Process Control for Pumps and Compressors (Advances in Industrial Control) 3031431219, 9783031431210

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Advances in Industrial Control

Steve S. Niu

Process Control for Pumps and Compressors

Advances in Industrial Control Series Editor Michael J. Grimble, Industrial Control Centre, University of Strathclyde, Glasgow, UK Editorial Board Graham Goodwin, School of Electrical Engineering and Computing, University of Newcastle, Callaghan, NSW, Australia Thomas J. Harris, Department of Chemical Engineering, Queen’s University, Kingston, ON, Canada Tong Heng Lee , Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Om P. Malik, Schulich School of Engineering, University of Calgary, Calgary, AB, Canada Kim-Fung Man, City University Hong Kong, Kowloon, Hong Kong Gustaf Olsson, Department of Industrial Electrical Engineering and Automation, Lund Institute of Technology, Lund, Sweden Asok Ray, Department of Mechanical Engineering, Pennsylvania State University, University Park, PA, USA Sebastian Engell, Lehrstuhl für Systemdynamik und Prozessführung, Technische Universität Dortmund, Dortmund, Germany Ikuo Yamamoto, Graduate School of Engineering, University of Nagasaki, Nagasaki, Japan

Advances in Industrial Control is a series of monographs and contributed titles focusing on the applications of advanced and novel control methods within applied settings. This series has worldwide distribution to engineers, researchers and libraries. The series promotes the exchange of information between academia and industry, to which end the books all demonstrate some theoretical aspect of an advanced or new control method and show how it can be applied either in a pilot plant or in some real industrial situation. The books are distinguished by the combination of the type of theory used and the type of application exemplified. Note that “industrial” here has a very broad interpretation; it applies not merely to the processes employed in industrial plants but to systems such as avionics and automotive brakes and drivetrain. This series complements the theoretical and more mathematical approach of Communications and Control Engineering. Indexed by SCOPUS and Engineering Index. Proposals for this series, composed of a proposal form (please ask the in-house editor below), a draft Contents, at least two sample chapters and an author cv (with a synopsis of the whole project, if possible) can be submitted to either of the: Series Editor Professor Michael J. Grimble: Department of Electronic and Electrical Engineering, Royal College Building, 204 George Street, Glasgow G1 1XW, United Kingdom; e-mail: [email protected] or the In-house Editor Mr. Oliver Jackson: Springer London, 4 Crinan Street, London, N1 9XW, United Kingdom; e-mail: [email protected] Proposals are peer-reviewed. Publishing Ethics Researchers should conduct their research from research proposal to publication in line with best practices and codes of conduct of relevant professional bodies and/or national and international regulatory bodies. For more details on individual ethics matters please see: https://www.springer.com/gp/authors-editors/journal-author/journal-author-helpdesk/ publishing-ethics/14214.

Steve S. Niu

Process Control for Pumps and Compressors

Steve S. Niu Idmation Houston, TX, USA

ISSN 1430-9491 ISSN 2193-1577 (electronic) Advances in Industrial Control ISBN 978-3-031-43121-0 ISBN 978-3-031-43122-7 (eBook) https://doi.org/10.1007/978-3-031-43122-7 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

To my wife, Min, whose unwavering love, patience, and support have been the driving force behind my pursuit of knowledge and the completion of this book.

Series Editor’s Foreword

Control engineering is viewed rather differently by researchers who produce general theories and engineers who must design, calibrate, implement, and maintain industrial control systems. Researchers often develop algorithms for control problems with a well-defined mathematical basis; engineers have more immediate concerns over the limitations of equipment, quality of control, safety, security, and system downtime. The monograph series Advances in Industrial Control (AIC) attempts to bridge this divide by encouraging the consideration of advanced control techniques when they offer real benefits. The rapid development of new control theory, techniques, and technology has an impact on all areas of engineering. This series focuses on applications of advanced control that may even stimulate the development of new industrial control paradigms. This is desirable if the different aspects of the “control design” problem are to be explored with the same dedication that “analysis and synthesis” problems have received in the past. The series enables researchers to introduce new ideas motivated by challenging problems in the applications of interest. It raises awareness of the various benefits that advanced control can provide at the same time as acknowledging the challenges that can arise. This AIC monograph was produced by Steve S. Niu who previously contributed to the series with the text Process Control - Engineering Analysis and Best Practices (978-3-030-97066-6). This new volume is concerned with two of the most important components in a process plant, namely, pumps and compressors. The topic is introduced in Chap. 1, including an overview of equipment and some discussion of practical aspects. Chapter 2, on the characteristics of pumps and compressors, introduces topics needed to understand and model these components and covers problems such as surge in compressors. Chapter 3 considers the use of these components in the wider system of the process plant and discusses their operating characteristics that are important for control design. Chapter 4 is concerned with the control strategies that can be applied

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including so-called “Protective Control” that prevents a machine from violating operating limits. If the regulatory control fails to hold the plant at the setpoint, the protective controller should respond quickly to bring the operating point back within the operating envelope. Anti-surge control is an example. Chapter 5 discusses coordinate systems and various approaches to defining surge indicators that are needed for online control, including the anti-surge control application. Chapter 6, on basic control systems, describes practical solutions that are tailored to the application. Chapter 7, on advanced control solutions, includes load-balancing control for compressor trains. The problem of complexity—a significant problem in real systems—is discussed. Integrated control design and feedforward control are covered, as is multi-machine optimization. A plant-wide control example is provided involving an integrated oil-and-gas production facility. The final chapter, Chap. 8, on the commissioning, startup, and monitoring of the process control solution, concerns an area often neglected in more academic texts but very important in a real industrial process. This should be a very useful text for anyone working on real process plant controls. It should be valuable to process plant engineers and managers, researchers in process control, and to engineering students looking for a future in the chemicals, petrochemicals, or pharmaceutical industries. Glasgow, UK July 2023

Michael J. Grimble

Foreword

This is the most in-depth and insightful book on the subject I have ever read—on all fronts and is most likely unique. Despite the complexity of the subject (and it is very complex on many fronts!), this book is an “easy read.” The language used is very grounded, practical, and understandable, with no academic intellectualization. The descriptions are extremely well written and easy to comprehend, and the diagrams are very well presented. I really liked the approach of getting the context going with machine performance characteristics, then zooming down to the basic control levels, then progressively broadening the control and safeguarding scopes, combining the practical with theoretical, and covering not just the technical side of things, but also the approaches and insights to the large number of side issues surrounding the discipline. These may not be appreciated initially by students of this subject until they become engaged, at which point the penny will drop (“Ah, that’s what Steve meant in Chapter x…”). The balance between the specialist, mechanical, technical, process, operational, off-normal situations, design, control, and safeguarding is great, as is highlighting the difference between vendor and client objectives. The insights, descriptions, explanations, and practical considerations given are first class—from concept through all phases to operation. It is a great achievement! I would recommend this book. Melbourne, Australia May 2023

George Prattos ex FIEAust, NER, RPEQ, FSEng (TUV), MIICA; Principal Process Control Engineer—StarOpt Controls (retired)

