in the control loop. Each control loop has at least one input and one output. There are two types of control loops: open loop and closed loop. Refer to the section of this manual, Review of Feedback Control Fundamentals. In this section we use simple math to derive a compensated output signal for a control loop with disturbance acting on the system, for a given set point using a process feedback signal to maintain the desired set point with proportional control having a minimal offset from the set point. In an open loop system, the controller does not have a feedback signal from the system. The controller has a set point and an output signal. The system process variable varies, due to system disturbances regardless of the set point signal and fixed controller output signal. An example of an open loop system would be a car, when using the accelerator pedal only. The accelerator pedal is held in fixed position. When the car goes up a hill, the car will tend to slow down. The decrease in speed is inversely proportional to the increase in slope. In a closed loop system, the controller does have a feedback signal from the system. The controller has a set point, a feedback input signal and a varying output signal. The output signal increases or decreases proportionally to the the error of the set point compared to the input signal. The input signal varies proportionally to the system disturbances and the gain of the measurement sensor. An example of a closed loop system would be a car, when using the speed control only. When the car goes up a hill, the car will tend to speed up to maintain the set point speed, regardless of increase in slope. The increase in slope is a system disturbance, but there can be more than one disturbance on a system. A head wind would add to the error of increasing slope, requiring the car to give even more power to increase the speed to the set point, say 55 mph. All control systems have their limitations of control: either the ability to respond to a fast changing system disturbance, frequency response limitations due to the design of the system, or limitations in adding energy to the system or removing energy from system. For example: a valve is at 0% or 100% or the heat exchanger is at maximum capacity. When responding to a system upset, the valve or servo mechanism has limited speed of movement due to mechanical design. There is always a slew rate (delay of movement or travel) of the mechanical or electrical parts. The valve or servo mechanism can only move so many inches or degrees in a period of time. The electrical components can only charge or discharge so fast in time. These response limitations are typically in frequency, as in hertz or cycles per second (cps), and the oscillation period in time is the reciprocal of the frequency.

225

The process variable or feedback input signal is always measured in 0% to 100% and is typically evenly divisible by 4 or measured at 25% increments. Examples: 3 to 15 PSI 12 PSI span 4 to 20 mA 16 mA span 1 to 5 volts 4 volt span Modes Familiarize yourself with the different control modes and the ISA standards and symbols for representing the modes on a P&ID (piping and instrumentation diagram). The most common types of closed loop control modes are: feedback, feedforward, cascade, and ratio.

Feedback Control Loop

Feedforward Control Loop

Cascade Control Loop

Ratio Control Loop

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Time Proportional Control Mode An underused control strategy that offers significant benefits is time-proportional control (TPC). Unlike traditional proportional or even PID control that requires a varying output to a modulating control device, time-proportional control can achieve a proportional control response to process variation using an on/off device by varying on and off times in a defined control period. The on/off device is generally a simpler, less expensive control device. Time-proportional control is a less widely used method for achieving proportional control, and has the advantage that it is used in lower cost on/off control devices, such as a solenoid valve or fixed output pump. By proportioning the on-time versus off-time of the control device within a fixed time period (sample period), a proportional response is achieved. This type of control mode is used frequently in industrial heating applications with furnaces using SCRs and solid state relays, as well as tank filling applications and pH correction systems using pneumatic pumps. See the section in this manual Process Analyzers / Control of pH values in processes for more information on pH control.

Process Loop Gain (Gp) The goal here is control loop stability. This is done by making the loop response to load changes as linear as possible and by keeping the loop gain more or less constant. The gain of any device is the ratio of its output divided by its input. The loop gain (Lg) is the product of the gains of the loop components: the process gain (Gp), sensor gain (Gs), controller gain (Gc), and valve gain (Gv). Tuning the loop means that if our goal is quarter-amplitude damping, we adjust the controller so that the loop gain will be about 0.5. All gains put together are called the Total Process Gain (TPG):

Loop Gain = (Gp)(Gs)(Gc)(Gv) = TPG ≈ 0.5 Linear valve application If the TPG = (Gp)(Gs)(Gv), is more or less constant and does not change much with the process load, linear valves should be used. In a linear, constant gain valve, a 1% change in lift results in a 1% change in flow (Gv = 1.0). Linear valves are acceptable if TPG = (Gp)(Gs)(Gv) ≈ 0.5 to 2.0, as the load varies between its minimum and maximum limits. Linear valves are used in most process applications except temperature control and heat transfer. See the figure to the right. If the process is nonlinear (Gp varies with load), the product of the loop gain (Lg) should be held more or less constant by compensating for the variation in Gp by using a non-linear valve with inverse Gv non-linearity.