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Preface

Industrial operations involve the continuous processing and movement of materials through interconnected piping and equipment. Material processing is primarily performed by static equipment such as vessels, distillation columns, and chemical reactors, while rotating equipment like motors, turbines, pumps, and compressors handle material movements. Any critical equipment failure can cause partial or complete plant shutdown, resulting in significant losses ranging from thousands to millions of dollars. Furthermore, rotating equipment is a major energy consumer. According to Stoffel (2015), Electric Motor-Driven Systems (EMDS) account for 43–46% of global electricity consumption, with compressors, pumps, and fans consuming 39%, 19%, and 19%, respectively. Therefore, the safe and efficient operation of pumps and compressors is critical for process operation and has significant economic incentives. While static equipment is considered an integral part of the process configuration, rotating equipment such as pumps and compressors have received much less attention in the process control community. They are often viewed as specialized equipment requiring proprietary technology implemented by dedicated specialists from equipment manufacturers or their partners. As a result, the control of rotating equipment is usually excluded from mainstream process control discussions and outside the job scope of process control engineers. Rotating equipment control system is hosted in dedicated hardware separate from the existing control system (e.g., DCS or PLC) and rotating equipment control scheme is treated as a black-box component in process control solution. This approach has serious drawbacks. Relying on proprietary technology, hardware, software, and services from third parties throughout the equipment control solutions’ life cycle can be very costly. For example, a compressor control malfunction may require an overseas service trip by the compressor control vendor that could take days or weeks to accomplish, resulting in multiple-week production shutdowns or deferments. However, with an open-platform solution, a site instrument technician may pinpoint the problem to a simple instrument failure and fix it in a few hours. The current trend is to migrate from equipment-centric solutions to processcentric solutions and from proprietary to open platforms, which will positively impact xi

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equipment control. The recent acquisition of Compressor Control Company (CCC) by Honeywell marks a significant shift away from proprietary technology and closed systems toward open-platform solutions. This move is expected to drive innovation and efficiency in the compressor control industry. Process control engineers will play a crucial role in this migration. Moreover, the equipment-centric control approach focuses on protecting the equipment and pays much less attention to its integration with process control, resulting in lower reliability and efficiency. For instance, centrifugal pumps and compressors’ most crucial control requirements are capacity control and anti-surge control. Capacity control is a requirement at the process level and anti-surge control at the equipment level. Process control requirements dictate the capacity control design, which interacts with anti-surge control for improved performance. The best efficiency can only be achieved from a sound overall process control strategy, which determines how the equipment should be controlled. A black-box approach for antisurge control renders this integration and optimization difficult, if not impossible. A process-centric solution is thus required, starting with a holistic view of the process flow and ensuring the overall stability and efficiency of the control strategy. A sound overall control strategy provides favorable operating conditions for the equipment. As a result, a process-centric solution tends to be more reliable and efficient than an isolated equipment-centric solution and is typically also more operator-friendly. Although a pump or compressor works by different principles than a distillation column or chemical reactor, they are not more complex from the process control perspective. The characteristic information required by control design common to all processes and equipment, such as the supply-and-demand relationship, causeand-effect relationship, and dynamic response behavior, can be extracted using the same skills and procedures as with any other complex process. Therefore, pump and compressor control can be treated as a standard process control problem, designed with standard technologies, and implemented on standard control system hardware and software. Once implemented, the final control solution can be operated by the same operators and maintained by the same maintenance team as other standard process control solutions. Despite the critical role of process control in pumps and compressors, books providing systematic discussions on this topic are scarce. As noted in the preface of Elliott and Bloch’s 2021 book on compressor technology, “… changing technology made some books outdated, … the existing books on compressor technology did not at all, or did not sufficiently, delve into the details of compression technology of interest to us in 2020.” The same is true for books on compressor control. This book provides a comprehensive guide to designing and operating integrated control solutions for processes that involve pumps and compressors. Its goal is to equip readers with the essential knowledge and skills from the machine characteristics and overall control strategy to detailed design and best practices. This book is titled Process Control for Pumps and Compressors rather than Pump and Compressor Control to emphasize that pumps and compressors are a part of the overall process flow and should not be treated in isolation when it comes to control.

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This book aims to equip readers with the following knowledge and skills for designing and operating integrated control solutions for processes with pumps and compressors: • To provide readers with an understanding of the critical roles that pumps and compressors play in the continuous operation of oil and gas, refining, petrochemical, and chemical plants, as well as their dynamic behaviors and characteristics, including the surge and choke phenomenon that can limit the machine’s operation. • To equip readers with the ability to design and implement capacity control, antisurge control, safeguarding logic, and real-time monitoring solutions based on operating requirements, dynamic supply/demand model, cause/effect relationship, online and offline data, and close collaboration with other engineering specialties. • To enable readers to support the day-to-day operation of the in-house openplatform compressor control applications, including the ability to troubleshoot and fix common problems. • To provide readers with a basic understanding of the principles of third-party proprietary technologies to support decision-making between in-house and thirdparty solutions for new applications and when vendor support is required to troubleshoot existing third-party applications. Pumps and compressors share fundamental operating principles, and therefore their analysis and control methods are similar. This book takes a unified approach to their treatment, highlighting their commonalities and differences to help readers gain a deeper understanding of both. This book is intended for process control engineers responsible for designing and maintaining process control solutions for pumps and compressors. It can also serve as a valuable resource for undergraduate process control courses to increase their coverage on pump and compressor control. Front-line personnel such as process engineers, rotating equipment engineers, and reliability engineers who seek to better understand the perspective and requirements of process control will also find this book useful. To further aid readers’ comprehension of compressor characteristics and the design of anti-surge control, an Excel1 software tool called CPACS (Compressor Performance Analysis and Control Support) is provided as a companion to this book. This convenient tool is suitable for both learning and practical applications, as most control engineers have access to Excel on their desktops. Considering the readers’ diverse backgrounds, this book’s content is arranged in the following manner: • Chapter 1: This chapter provides readers with an overview of pumps and compressors and their critical role in the process industry, which is essential background information for process control. The chapter also highlights the basic control

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Excel® is a registered trademark of Microsoft Corporation.