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Non-Linear Valve applications If the valve gain rises as the valve opens, its characteristic is called equal percentage; if its gain drops as it opens, it is called quick-opening. Special, custom-made valves can provide other non-linearities, for example, characterized v-ball valves have gains that are the inverse of the pump curves. Therefore, compensation is provided by using an inverse valve characteristic (Gv = 1/Gp), so that the installed characteristics of the total process will be more or less linear (TPG ≈ 0.5 to 2.0). Naturally, Gv can never be the exact inverse of Gp, but as long as the selected valve characteristic keeps the TPG within 0.5 and 2.0, instability and limited cycling can usually be avoided by good controller tuning (assuming TPG = 1.0 when adjusting Gc).

Process Signal Linearization The installed flow characteristic of a control valve directly affects the process gain. It is essential that the installed characteristic is linear. In the figure to the right, look at the install characteristic, it can be seen that the process gain is constant, regardless of the controller output. If the installed gradient of the curve varies by more than a factor of two, control loop performance will be noticeably affected. This means the controller has to have different tuning parameters for different ranges in the controller output. If nothing is done to linearize the valve, the controller will have to be detuned to accommodate the maximum process gain. This leads to sluggish control loop response over much of the valve’s operating range. A nonlinear flow characteristic should be linearized to obtain good control performance throughout the valve’s s operating range. This is done with a linearizer (also called a characterizer). The linearizer is a control block, function generator, f(x) curve, or a lookup table, placed between the controller and the valve (see the figure below). Although the linearization can be done in a digital positioner, the DCS/PLC is the best location for it. This allows replacement of the positioner without having to reprogram the linearization curve in the new positioner.

Linearizing a Nonlinear Valve Characteristic

How a Linearizer Works

Linearization is done with an X-Y curve or function generator that is configured to represent the reciprocal (inverse) of the control element’s flow curve, see the figure above to the right. To design the linearizer, you have to first determine the flow characteristic curve of the valve operating in the actual process. For this you should take readings of the flow or process variable (PV) and controller output (CO or C) under steady-state conditions at various controller output levels. You need a minimum of three pairs of data from a closed loop process response curve. More pairs of data would provide a much better response curve for characterizing a nonlinear relationship. Make sure you span the entire operating range of the controller output, and try to obtain readings spaced equally across the controller output span. You can do process tests to obtain these values, or examine

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the data from your process historian. Then convert the process variable data from engineering units to a percentage of full scale of the measurement. Sort the data pairs in ascending order and enter them into a function generator. The PV readings in percent become the X values (input side) and the CO readings in percent become the Y values (output side). Include a zero (0, 0) point if you don’t already have one in your dataset and be sure to estimate a full span (100, Y) point if you don’t have one. Also, if your valve opens as the CO decreases, your Y column will obviously have to reflect this.

Linearizing of the signal is typically seen in controllers, but some valve positioners and transmitters can have an 8- or 16-segment curve to correct for a non-linear measurement and then send the input signal to the DCS or PLC. The points are fitted by a curve and the output signal is interpolated between preset entered points. This is popular in digital valve controllers and transmitter of nonlinear measurements, such as radiometric or Gama radiation transmitters for levels or thickness, as well as in power monitoring such as in a GE Multilin power monitor for compressors and very large motors.

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Signal Filtering in Process Control Signal noise is generated due to pulsating characteristics of process control applications, such as fluctuations in the process streams comprised of liquids, gases, powders, slurries, and melts. These noises can be generated by pressure pulsations from the design of pumps, or sloshing in agitated tanks, or cavitation of fluids. The derivative mode of a PID controller, rate action, can cause the noise in the measured process variable (PV) and make the controller output (CO) become erratic. Noise in the PV will be amplified by the controller output (CO) signal and will produce “chatter” in the final control element. This extreme control action will increase the wear on a mechanical final control element, such as a valve, leading to increased maintenance and making it harder to stabilize the process. This higher frequency noise must be filtered out. First look into the transmitter and the process equipment for a solution. If the noise cannot be reduced, a filter must be applied to the process variable and or controller signals.

Appling Signal Filters External Filters in Control There are three popular places to put external filters in the feedback loop. By “external,” we mean that the filters are designed, installed ,and maintained separately from the controller.

Internal Filters in Control For feedback control, filtering need only be applied to the signal feeding the derivative term. As stated before, noise does not present a problem for proportional and integral action. These elements will perform best without the delay introduced from a signal filter. First Order Filter

The Derivative Term of the PV Filtered

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Plot of the Process Variable Signal Filtered The plot below shows the random behavior of a raw (unfiltered) PV signal and the smoother trace of a filtered PV signal.

Filter Time Constant and Sample Time From the plot above it can be seen that the derivative mode would add to the output tremendously, without filtering. It can be seen the derivative mode (rate action), would see a gain of about 10/1 compared to 0.5/1 in the signal filtered. To select a filter time for attenuation of noise or to eliminate the noise in the process signal (PV) signal, we would take the reciprocal of the angular frequency, 2 Hz or 2 (cps) , of the noise signal and select a filter time constant that is equal to or greater than the time constant of the corner frequency. For the first order filter, we must pick a corner frequency ( f C ) that is smaller or less than that of the frequency of the noise we wish to attenuate. This will allow the lower frequencies of the process signal (PV) to pass through the filter to the controller amplifier section, allowing the system to respond to the lower frequency upsets in the system. Remember that the time constant of the corner frequency is:

Tc 

1 2 f c

The time constant and frequency as used in the first order filter:

Tc * 2 f c  1 where   Tc & S  c  2 f c used in the equation for 3dB  0.707 

1 12   2 f C TC 

2

1 1  S

where TC * 2 f C  1

It can be seen in the transfer function for the first order filter: at corner frequency the noise signal will be attenuated to -3dB or 70.7%. All frequencies above or greater than corner frequency will be drastically attenuated or fall off in amplitude ratio. The trick here is to pick a frequency as low as can be tolerated and still keep the process control system responsive.

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If you do not understand how the first order filter works, review the section in this manual Review of Frequency Response Fundamentals.

 1  Signal in *    Signal out  1  St  The sampling theorem states the sampling time should be at least twice the highest frequency of the process signal. If the process signal was 10 seconds, the process frequency is (0.1 cps) = (1/10 sec). The sampling frequency should be two times the process signal frequency to make the system responsive. So 2 * 0.1 = 0.2 cps; therefore, the maximum sample time should be 1/0.2 cps = 5 seconds.

Example of Filter Time Selection The process signal has a noise frequency of 5 cps (cycles per second). The process signal has periods of 10 seconds or greater. Make the acceptable choice between the time constant for the filter and the sample time for the DCS. Remember, the smaller the DCS sample time the better the system response. Choose from the selections below: Corner Frequency fC a. b. c. d. e.

10 Hz 5 Hz 2 Hz 1 Hz 0.5 Hz

(62.8 rads/sec) (31.4 rads/sec) (12.56 rads/sec) (6.28 rads/sec) (3.14 rads/sec)

Filter Time Constant Tf (sec)

Sampling Time TS (sec)

0.016 0.032 0.080 0.159 3.140

0.5 1 5 8 10

Attenuation of 5 Hz noise -0.98 db -3.01 db -8.64 db -14.14 db -39.88 db

The best answer here is (c).   





Choice (a.) will never attenuate the noise signal. The filter is low pass, so the noise is passed. Choice (b.) the corner frequency is the noise frequency, so 70.7 % of the noise will still pass. The DCS scan time is acceptable because it is smaller than the required 5 second period for samples. Choice (c.) is the best answer; the noise will be attenuated by 63.02%. Only 36.98% of the 5 Hz noise in the process variable signal (PV) will pass to the controller and the DCS scan time is still fast enough to respond to the 5 second recommended sample time period of the process. Choice (d.) is acceptable, the noise will be attenuated by 80.36% of the 5 Hz noise in the process variable signal (PV), but the DCS scan time is not fast enough to respond to the 5 second recommended sample time period of the process. Choice (e.) will work but the DCS scan time is on the borderline of seeing the process upset and being able to respond. Low frequency oscillations will be filtered out. If the process was to cycle at a period of say 6 or 8 seconds, the DCS will not be able to respond to that upset and the system will become unresponsive and possibly unstable.

Choice C: The noise to be filtered is 5 Hz or 5 cps and filter time constant = 0.080 seconds:

Gn  Gain or Attenuation of the signal by the first order filter

Gn 

1 1   2 5 0.080  2

2

= 0.3699 or 36.99% signal let-through

db = 20 log Gn = -8.64db

If the fundamental signal frequency of 8 Hz or 8 cps and a filter time constant = 0.080 seconds:

Gn 

1 1   2 8 0.080  2

2

= 0.2414 or 24.14% signal let-through

db = 20 log Gn = -12.34db

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DCS/PLC Sample and Scan Time Consideration Sampling time If the sampling time is too large (long time between samples), oscillations in the process may not be detectable. On the HMI, the process may look fairly stable when, in reality, the process is fluctuating quite rapidly. This can lead to bad product that may not meet specifications. On the other hand, if the sample time is too small (short time between samples), you can read and respond to unnecessary process noise which can also be a waste of processor time that may be dedicated to more critical processes. The figure below shows various frequencies that may be riding on the process variable input signal. If the sample time is too low or too slow; the higher frequencies (the oscillations in the process or upsets), may not be detected. Notice how the higher frequencies look as if they are 1 Hz oscillations at a sample time of 0.25 second intervals. This noisy process will plot as a fairly smooth trend graph on the operator’s HMI.