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concepts and prevalent technologies, preparing the reader for the discussions in later chapters. Chapter 2: The core theory and essential knowledge related to pump and compressor characteristics, such as performance curves, system resistance, minimum flow requirements, and surge and choke phenomenon, are presented in this chapter. Due to the complex behavior of these machines and the vast information available, it is necessary to delineate control-related knowledge from other irrelevant information. This knowledge forms the basis for operation and control. Chapter 3: This chapter provides an overview of the operating requirements and control philosophy, highlighting the typical ends and means of operation and control. The requirements and principles apply to both manual operation and automatic control, serving as the foundation for the overall control strategy in Chap. 4. Chapter 4: The overall control strategy for pumps and compressors in the process control context is discussed in this chapter. While the control strategy may vary with the process configuration, the basic principles and general guidelines remain the same, which are provided to assist with detailed design. Chapter 5: The description of the behavior of pumps and compressors in practical applications differs from what are used in theoretical analysis and conceptual understanding. This chapter provides detailed discussions on common approaches to defining the surge indicators, which are essential for online control, especially anti-surge control. Chapter 6: Several typical control schemes for simple applications involving only a single pump or compressor are presented in this chapter. The intention is to demonstrate how the concept and analysis presented in Chaps. 4 and 5 are applied to real-world applications. These design examples also serve as building blocks for advanced control schemes discussed in Chap. 7. Chapter 7: Several control solutions to address more complex applications that involve multiple pumps and compressors are presented in this chapter. These examples use the basic design schemes from Chap. 6 as building blocks and follow the overall control strategy in Chap. 4 to address more complex application scenarios. Given the infinite variations in process flow configuration, the focus is on the thinking process and general methodology of analysis design. Chapter 8: This chapter presents practical considerations in implementing the process control solution in the field, including the commissioning, monitoring, and troubleshooting of the control solution. Performance monitoring and problem troubleshooting are essential aspects of daily operations. Inferential properties and exception-based monitoring are application areas that are receiving increasing attention. Appendix A: Anti-surge control is a critical part of the process control solution, and calculating the surge indicator is central to anti-surge control. While surge indicator calculation can be performed manually based on the discussions in this book, it can become extremely tedious and error prone as the problem becomes complex with a large amount of data. Software tools are typically needed to

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facilitate control design. This appendix demonstrates the work process of surge indicator calculation, with the help of the companion CPACS software tool. The first three chapters of this book require minimal background knowledge in process control. They can be helpful for engineers in various fields, including process, mechanical, instrumentation, and rotating equipment to gain a better understanding of the perspective and requirements of process control. Rotating equipment is a complex and crucial field requiring specialized engineering expertise. As a process control practitioner or researcher, it is unnecessary to have the same level of knowledge as a rotating equipment engineer. Therefore, it is essential for process control practitioners to determine the appropriate level of understanding required for their work and focus their effort on pertinent information related to process control. To this end, this book offers a balanced discussion between theory and application, with a practical-oriented theme emphasizing essential knowledge and best practices for practical applications. Diagrams and tables are used throughout the book to facilitate the discussions and enhance comprehension. Nonetheless, readers are expected to have sufficient background in several overlapping areas, including process engineering, operations, instrumentation, mechanics, and fundamental process control theory and techniques. Advanced topics are identified with a † or ‡ symbol in the section titles for easy reference. The author would like to express sincere gratitude to Prof. Deyun Xiao of Tsinghua University in Beijing and George Prattos of StarOpt Controls in Melbourne for their invaluable contribution in providing insightful feedback and proofreading the manuscript. Additionally, the author would like to acknowledge the contributions of former colleagues from multiple teams who engaged in rigorous discussions in the office and close collaboration in control rooms in designing and commissioning the many compressor control applications. Finally, the author would like to thank Editor Oliver Jackson for his unwavering dedication in guiding and shaping the manuscript with his professional expertise. Houston, USA May 2023

Steve S. Niu

Contents

1 Introduction to Pumps and Compressors . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Type of Pumps and Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 Rotating Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.2 Pumps and Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.3 Centrifugal and Reciprocating Machines . . . . . . . . . . . . . . . . 1.1.4 Fans and Blowers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Applications of Pumps and Compressors . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Liquid Pumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Gas Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Operation and Control of Pumps and Compressors . . . . . . . . . . . . . . 1.3.1 Operating Requirements and Control Objectives . . . . . . . . . . 1.3.2 Overall Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Process Control Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.4 Monitoring and Safeguarding . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Practical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Process-Centric Versus Equipment-Centric Solutions . . . . . . 1.4.2 In-House Versus Third-Party Solutions . . . . . . . . . . . . . . . . . . 1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 1 2 3 6 6 6 8 11 11 12 14 19 20 20 21 22 22

2 Characteristics of Pumps and Compressors . . . . . . . . . . . . . . . . . . . . . . . 2.1 Basic Properties of Fluids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Basic Principles of Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . 2.1.2 Basic Principles of Thermodynamics . . . . . . . . . . . . . . . . . . . 2.1.3 Gas Compression Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Liquid Transport Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Description of Pumps and Compressors . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Three Variables: Speed, Head, and Flow . . . . . . . . . . . . . . . . . 2.2.2 Two Curves: Performance and Resistance Curves . . . . . . . . . 2.2.3 One Point: Operating Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 † Other Variables and Curves . . . . . . . . . . . . . . . . . . . . . . . . . .

25 25 26 27 29 31 33 33 37 42 43

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2.3 Behaviors of Dynamic Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Relationship Among Head, Flow, and Speed . . . . . . . . . . . . . 2.3.2 † Suction and Discharge Relationship . . . . . . . . . . . . . . . . . . . 2.3.3 ‡ Euler’s Equation and Slope of Performance Curve . . . . . . . 2.3.4 ‡ System Resistance and Slope of Resistance Curve . . . . . . . 2.4 Surge and Choke Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Surge and Choke Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Surge Line and Choke Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Operating Requirements and Control Objectives . . . . . . . . . . . . . . . . . . 3.1 Operating Objectives and Requirements . . . . . . . . . . . . . . . . . . . . . . . 3.2 Maintaining the Operating Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Operating with Single Control Handle . . . . . . . . . . . . . . . . . . 3.2.2 Operation with Multiple Control Handles . . . . . . . . . . . . . . . . 3.2.3 † Capacity Turndown . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Protecting the Operating Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Operation Under Abnormal Operating Conditions . . . . . . . . 3.3.2 ‡ Flow in System Resistance Components . . . . . . . . . . . . . . . 3.4 Transitioning Between Operating Modes . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Startup of Centrifugal Machines . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Shutdown of Centrifugal Machines . . . . . . . . . . . . . . . . . . . . . 3.4.3 † Crippled Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67 67 69 69 73 76 77 77 80 82 82 85 86 87 88

4 Overall Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Overall Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 General Control Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Overall Control Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Layered and Integrated Design . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Migration from Proprietary to Open-Platform Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Regulatory Control: Capacity Control . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Capacity Control Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Process Dynamics and Cause-and-Effect Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Process Measurements and Controlled Variables . . . . . . . . . . 4.2.4 Final Control Elements and Manipulated Variables . . . . . . . . 4.2.5 Capacity Control Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Protective Control: Anti-surge Control . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Protective Control Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Process Dynamics for Operating Envelope . . . . . . . . . . . . . . . 4.3.3 Measurements and Controlled Variables . . . . . . . . . . . . . . . . .