Time per scan cycle Most DCS control systems allow for vector programming. The time required for reading and writing each individual input or output can be defined. With PLC control systems, all inputs and outputs are read at the same time in sequence. This is called the scan cycle. First the inputs are read and then the outputs are written. You must be aware of the time necessary for safe reading and writing of all inputs and outputs. The PLC scan time may need to be adjusted, so critical process updates are not missed or skipped over.

Another thing to consider is using multiplexers in DCS and SCADA systems. They will require much more time to gather and update their process variables into the words of the DCS or PLC. Multiplexers are typically used on slow process variables, such as thermocouples, for taking multiple readings, such as the temperature over the length of a heater or distillation column. It is important to consider the slots that are filled with I/O cards in a DCS system, such as the Foxboro I/A DCS system. Just because there are slots available, it does not mean they can be used. The fieldbus controller for communications can only process and communicate so many words in time. The amount of words per card varies. You must count the total words required for all cards to determine the maximum

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card population per rack.

Tuning of Process Controllers Many undergraduate engineering programs teach the Ziegler-Nichols tuning methods, developed by John G. Ziegler and Nathaniel B. Nichols in the 1940s. This tuning method has a large controller gain and short integral time, and sometimes creates process oscillations, which are not good for most chemical engineering applications. As a result, many process control engineers resort to tuning by feel, individual control loops are tuned as fast as possible without disrupting the upstream and downstream control loops. However, by tuning only individual loops, the overall process performance and the ability to recover from disturbances are reduced. When a process has been tuned by feel, console operators often need to put controllers into manual operation to settle the process down after a major process disturbance. Automatic process control attenuates disturbances and maintains control of the process variables to match the desired set point; appropriate tuning enables this capability. This section describes process controller basics and details a step-by-step process for control loop tuning as recommended by Tim Olsen and Norman Ito of Emerson Process management. Process controllers can be tuned in two ways, open loop and closed loop. In open loop the controller is put into manual mode, opening the measurement feedback loop. A change is made in the output to the final correction device and a process reaction curve is read to tune the controller. In closed loop the controller uses the feedback signal in automatic mode. Gain is increased until a sustained oscillation is achieved. The plot of the oscillation is then used to retrieve the tuning parameters. First we will look at the Ziegler-Nichols tuning methods, which will more than likely be presented on the CSE examination, and then we will look at more advanced methods of tuning a control loop as taught by Emerson Process Management. They will be the Integral Criteria Method and LAMBDA tuning methods. Tuning We will now look at two different methods for tuning a controller, the Ultimate Gain (Continuous Cycling), and Process Reaction Curve (Step Response) methods. We will use the Ziegler-Nichols method but the Cohen-Coon or Integrated Absolute Error method could be used instead.

Closed Loop Tuning of the Controller Tuning based on the ultimate gain method Essentially, the tuning method works by oscillating the process. Turn off the integral mode or set time to zero (0), and turn off the derivative mode. Increase the gain of the controller and make a slight set point change. Repeat the process and gradually increase the gain of the controller each time, until a sustained oscillation is achieved as shown in the following figure. This is called the ultimate gain (Ku). It is the gain of the controller necessary to make the process sustain oscillation. The proportional band gain (Pu) is the reciprocal of the ultimate gain (Ku).

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Tune the controller by entering the new Ziegler-Nichols values from the calculations in Table 8 below. The table values are to be entered as gain. If you need to convert gain to proportional band, then Pu=1/Ku and Ku=1/Pu. If Pu is used for the controller, then convert back to proportional band after applying the table calculations. Proportional band = 1/Gain

Gain = 1/Proportional band

The period or time constant, equals Tu in minutes. The time calculation will be entered as minutes per repeat for integral time and derivative time as minutes. Remember when entering the integral time: Minutes per repeat = 1/ Repeats per minute Repeats per minute = 1/ Minutes per repeat Proportional band is typically displayed as %, for example: 0.50 Kc = 200% PB, 2.00 Kc = 50% PB

Example: Tune Using Ultimate Gain (continuous cycling) Period Time TU: 12 minutes

Gain Ku: 2.2

Note: TI  minutes per repeat

Kc  0.6Ku   0.6  2.2  1.32 T 12 TI  U   6 min 2 2 T 12 TD  u   1.5 min 8 8

Kc  standard gain of controller (output / input) Pu  proportional gain of controller (input / output) Ku  gain necessary to make the process cycle

Table 8 - Tuning parameters for the closed loop Ziegler-Nichols method Controller type

Gain, Kc

Integral Time, TI

P

0.5Ku

PI

0.45Ku

Tu 1.2

PID

0.6Ku

Tu 2

Derivative Time, TD

Tu 8

Table 9 - Tuning parameters for the open loop Ziegler-Nichols method Controller Type P

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Gain, Kc

Integral Time, TI

Derivative Time, TD

 KP 

PI

0.9  KP 

 0.3

PID

1.2  KP 

 0.5

0.5

Note: This table of tuning parameters has (  = lag time) in the equation for a lag time of 62.3% of delta process measurement, (Ѳ = Dead Time) of the process.

Open Loop Tuning of the Controller Tuning based on the process reaction curve In process control, the term ’reaction curve’ is sometimes used as a synonym for a step response curve. Many chemical processes are stable and well damped. For such systems the step response curve can be approximated by a first-order plus dead time (FOPDT) model. It is relatively straightforward to fit the model parameters to the observed step response. Look at the reaction curve below. Essentially, the tuning method works by manually causing a step change in the process. This is accomplished by putting the controller in manual and forcing an output change of the controller. Record the step change process reaction curve on the chart recorder and follow the setup instructions below.

1.

Locate the point where the curve stops curving upwards from the left and bottom and starts to complete the curve up to the right and settle at a new process measurement level. This will be about half way up the reaction curve. It is the inflection point.

2.

Draw an asymptote line tangential to the point of the inflection. Where the asymptote line crosses the bottom of the process reaction curve, the previous output is assumed to be zero (it is the measurement before the set point change was made, which is now zero to the measurement of the process change). It may be equal to 50 psi or 500 degrees, but set it to a live zero. The time between the start of the output step change and the start of the asymptote line at the live zero of the process measurement is the apparent time delay or dead time (TD) of the system. When the asymptote line reaches the steady state value of 63.2% of delta measurement, the time difference between the end of the dead time measurement (TD) and the end of the 63.2% of delta measurement, is called the time constant for the process (). Draw a line straight down from the 63.2% point to the live zero line. These are the values of ( ) the time constant of the process and (TD) the dead time of the process.

3.

The gain of the system KP (the slope of the asymptote line) is given by:

KP =

Δmeasurement Δmeasurement  Δvalve change Δcontroller output Typical Process Reaction curve for tuning controller in open loop

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Table 10 - Tuning parameters for the open loop Cohen-Coon method Controller Type

Integral Time, TI

Gain, KP

P

1    1   K P   3 

PI

1  9     K P   10 12 

 30  3  /   

PID

1  4    K P   3 4 

 32  6  /   

Derivative Time, TD

9  20  /  

13  8  /  

4 11  2  /  

Note: This table of tuning parameters has (  = lag time) in the equation for a lag time of 62.3% of delta process measurement, (Ѳ = Dead Time) of the process. Table 10 IAE1 - Tuning parameters for the Integrated Absolute Error (load change) Controller Type

Integral Time, TI

Gain, KP

  A   KC    KP

B

A

B

P

0.902

-0.985

PI

0.984

PID

1.435

TI 

Derivative Time, TD

   A   

B

  TD  A     

B

A

B

-0.986

0.608

-0.707

-0.921

0.878

-0.749

A

B

0.482

1.137

Note: This table of tuning parameters has (  = lag time) in the equation for a lag time of 62.3% of delta process measurement, (Ѳ = Dead Time) of the process. Table 10 IAE2 - Tuning parameters for the Integrated Absolute Error (set point change) Controller Type

Integral Time, TI

Gain, KP

  A   KC    KP

B

TI 

 AB

Derivative Time, TD B

  TD  A     

 

A

B

A

B

PI

0.758

-0.861

1.020

-0.323

PID

1.086

-0.869

0.740

-0.130

A

B

0.348

0.914

P

Note: This table of tuning parameters has (  = lag time) in the equation for a lag time of 62.3% of delta process measurement, (Ѳ = Dead Time) of the process .

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Example: Tuning using Process Reaction Curve (Step Response) We will use the following graph of the process reaction curve (the step response) to tune the controller for this worked example.

(See Table 9 - Tuning parameters for the open loop Ziegler-Nichols method.) Data given: Time Constant  : 8 minutes

Solve for tuning parameters:

KP 

PV % 30%   1.5 Output % 20%

Delta Output: 55%-35% = 20%

Kc 

1.2 1.2 8    2.134 KP 1.5  3 

Note: KC  controller gain setting

TI 

Dead Time Ѳ: 3 minutes Delta PV: 82%-52% = 30%

TI  minutes per repeat

TI 1  repeats per minute TD  minutes

 0.5



3  6 min 0.5

TD  0.5   0.5  3   1.5 min

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Advanced Tuning Methods for Controllers The Integral Criteria Method General Definition: An integral criterion is a performance measure that is based on the integral of some function of the control error and on possibly other variables (such as time). Response to an IAE set point change

Response to an IAE load change

The integral criteria method is an open loop method that calculates the controller tuning parameters from the coefficients in a time-constant plus dead time model. The relationships provide the values of the tuning coefficients that minimize an integral criterion. Although others are available, we shall present relationships for only the following two integral criteria: 