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4.3.4 Recycle Valve and Manipulated Variables . . . . . . . . . . . . . . . 4.3.5 Protective Control Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Control Integration and Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Sequential Control: Mode Transition . . . . . . . . . . . . . . . . . . . . 4.4.2 Instrumented Safeguarding Against Failures . . . . . . . . . . . . . 4.4.3 Online Performance Monitoring . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 † Integration of Capacity and Anti-surge Control . . . . . . . . . 4.4.5 ‡ Load Balancing and Optimization . . . . . . . . . . . . . . . . . . . . . 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

107 109 111 112 112 113 113 116 119 119

5 Invariant Coordinates and Surge Indicators . . . . . . . . . . . . . . . . . . . . . . 5.1 Inlet Conditions and Invariant Coordinate Systems . . . . . . . . . . . . . . 5.1.1 API Datasheet for Compressor . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 † Impact of Inlet Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.3 Invariant Coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Equivalent Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 † Alternative Variables for Polytropic Head . . . . . . . . . . . . . . 5.2.2 † Alternative Variables for Volumetric Flow . . . . . . . . . . . . . . 5.2.3 † Equivalent Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . 5.3 Surge Reference Line and Surge Indicators . . . . . . . . . . . . . . . . . . . . . 5.3.1 Surge Reference Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Surge Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Calculation of Anti-surge Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

121 121 122 123 127 128 128 129 130 132 133 135 142 148 149

6 Basic Control Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Centrifugal Pumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Capacity Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Minimum and Maximum Flow Control . . . . . . . . . . . . . . . . . . 6.1.3 A Complete Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Centrifugal Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Capacity Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Anti-surge Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Anti-surge Parameter Calculation . . . . . . . . . . . . . . . . . . . . . . . 6.2.4 † Flowmeter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.5 Instrumented Safeguarding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.6 A Complete Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Reciprocating Pumps and Compressors . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Capacity Control for Reciprocating Machines . . . . . . . . . . . . 6.3.2 Protective Control for Reciprocating Machines . . . . . . . . . . . 6.4 Practical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Speed of Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 † Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

151 151 152 157 164 165 166 169 172 175 180 183 185 185 186 186 186 188

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Contents

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 7 Advanced Control Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Integration Between Capacity and Anti-surge Control . . . . . . . . . . . . 7.1.1 Capacity Control Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 An Unintegrated Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.3 Integrated Design of Capacity and Anti-surge Control . . . . . 7.1.4 † Integrated Design with Feedforward Compensation . . . . . 7.2 Load-Balancing Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 † Load Balancing Among Compressor Trains . . . . . . . . . . . . 7.2.2 ‡ Load Balancing Among Stages . . . . . . . . . . . . . . . . . . . . . . . 7.3 A Fully Integrated Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 A Complete Solution for Compressor Control . . . . . . . . . . . . 7.3.2 † Integration Between Control and Safeguarding . . . . . . . . . 7.3.3 A Real-World Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Multi-Machine Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 † Pumps and Compressors in Parallel . . . . . . . . . . . . . . . . . . . 7.4.2 † Pumps and Compressors in Series . . . . . . . . . . . . . . . . . . . . 7.5 Implementation Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.1 Naming Convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.2 Manual Versus Automatic Operation . . . . . . . . . . . . . . . . . . . . 7.5.3 † Controller Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

191 191 191 194 195 198 199 200 202 205 205 208 208 211 211 213 215 215 216 216 218 218

8 Commissioning, Startup, and Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Application Life Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Commissioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Factory Acceptance Test (FAT) . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Site-Acceptance Test (SAT) . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Plant Startup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 Incipient Surge Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Pre-Startup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.3 During Startup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.4 Post-Startup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Performance Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Performance Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.2 Performance Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Troubleshooting and Problem-Solving . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.1 † Surge Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5.2 † Troubleshooting of Surge Control Scheme . . . . . . . . . . . . . 8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

219 219 220 221 223 227 227 229 229 230 232 232 235 236 237 238 239 240

Contents

xxi

A Performance Analysis and Control Design with Software Tool . . . . . . . 241 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

Symbols and Abbreviations

Symbols Letters β η κ ω ρ τ A C Cv Cp D F H M N P R S T U W Z d h n r P

Impeller backlean angle Efficiency Ratio of specific heat Angular velocity Density Torque Area (m 2 ) Constant coefficient Specific heat at constant volume Specific heat at constant pressure Pipe diameter Mass flow rate Head Molecular weight (kg/kmol); Mach number Rotational speed (rpm) Pressure (kPa) Gas constant Slope Temperature Impeller tip speed Power Compressibility Orifice diameter (m) Fluid head in height (m) Polytropic exponent Radius Differential pressure xxiii

xxiv

Symbols and Abbreviations

Constants g P0 R T0

Gravitational Acceleration, g = 9.80665 m/s2 Atmospheric pressure, 101.35 kPa Gas constant, R = 8.31446 J · K−1 · mol−1 Absolute zero temperature, −273.15 ◦ C

Functions cot ln log

Cotangent Base-e logarithm (natural) Base-10 logarithm

Subscripts s d v m e p 0 r

Suction side, e.g., suction pressure Ps Discharge side, e.g., discharge pressure Pd Volumetric, e.g., volumetric flow Fv Mass, e.g., mass flow Fm Equivalent, e.g., equivalent flow Fe Polytropic, e.g., polytropic head H P Standard, e.g., standard flow F0 Reference condition, e.g., reference pressure Pr

Fonts Italics Typewriter

Used for emphasis or for special terminologies Used for tag names, DCS variables, or programming codes

Symbols and Abbreviations

Abbreviations AI AO API ARWU ASC ASCV ASME ASP AUTO BEP BHP BPD CAPEX CAS CCL CET CGC COD CPM DCS DD DP DWD E&P EOS ESD FAT FCCU FCE FEED FGS GT HMI HVAC I/O IGV ISA ISO KPI LNG MAN MCSF

Analog In Analog Out American Petroleum Institute Anti-reset windup Anti-surge Control Anti-surge Control Valve American Society of Mechanical Engineers Anti-surge Parameter Automatic Mode Best Efficiency Point Brake Horsepower Barrels Per Day Capital Expenditure Cascade Mode Capacity Control Line Cause-and-effect Table Cracked Gas Compressor Control Overview Diagram Control Performance Monitoring Distributed Control System Detailed Design Differential Pressure Deep water disposal Exploration and Production Equation of State Emergency Shutdown Factory Acceptance Test Fluid-bed Catalytic Cracking Unit Final Control Element Front End Engineering Design Fire and Gas System Gas Turbine Human–Machine Interface Heating, Ventilation, and Air Conditioning Input/Output Inlet Guide Vane Instrument Society of America International Standard Organization Key Performance Index Liquefied Natural Gas Manual Mode Minimum Continuous Stable Flow (of a pump)

xxv

xxvi

MGI MMSCMD MOC MOL NPSH NPSHA NPSHR NRV OPEX P&ID PAS PCN PFD PGC PI PID PLC PV RO SAT SCL SIS SLL SOP SRL STL VFD VRU VSGB

Symbols and Abbreviations

Miscible Gas Injection Million Standard Cubic Meters per Day Management of Change Main Oil Line Net Positive Suction Head (of a pump) Net Positive Suction Head Available (of a pump) Net Positive Suction Head Required (of a pump) Non-return Valve Operational Expenditure Piping and Instrument Diagram Process Automation System Process Control Narratives Process Flow Diagram Produced Gas Compressor Proportional–Integral Algorithm Proportional–Integral–Derivative Control Programmable Logic Control Process Variable Restriction Orifice Site-acceptance Test Surge Control Line Safety Instrument System Surge Limit Line Standard Operation Procedure Surge Reference Line Surge Trip Line Variable Frequency Drive Vapor Recovery Unit Variable-Speed Gearbox