Integral of Absolute Error (IAE) =

E

dt

0



Integral of Time and Absolute Error (ITAE) =  E t dt 0

(See Tables 10 IAE1 and IAE2 fpr tuning parameters for the Integrated Absolute Error “IAE” tuning.) formulas) Lambda Tuning Concepts Lambda tuning is a model-based method related to Internal Model Control and Model Predictive Control. The math behind it uses pole-zero cancellation to achieve the desired closed loop response. However, to apply the method you need only simple arithmetic if your process dynamics fit any of the following models: First Order Integrator Integrator, First Order Lag Integrator, First Order Lead Integrator, Non-Minimum Phase Second Order, Overdamped Second Order, Underdamped Second Order, Lead Second Order, Lead with Overshoot Second Order, Non-Minimum-Phase

The Lambda tuning rules, sometimes called Internal Model Control (IMC) tuning, offer a robust alternative to tuning rules aiming for speed, like Ziegler-Nichols, Cohen-Coon, etc. Although the Lambda and IMC rules are derived differently, both produce the same rules for a PI controller on a self-regulating process.

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While the Ziegler-Nichols and Cohen-Coon tuning rules aim for quarter-amplitude damping, the Lambda tuning rules aim for a first-order lag plus dead time response to a set point change. The Lambda tuning rules offer the following advantages: 1. The process variable will not overshoot its set point after a disturbance or set point change. 2. The Lambda tuning rules are much less sensitive to any errors made when determining the process dead time through step tests. This problem is common with lag-dominant processes, because it is easy to under or overestimate the relatively short process dead time. Ziegler-Nichols and Cohen-Coon tuning rules can give really bad results when the dead time is measured incorrectly. 3. The tuning is very robust, meaning that the control loop will remain stable even if the process characteristics change dramatically from the ones used for tuning. 4. A Lambda-tuned control loop absorbs a disturbance better, and passes less of it on to the rest of the process. This is a very attractive characteristic for using Lambda tuning in highly interactive processes. Control loops on paper-making machines are commonly tuned using the Lambda tuning rules to prevent the entire machine from oscillating due to process interactions and feedback control. 5. The user can specify the desired response time (actually the closed loop time constant) for the control loop. This provides one tuning factor that can be used to speed up and slow down the loop response. Unfortunately, the Lambda tuning rules have a drawback too. They set the controller’s integral time equal to the process time constant. If a process has a very long time constant, the controller will consequently have a very long integral time. Long integral times make recovery from disturbances very slow. It is up to you, the controls engineer, to decide if the benefits of Lambda tuning outweigh the one drawback. This decision must take into account the purpose of the loop in the process, the control performance objective, the typical size of process disturbances, and the impact of deviations from the set point. Below are the Lambda tuning rules for a PI controller. Although Lambda / IMC tuning rules have also been derived for PID controllers, there is little point in using derivative control in a Lambda-tuned controller. Derivative control should be used if a fast loop response is required, and should, therefore, be used in conjunction with a fast tuning rule (like Cohen-Coon). Lambda tuning is not appropriate for obtaining a fast loop response. If speed is the objective, use another tuning rule. To apply the Lambda tuning rules for a self-regulating process, follow the steps below: 1. Do a step-test and determine the process characteristics a) Place the controller in manual and wait for the process to settle out. b) Make a step change in the controller output (CO) of a few percent and wait for the process variable (PV) to settle out. The size of this step should be large enough that the PV moves well clear of the process noise/disturbance level. A total movement of five times the noise/disturbances on the process variable should be sufficient. c) Calculate the process characteristics as follows:

Process Gain (KP) KP = change in PV [%] / change in CO [%] Dead Time (Ɵ) Note: Make this measurement in the same time-units your controller’s integral mode uses. For example, if your controller’s integral time is in minutes, use minutes for this measurement.

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Find the maximum slope of the PV response curve. This will be at the point of inflection. Draw a line tangential through the PV response curve at this point. Extend this line to intersect with the original level of the PV before the step in CO. Take note of the time value at this intersection. Ɵ = time difference between the change in CO and the intersection of the tangential to PV level change the time constant tau Calculate the value of the PV at 63.2% of its total change. On the PV reaction curve, find the time value at which the PV reaches this level. The time constant tau () equals the time difference between the intersection at the end of dead time and the PV reaching 63.2% of its total change. Note: Make this measurement in the same time-units your controller’s integral mode uses. For example, if your controller’s integral time is in minutes, use minutes for this measurement. d) Repeat steps b) and c) two more times to obtain good average values for the process characteristics. If you get vastly different numbers every time, do even more step tests until you have a few step tests that produced similar values, then use the average of those values. Step Test for Lambda Tuning 2. Pick a desired closed loop time constant (cl) for the control loop A large value for  will result in a slow control loop and a small value will result in a faster control loop. Generally, the value for  should be set between one and three times the value of tau. Use ( = 3 *  to obtain a very stable control loop. If you set  to be shorter than  the advantages of Lambda tuning listed above soon disappear. 3. Calculate PID controller settings using the equations below

τ K P  λ+ θ 

Controller Gain (Kc)

Kc =

Integral Time (Ti)

Ti = tau ( τ )

Derivative Time (Td)

Td = zero

Important Notes!  

 241

The tuning equations above are designed to work on controllers with interactive or non-interactive algorithms, but not controllers with parallel (independent gains) algorithms. The rules calculate controller gain (Kc) and not proportional band (PB). PB = 100/Kc. The rules assume the controller’s integral setting is integral time Ti (in minutes or seconds), and not integral gain Ki (repeats per minute or repeats per second). Ki = 1/Ti.

Example Reactor Ratio Timing When a facility implements a ratio control on the DCS, depicted in the figure below, the assumption is that the ratio will be maintained consistently. However, there are inherent differences in control valve characteristics based on valve type (e.g., a globe valve has a wider range of process gam than a butterfly valve). Depending on where the control valve is operating, the initial response of each valve can be very different when the set point is changed. In the control loop below, Ziegler-Nichols tuning was performed on two ratio-controlled flow loops. The loop for Component A uses a 2-in. equal-percentage control valve, and the loop for Component B has a 3-in. linear control valve. The graphs on the left are the flow set point changes. The graphs on the right are the total of ratio components (32% B) + (68% A) = 100% product. When the overall process flow changes, the change in ratio can vary by as much as 10%. This can result in lower yield of the desired product and higher yield of undesired side reactions. If both controllers are tuned with the same lambda value, any change in demand flow will result in both upstream reagent flows reaching both new set points at the same time. The result is that the ratio of components remains the same regardless of process demand flow changes!

If Ziegler-Nichols tuning is performed on two ratio-controlled flow loops, when the overall process flow changes, the change in ratio can vary by as much as 10%.

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If the flow controllers are tuned with the same lambda value, a disturbance in the process flow will result in the same change for both flow controllers. That way, both loops will reach their set point value at the same time. Summary Lambda Tuning Rules The tuning constants are calculated from formula developed by Chien: Self-regulating process:

KC 

τ

KP   + θ 

Ti   , Td  0

Integrating process:

KC 

2 + θ KP   + θ 

Ti  2 + θ, Td  0

IMC Tuning Method Lambda tuning is an example of internal model control (IMC) tuning. It is developed using a technique known as direct synthesis. It can be applied to higher order processes and to all types of controllers. The principle is to synthesize a controller that will respond to a SP change according to a defined trajectory. However the result may not have the form of the PID algorithm and so approximations have to be made. The IMC function block can be used in place of a PID function block with the advantage over the PID control variable when controlling processes with large dead times. For an integrating process type (such as level control and position control), an internal non-integrating model is used to approximate the integrating process. The Factor parameter is used to convert the identified integrating-process model to a non-integrating internal model that is used for the CV (control variable) calculation. This is necessary to provide for stable IMC execution. The value of  (lambda) required to give a required MV overshoot (e.g., 15%) varies as the

 ratio varies. 

This is the desired time constant of the process response to a SP change and gives the engineer the ability to make the controller more or less aggressive. Table 10 IMC - IMC Tuning Formula (Internal Model Control) Process Type

Self-regulating

Integrating

KC

TI

TD

KC

PID (non-interactive)

1  KP   

  2

 2  

1 2   2 KP     2   

PID (interactive)

1  KP   



PID

1  KP   



TI

TD

2  

1 2   2 KP     2   





 2

2  1 2 2 KP      2   1 2   K P     2

2 

 2

 2

2  

Note: This table of tuning parameters has ( = lag time open loop) in the equation for a lag time of 62.3% of delta process measurement, (Ѳ = Dead Time) of the process, (λ = closed loop time constant).

243

PID Controller Models

Trial and Error Tuning Method Most plants find that the engineer or technician will tend to tune a control loop by “feel” or trial and error. They tune the loop by the Ziegler-Nichols equations and then they will fine tune the controller by nudging the parameters for the proportional, integral, and derivative. Dead Time and PID Control The best way to get better control of a dead time process is to reduce the dead time. A PI controller with proper tuning gives a fast, stable response and it can be adaptive. There are some other tricks that can help the response. For example applying a small filter to the process variable can smooth the response. Also if the process has a small lag, you can use a little derivative very carefully. For a process with a larger lag, using derivative can usually help response. The optimal tuning of a PI controller for a dead time only process can be tuned as follows: Controller gain = 0.3 / (process gain) Integral time = 0.42 * (process dead time)

PID Tuning Video - Parameters in Action If the PID tuning parameters video does not run in your PDF viewer, then click the button below to run the MP4 video from the official web site: http://learncontrolsystems.com/pid_tuning.mp4.