List of Figures

Fig. 1.1 Fig. 1.2 Fig. 1.3 Fig. 1.4 Fig. 1.5 Fig. 1.6 Fig. 1.7 Fig. 1.8 Fig. 1.9 Fig. 1.10 Fig. 1.11 Fig. 1.12 Fig. 1.13 Fig. 1.14 Fig. 1.15 Fig. 1.16 Fig. 1.17 Fig. 1.18 Fig. 1.19 Fig. 1.20 Fig. 2.1 Fig. 2.2 Fig. 2.3 Fig. 2.4 Fig. 2.5

Type of rotating equipment by principle of work . . . . . . . . . . . . . Type of compressors by capacity . . . . . . . . . . . . . . . . . . . . . . . . . Reciprocating compressor and bicycle pump . . . . . . . . . . . . . . . . Example: human heart as a reciprocating machine . . . . . . . . . . . A simple pumping process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Large pumps in pipeline operation . . . . . . . . . . . . . . . . . . . . . . . . A complete surface facility with pumps and compressors (reproduced, with permission, from Niu and Xiao (2022)) . . . . . A typical gas compression process (reproduced, with permission, from Niu and Xiao (2022)) . . . . . . . . . . . . . . . . A compressor system with two compressors in parallel . . . . . . . Multi-phase depletion compressors . . . . . . . . . . . . . . . . . . . . . . . . A typical ethylene plant with compressors . . . . . . . . . . . . . . . . . . Process automation system (PAS) (reproduced, with permission, from Niu and Xiao (2022)) . . . . . . . . . . . . . . . . Closed-loop control (feedback control) . . . . . . . . . . . . . . . . . . . . A process with noise and disturbance . . . . . . . . . . . . . . . . . . . . . . Process measurement components . . . . . . . . . . . . . . . . . . . . . . . . Valve characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control objectives and constraints (reproduced, with permission, from Niu and Xiao (2022)) . . . . . . . . . . . . . . . . On/off control and PID control . . . . . . . . . . . . . . . . . . . . . . . . . . . Structure of a PID control loop . . . . . . . . . . . . . . . . . . . . . . . . . . . Layers of process safety protections (reproduced, with permission, from Niu and Xiao (2022)) . . . . . . . . . . . . . . . . Conservation of mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bernoulli’s equation for flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gas density calculation in a flowmeter datasheet . . . . . . . . . . . . . Compression cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three basic variables for pump performance description . . . . . .

2 3 4 5 6 7 7 8 10 10 11 13 14 15 16 16 17 17 18 20 26 27 30 32 33

xxvii

xxviii

Fig. 2.6 Fig. 2.7 Fig. 2.8 Fig. 2.9 Fig. 2.10 Fig. 2.11 Fig. 2.12 Fig. 2.13 Fig. 2.14 Fig. 2.15 Fig. 2.16 Fig. 2.17 Fig. 2.18 Fig. 2.19 Fig. 2.20 Fig. 2.21 Fig. 2.22 Fig. 2.23 Fig. 2.24 Fig. 2.25 Fig. 2.26 Fig. 2.27 Fig. 2.28 Fig. 3.1 Fig. 3.2 Fig. 3.3 Fig. 3.4 Fig. 3.5 Fig. 3.6 Fig. 3.7 Fig. 3.8 Fig. 3.9 Fig. 3.10 Fig. 3.11 Fig. 3.12 Fig. 3.13

List of Figures

Three basic variables for compressor performance description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Impellers and diffusers in a centrifugal machine . . . . . . . . . . . . . Three basic variables: head, flow, and speed . . . . . . . . . . . . . . . . Head and pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pump performance curve at constant speed . . . . . . . . . . . . . . . . . Pump performance curves: fixed speed versus variable speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compressor performance curves: fixed speed versus variable speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical pump curves (reproduced, with permission, from Niu and Xiao (2022)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical compressor curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Composite performance curves . . . . . . . . . . . . . . . . . . . . . . . . . . . System resistance curve and process dynamics . . . . . . . . . . . . . . Operating point on performance and resistance curves . . . . . . . . Best efficiency point and efficiency ellipse . . . . . . . . . . . . . . . . . . Cause-and-effect relationship among speed, head, and flow . . . . Flow, head, and power under affinity laws . . . . . . . . . . . . . . . . . . Impellers and Euler’s equation . . . . . . . . . . . . . . . . . . . . . . . . . . . Reverse relationship between head and flow . . . . . . . . . . . . . . . . Reverse relationship between head and flow for radial blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Basic slope” and performance curves . . . . . . . . . . . . . . . . . . . . . System resistance and process flow components (reproduced, with permission, from Niu and Xiao (2022)) . . . . . Flow and system resistances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slope of the performance curves . . . . . . . . . . . . . . . . . . . . . . . . . . Compressor surge cycle (reproduced, with permission, from Niu and Xiao (2022)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A typical compression process for upstream E&P facility (reproduced, with permission, from Niu and Xiao (2022)) . . . . . Control handles for centrifugal compressor control . . . . . . . . . . . Capacity control with centrifugal machines . . . . . . . . . . . . . . . . . Capacity control with reciprocating machines . . . . . . . . . . . . . . . Three flows in pumps and compressors . . . . . . . . . . . . . . . . . . . . Process flow, machine flow, and recycle flow . . . . . . . . . . . . . . . . Capacity control with inlet guide vane . . . . . . . . . . . . . . . . . . . . . Capacity control with centrifugal machines . . . . . . . . . . . . . . . . . A two-speed hair dryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow turndown below surge limit . . . . . . . . . . . . . . . . . . . . . . . . . Compressor operating point and envelope . . . . . . . . . . . . . . . . . . Compressor stonewall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flow through an orifice plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34 34 35 36 37 38 39 39 40 41 42 43 46 49 51 56 56 57 58 59 59 62 63 68 69 71 71 72 73 74 74 75 76 78 79 80

List of Figures

Fig. 3.14 Fig. 3.15 Fig. 3.16 Fig. 3.17 Fig. 3.18 Fig. 4.1 Fig. 4.2 Fig. 4.3 Fig. 4.4 Fig. 4.5 Fig. 4.6

Fig. 4.7

Fig. 4.8 Fig. 4.9 Fig. 4.10 Fig. 4.11 Fig. 4.12 Fig. 4.13 Fig. 4.14 Fig. 4.15 Fig. 4.16 Fig. 4.17 Fig. 4.18 Fig. 4.19 Fig. 4.20 Fig. 5.1 Fig. 5.2 Fig. 5.3 Fig. 5.4 Fig. 5.5 Fig. 5.6 Fig. 5.7 Fig. 5.8