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Process Characteristics from the transfer function We will now look at the controller and control loop characteristics. Mathematically we will describe the response of a control loop and calculate the overshoot and damping of a typical control loop. If you do not understand what a transfer function is or where it comes from, refer to the section of this manual Review of Feedback Control Fundamentals. It will explain how a feedback control loop works, the mathematics and the calculated output will be based on the closed loop and open loop system gain. We will derive a block diagram of the transfer function. If you do not understand frequency response and what it means or where the transfer function comes from, refer to the section of this manual Review of Frequency Response Fundamentals. It will cover how the transfer function is derived, how the signal is attenuated and phase shifted, and how the system response is plotted, so you may understand what is happing in the system. First an electrical RC circuit is introduced and the characteristics are discussed, how a varying frequency changes the reactance of the circuit. Then a hydraulic circuit is discussed, how a constant capacitance with a varying valve position changes the frequency of tank head in time. A varying time constant of RC also exists. It is a change of the valve position multiplied by the capacitance of the system. To the right is a graph showing a typical controller response to a set point change. Most engineers use 0.25 amplitude damping for control of loops in the process industry. Let us find out how to solve for the abovementioned criteria.

Poles, Zeros, and Dampening from the Transfer Function When the pole is rising upward, the output is trying to go to infinity and the zero is trying to pull the output back down to zero output. Example, if you define “impedance of the circuit” as the transfer function for the plant, then, Z(s) = N(S) / D(S). This is just a way of saying; the function has a numerator and denominator, both of which depend on "S", some frequency. So, clearly, if N(s) goes to zero, the transfer function Z(s) will go to zero. If the D(s) goes to zero, the transfer function Z(s) will go to infinity. This means the impedance of the circuit varies at different frequencies and has phase shifts and oscillations and tends to resonate at the pole frequency. When “s” (the frequency) goes to zero, we have only a pure DC gain and a steady state output for control.

245

Find the Poles from the Function Equation given:

Find Poles:

G(s)=

n2 s 2  2n s  n2

p1 ; p2 

G(s)=

25 s  5s  25

p1 ; p2 

2

Pole1: -2.5+j4.33

p1 ; p2 

b  b 2  4 AC 2 5  25  4  25  2 5 

25  100 2

Pole2: -2.5-j4.33

 2.5  j 4.33

Find the Damping from the Function Equation given:

G(s)= G(s)=

n2 s 2  2n s  n2 25 s  5s  25 2

  Damping Ratio Damping: 0.5

Solve for the equation:

s 2  5s  25

s 2  2n s  n2 ; n  25 2n s  5s



5 2n

;

5 2 25



5  0.5 10

We will now calculate the rise time, natural frequency, and the settling time. We will refer to the graph to the right and the previously used graph for the peak amplitude designations. Notice the rise time in the graph on the right. It rises in a vertical line from 10% to 90% of steady state value. This is the definition of rise time. Notice the step response in the graph on the right. It rises in a vertical line from 0% to 63.2% of peak value. This is the definition of step response time. The time constant will be the step response time minus the dead time or lag time.

246

Find the Time Constant Data given

Solve for time constant:

Step response time: 6 seconds Dead time: 1 second

  Tsr  Td   6 1   5 seconds

Find the Period Data given:

Solve for period:

Step response time: 6 seconds Dead time: 1 second Time Constant: 5 seconds Damping: 0.5

P

P

2 1 2 6.28  5  1  0.52

P  32.26 seconds

Find the Time Constant from the Period Data given:

Solve for time constant from period:

Period: 36.26 seconds Damping: 0.5



1  2 P 2



1  0.52 36.26 6.28

  5 seconds

Find Overshoot and Peak Value Process variables given: A% = 50 PSI; ζ (dampening) = 0.5

The percent overshoot and peak is:

The first overshoot is:

A%  100e 0.5

A%  100e

A%  100e1.57 A%  100e1.812

1 2

The second overshoot is:

C %  100e3

247

1 2

10.52 0.75

A%  100  0.163 A%  16.3% 50 psi  0.163  8.15 psi overshoot 50 psi  8.15 psi  58.15 psi peak

Block Diagram Algebra Simplification Method Original Block Diagram

Equivalent Block Diagram

248

Example of Block Diagram Algebra Reduction This may be on the CSE exam. Start at figure (a), the original multivariable diagram, and simplify.

Figure (a)

Figure (b)

Figure (c)

Figure (d)

Figure (e) 249

Nyquist Stability Criterion This may be on the CSE exam. Most closed-loop systems are open-loop stable and do not have any pole (open-loop pole) in the right half of the s plane. Closed-loop systems that are stable will not have any root in the right half plane. The Nyquist diagram of an open-loop stable system does not encircle the (–1, j0) point. Note: The curve cannot encompass the stability point (-1, j0) in the polar plot or the system will become unstable. This can be seen in the last polar plot below. Encompassing the phase margin point (1