DP versus flow in an orifice plate and head versus flow in a compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pump startup with a throttling valve . . . . . . . . . . . . . . . . . . . . . . . Trajectory of operating point during cold startup . . . . . . . . . . . . . Trajectory of operating point during shutdown . . . . . . . . . . . . . . Process flow of a 2 × 2 compressor network . . . . . . . . . . . . . . . . Layers of process safety protections for pumps and compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compressor operating point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control target and handles for centrifugal compressor control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Supply-driven versus demand-driven control . . . . . . . . . . . . . . . . Capacity control of reciprocating machines . . . . . . . . . . . . . . . . . Overall control strategy for a general E and P process, supply driven (reproduced, with permission, from Niu and Xiao (2022)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overall control strategy for a general E and P process, demand driven (reproduced, with permission, from Niu and Xiao (2022)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Supply-driven control, speed versus throttling valve . . . . . . . . . . Capacity turndown, fixed speed versus variable speed (reproduced, with permission, from Niu and Xiao (2022)) . . . . . Compressor operating envelope . . . . . . . . . . . . . . . . . . . . . . . . . . Sizing of recycle valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recycle surge volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Auxiliary performance lines for centrifugal machine control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overall control strategy for pumps and compressors . . . . . . . . . . Compressor control as multivariable control with interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unintegrated capacity control and anti-surge control . . . . . . . . . Integrated capacity control and anti-surge control . . . . . . . . . . . . Load balancing improves energy efficiency . . . . . . . . . . . . . . . . . Load balancing among parallel compressors . . . . . . . . . . . . . . . . Load balancing among compressor stages . . . . . . . . . . . . . . . . . . Compressor design conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operating scenarios on performance map . . . . . . . . . . . . . . . . . . Impact of gas molecular weight . . . . . . . . . . . . . . . . . . . . . . . . . . Polytropic head versus mass flow . . . . . . . . . . . . . . . . . . . . . . . . . Polytropic head versus volumetric flow, an invariant coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance curves under equivalent coordinate systems . . . . . . Surge line and surge reference line . . . . . . . . . . . . . . . . . . . . . . . . Surge reference line: flow versus flow squared . . . . . . . . . . . . . .

xxix

81 83 84 85 87 91 94 96 99 100

100

101 101 102 103 108 109 110 112 114 115 115 117 117 118 123 124 125 126 127 132 133 134

xxx

Fig. 5.9 Fig. 5.10 Fig. 5.11 Fig. 5.12 Fig. 5.13 Fig. 5.14 Fig. 6.1 Fig. 6.2 Fig. 6.3 Fig. 6.4 Fig. 6.5 Fig. 6.6 Fig. 6.7 Fig. 6.8 Fig. 6.9 Fig. 6.10 Fig. 6.11 Fig. 6.12 Fig. 6.13 Fig. 6.14 Fig. 6.15 Fig. 6.16 Fig. 6.17 Fig. 6.18 Fig. 6.19 Fig. 6.20 Fig. 6.21 Fig. 6.22 Fig. 6.23 Fig. 6.24 Fig. 6.25 Fig. 6.26 Fig. 6.27 Fig. 6.28 Fig. 6.29 Fig. 6.30

List of Figures

Slope of the operating point versus the slope of the surge reference line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surge reference lines with one to four parameters . . . . . . . . . . . . Compressor performance curve . . . . . . . . . . . . . . . . . . . . . . . . . . . Surge reference lines calculated with Excel . . . . . . . . . . . . . . . . . Surge reference lines calculated with CPACS tool . . . . . . . . . . . . Example of performance map . . . . . . . . . . . . . . . . . . . . . . . . . . . . A typical process control solution with a centrifugal pump (reproduced, with permission, from Niu and Xiao 2022) . . . . . . Performance curve for a centrifugal pump . . . . . . . . . . . . . . . . . . A typical process control solution for a centrifugal pump with a fixed flow setpoint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance curve for a centrifugal fixed-speed pump . . . . . . . . A cascade control scheme for a centrifugal pump . . . . . . . . . . . . Demand-driven capacity control for a fixed-speed pump . . . . . . Supply-driven capacity control with demand override . . . . . . . . A typical process control solution with a centrifugal pump . . . . Performance curve for a centrifugal variable-speed pump . . . . . A typical process control solution with a centrifugal pump . . . . Minimum recycle flow control for centrifugal pump . . . . . . . . . . Minimum and maximum flow limits for a centrifugal pump . . . A typical process control solution with a centrifugal pump with variable flow setpoint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minimum flow controller with a fixed ASP setpoint . . . . . . . . . . Minimum flow control and end-of-curve control for a centrifugal pump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Capacity control and end-of-curve control . . . . . . . . . . . . . . . . . . A complete pump control solution . . . . . . . . . . . . . . . . . . . . . . . . A simple compression process with a single-stage compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Supply-driven capacity control with throttling valve . . . . . . . . . . Supply-driven capacity control with speed . . . . . . . . . . . . . . . . . . Demand-driven capacity control with speed . . . . . . . . . . . . . . . . Supply-driven capacity control with recycle . . . . . . . . . . . . . . . . Supply-driven capacity control with demand override . . . . . . . . Anti-surge control scheme, with flow measurement on suction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anti-surge control scheme, with flowmeter at discharge . . . . . . . Anti-surge control scheme, with differential pressure DP for flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Control target and handles for centrifugal compressor control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Essential components of a control loop . . . . . . . . . . . . . . . . . . . . The compressor API design data . . . . . . . . . . . . . . . . . . . . . . . . . . Performance map for a compressor . . . . . . . . . . . . . . . . . . . . . . . .

135 141 143 146 147 148 152 152 153 154 154 155 155 156 156 157 158 160 162 163 165 165 166 166 167 167 168 168 169 170 171 171 173 174 176 176

List of Figures

xxxi

Fig. 6.31 Fig. 6.32

179

Fig. 6.33 Fig. 6.34 Fig. 6.35 Fig. 6.36 Fig. 6.37 Fig. 6.38 Fig. 6.39 Fig. 7.1 Fig. 7.2 Fig. 7.3 Fig. 7.4 Fig. 7.5 Fig. 7.6 Fig. 7.7 Fig. 7.8 Fig. 7.9 Fig. 7.10 Fig. 7.11 Fig. 7.12 Fig. 7.13 Fig. 7.14 Fig. 7.15 Fig. 7.16 Fig. 7.17 Fig. 7.18 Fig. 7.19 Fig. 8.1 Fig. 8.2 Fig. 8.3 Fig. 8.4 Fig. 8.5 Fig. 8.6 Fig. A.1 Fig. A.2 Fig. A.3

Orifice-based flowmeter datasheet . . . . . . . . . . . . . . . . . . . . . . . . Compressor curves with maximum and minimum flow lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anti-surge trip conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Segregated safeguarding and control in implementation . . . . . . . Basic capacity and anti-surge control with fixed-speed drive . . . Basic capacity and anti-surge control with variable-speed drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reciprocating machine with capacity and protective control . . . Minimizing surge volume to increase speed of response . . . . . . Surge volume with hot recycle . . . . . . . . . . . . . . . . . . . . . . . . . . . Capacity turndown for centrifugal machines . . . . . . . . . . . . . . . . Capacity turndown for reciprocating machines . . . . . . . . . . . . . . A generic 2 × 2 compression process . . . . . . . . . . . . . . . . . . . . . . A minimal control design for capacity control . . . . . . . . . . . . . . . Trajectory of operating point for a primitive capacity control design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An improved control design for capacity control . . . . . . . . . . . . . Trajectory of operating point with improved capacity control design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The split-range control in compressor capacity control . . . . . . . . An integrated capacity control solution . . . . . . . . . . . . . . . . . . . . Load of different compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load balancing for parallel compressors . . . . . . . . . . . . . . . . . . . Load balancing among compressor stages . . . . . . . . . . . . . . . . . . Load balancing among compressor stages (example) . . . . . . . . . Components in a fully integrated compressor control solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A complete control design for the 2 × 2 compression process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process overview diagram of an E&P surface facility (reproduced, with permission, from Niu and Xiao 2022) . . . . . . Plant-wide control: normal regulatory control (reproduced, with permission, from Niu and Xiao 2022) . . . . . . . . . . . . . . . . . Load distribution with two compressors in parallel . . . . . . . . . . . Pressure profile with three compressors in series . . . . . . . . . . . . . Data flow in open control loop for factory acceptance test . . . . . Data flow in closed control loop for site-acceptance test . . . . . . . Startup sequence of a variable-speed compressor . . . . . . . . . . . . Startup sequence of a fixed-speed compressor . . . . . . . . . . . . . . . Control handles for centrifugal compressor control . . . . . . . . . . . Real-time monitoring of the operating point . . . . . . . . . . . . . . . . Data requirements for anti-surge parameter calculation . . . . . . . CPACS main menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ASP calculation menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

179 181 182 184 184 185 187 187 192 193 193 194 195 196 197 198 200 201 202 203 204 206 207 209 210 211 213 221 223 231 231 233 236 243 243 247

xxxii

Fig. A.4 Fig. A.5 Fig. A.6 Fig. A.7 Fig. A.8 Fig. A.9 Fig. A.10 Fig. A.11 Fig. A.12

List of Figures

Manual digitization of compressor performance curve . . . . . . . . Digitization of compressor performance curve with CPACS . . . Performance curve: head versus flow . . . . . . . . . . . . . . . . . . . . . . Performance curve: pressure ratio versus DP/P1 . . . . . . . . . . . . . Performance curve: ratio versus DP/P1 with limits . . . . . . . . . . . Pressure ratio versus equivalent flow coordinates . . . . . . . . . . . . Performance curves under pressure ratio versus reduced flow coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Performance curve with N2 gas . . . . . . . . . . . . . . . . . . . . . . . . . . . Anti-surge parameter (ASP) formula . . . . . . . . . . . . . . . . . . . . . .

248 249 251 252 252 253 254 254 255

List of Tables

Table 1.1 Table 1.2 Table 1.3 Table 2.1 Table 2.2 Table 2.3 Table 3.1 Table 3.2 Table 3.3 Table 3.4 Table 4.1 Table 4.2 Table 4.3 Table 4.4 Table 4.5 Table 5.1 Table 5.2 Table 5.3 Table 5.4 Table 5.5 Table 5.6 Table 5.7 Table 5.8 Table 6.1

Comparison of centrifugal and reciprocating machines . . . . . . . Common complex control loops . . . . . . . . . . . . . . . . . . . . . . . . . . Third-party solutions versus in-house solutions . . . . . . . . . . . . . Compression cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ratio of specific heat for some common gases . . . . . . . . . . . . . . Examples of process gas compositions . . . . . . . . . . . . . . . . . . . . Cause-and-effect table (CET) for pumps and compressors . . . . . Operating points of a hairdryer . . . . . . . . . . . . . . . . . . . . . . . . . . . Cause-and-effect table for a hairdryer . . . . . . . . . . . . . . . . . . . . . Flow turndown in a centrifugal machine . . . . . . . . . . . . . . . . . . . Cause-and-effect table for pump and compressor operation . . . . Typical control handles for pump and compressor operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical control strategies for pump and compressor operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical requirements and means of protective control . . . . . . . . Cause-and-effect table for protective control . . . . . . . . . . . . . . . . Compressor API datasheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Changes in inlet conditions with constant volumetric flow . . . . . Potential variables for Y-axis in alternative coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Potential variables for X-axis in alternative coordinate systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Potential variables for describing head versus flow characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example: compressor performance data . . . . . . . . . . . . . . . . . . . Example: compressor performance data, with compression ratio and equivalent flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example: compressor performance data, with anti-surge parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minimum flow calculation for pump . . . . . . . . . . . . . . . . . . . . . .

5 19 22 30 31 32 70 75 75 77 95 97 98 104 105 122 125 128 129 131 143 144 148 161 xxxiii

xxxiv

Table 6.2 Table 6.3 Table 6.4 Table 7.1 Table 7.2 Table 8.1 Table 8.2 Table 8.3 Table 8.4 Table A.1

List of Tables

Minimum flow calculation for pump, with anti-surge parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical process data for compressor control . . . . . . . . . . . . . . . . Data requirements for anti-surge control design . . . . . . . . . . . . . Capacity control with a split-range scheme . . . . . . . . . . . . . . . . . Power efficiency at different pressure ratios . . . . . . . . . . . . . . . . Process control deliverables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differential pressure from DP sensor and flow rate in DCS . . . . Flowmeter testing and calibration . . . . . . . . . . . . . . . . . . . . . . . . . Valve stroking from field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Engineering units in CPACS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163 173 174 197 215 220 225 225 226 250

Chapter 1

Introduction to Pumps and Compressors

Rotating equipment, including pumps and compressors, plays a critical role in the process industry by enabling material movement for continuous operation and production. However, due to their high capital cost and energy consumption, safe and efficient operation is essential for both operational and economic reasons. To achieve this, it is necessary to have a thorough understanding of the process flow configuration and operating requirements. This chapter provides an overview of pumps and compressors, specifically from the process control perspective. Additionally, the chapter introduces a process-centric control concept, an alternative approach to the traditional equipment-centric method, to better facilitate the understanding and control of the equipment in various industrial processes.

1.1 Type of Pumps and Compressors Pumps and compressors are essential members of the rotating equipment family. They are in direct physical contact with the material flow they work on and thus are of primary concern to process control.

1.1.1 Rotating Equipment Rotating equipment is ubiquitous. They typically include, but are not limited to, motors, engines, compressors, turbines, pumps, generators, blowers, and gearboxes, as illustrated in Fig. 1.1. Pumps, fans, blowers, and compressors have the so-called “wet end” with direct contact with the process fluid; Motors, engines, and gearboxes are at the “drive end” to provide the energy for operating the “wet end.” The prevalent examples of rotating equipment are pumps and compressors, as shown in the shaded boxes in Fig. 1.1. Pumps and compressors impart energy to a fluid (liquid, gas, and less commonly, solid) to cause the fluid to flow forward or raise © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. S. Niu, Process Control for Pumps and Compressors, Advances in Industrial Control, https://doi.org/10.1007/978-3-031-43122-7_1

1

2

1 Introduction to Pumps and Compressors

Fig. 1.1 Type of rotating equipment by principle of work

its energy to a higher level. For clarity and convenience, we will follow the below conventions: • Rotating equipment. We will use the term rotating equipment to refer to all the equipment listed in Fig. 1.1. • Centrifugal machines. Centrifugal machines refer to centrifugal pumps, centrifugal compressors, fans, and blowers that work on centrifugal principles. • Centrifugal pump. We will focus our discussion of pumps on centrifugal pumps and much less on reciprocating pumps. We refer to centrifugal pumps if a pump is mentioned without any modifier. • Centrifugal compressor. When a compressor is mentioned without a modifier, we refer to a centrifugal or axial compressor. Reciprocating compressors work on different principles and their control is relatively straightforward.

1.1.2 Pumps and Compressors Pumps and compressors are responsible for the continuous flow of process materials, including gas, liquid, and solids (granules) in an operating plant, from a low energy level to a higher one or from one location to another. A pump moves an incompressible fluid (e.g., liquid) whose volume does not (significantly) change with pressure and temperature. A compressor moves a compressible fluid (e.g., gas) whose volume is strongly influenced by pressure and temperature. Pumps and compressors are extremely widely used and consume enormous energy to operate. Stoffel (2015) reports that electric motor-driven systems (EMDS) account for 43–46% of the global electricity consumption, of which 39% is by compressors, 19% by pumps, and 19% by fans. The various industries are responsible for 64%

1.1 Type of Pumps and Compressors

3

Fig. 1.2 Type of compressors by capacity

of the consumption. In addition, a 2001 report by the Department of Energy of the United States claims that “… pumping systems account for nearly 20% of the world’s electrical energy demand and range from 25 to 50% of the energy usage in certain industrial plant operations” (DOE 2001, 2006). The reliable and efficient operation of pumps and compressors is thus of great economic incentive. The selection of pumps and compressors for a particular operation is determined by many factors, among which pressure and capacity are the most important considerations. Capacity refers to the amount of fluid conveyed per unit of time and can be expressed in volumetric or mass flow rate. Figure 1.2 illustrates the operating range of compressors in terms of pressure and flow (Elliott and Bloch 2021; Hanlon 2001; McMillan 1983). The mechanical and hydraulic aspects of pumps and compressors are extensively studied and published (Boyce 2003; den Braembussche 2019; Forsthoffer 2005a, b; Elliott and Bloch 2021; Forsthoffer 2017; Stewart 2019). Some examples of the mechanical aspects are vibration, seal compatibility, bearing selection, casing configuration, metallurgical suitability, and radial thrust and shaft deflection, which are of little interest to process control and will not be discussed. Our discussions in this book will focus exclusively on the control aspects of the equipment, including the variables describing the machine behaviors, the means of influencing the machine behavior, and the dynamic cause-and-effect relationship between the variables.

1.1.3 Centrifugal and Reciprocating Machines The two main types of pumps and compressors are positive displacement and dynamic. A positive displacement machine pressurizes the liquid by confinement.

4

1 Introduction to Pumps and Compressors

Fig. 1.3 Reciprocating compressor and bicycle pump

It increases the fluid pressure by operating on a fixed volume in a confined space. Reciprocating, sliding-vane, rotary lobe, and screw machines are examples of positive displacement machines. In contrast, a dynamic machine pressurizes the fluid by acceleration. It increases the pressure of the fluid by using blades to increase the velocity. Typical dynamic machines are axial and centrifugal machines. A centrifugal machine consists of a stationary inlet casing, a rotating impeller, and several fixed diverging passages. It uses rotating vanes or bladed discs to sequentially accelerate the fluids (gas or liquid) to increase their kinetic energy and then decelerate them to trade a portion of the kinetic energy for potential energy (See Fig. 1.3a). Standard centrifugal machines include centrifugal pumps and compressors, electric blowers, and fans, as shown in Fig. 1.1. Axial machines behave similarly to centrifugal machines, although they differ in applicability.1 A jet engine is an example of a complex axial compressor. The internal flow is in the axial direction, parallel to the shaft, as opposed to the radial exit direction in centrifugal machines. The dynamic characteristics of axial and centrifugal machines are very similar; thus, control analysis and design for centrifugal machines apply to axial machines almost without change. Reciprocating machines work on the same principle as bicycle pumps. A human heart is probably the most sophisticated reciprocating pump operating at variable speeds (Fig. 1.4). A fixed volume of gas or liquid is moved from a low-pressure to a high-pressure location on each stroke. The reciprocating machine is insensitive to system changes. It operates at approximately the same delivered volume flow 1

Axial flow compressors are more suitable for larger engines with smaller frontal areas (and drag) and can achieve 3–4% higher efficiency for the same duty than centrifugal compressors. For very small compressors with low-flow rates, the efficiency of axial compressors drops sharply, and blading is small and difficult to make accurately. Centrifugal machines are best suited for constantpressure and variable-flow applications. Axial compressors are more suitable for constant-flow and variable-pressure applications.

1.1 Type of Pumps and Compressors

5

"Non-Return Valves"

"Non-Return Valves"

"Pump"

"Pump"

Fig. 1.4 Example: human heart as a reciprocating machine

regardless of the fluid type or operating condition; see Fig. 1.3b for an illustration. Due to the reciprocating action, the flow is intermittent and usually requires a damper vessel downstream to minimize pulsation if a smooth flow is desired. Centrifugal machines have fewer moving parts than reciprocating machines and offer many advantages, such as simple construction, relatively low cost, low maintenance, quiet operation, and excellent reliability. They are often preferred over other machine types. On the other hand, the operation and control of centrifugal machines are more complex due to the surge and choke limits, which is a central topic of this book. Reciprocating machines have more moving parts than centrifugal machines and are typically less reliable; however, their operation and control are much more straightforward (see Table 1.1 for a summary). Table 1.1 Comparison of centrifugal and reciprocating machines Type Advantages Centrifugal machine

Axial machine

Reciprocating machine

Wide operating range Low maintenance High reliability High efficiency High flow High-speed capacity Head not affected by gas properties High efficiency (at low speed)

Disadvantages Surge at low flow Moderate efficiency Low pressure ratio Expensive blading Narrow flow range Limited capacity

6

1 Introduction to Pumps and Compressors

1.1.4 Fans and Blowers Fans and blowers are low-pressure compressors commonly used to supply air or gas to dryers, furnaces, and HVAC systems. According to the American Society of Mechanical Engineers (ASME), a device with a compression ratio of up to 1.11 is called a fan. A blower has a compression ratio of 1.11–1.2. Machines with a compression ratio above 1.2 are known as compressors. Blowers and fans work on the same principle as centrifugal compressors; therefore, most of the discussions on centrifugal compressors in this book also apply to blowers and fans. Fans play a crucial role in our discussions because the renowned fan laws (Sect. 2.3) were based on the observation of fan operations.

1.2 Applications of Pumps and Compressors A process stands for a series of unit operations to produce a material in large quantities, either continuously or in batches. Typical industrial processes include oil and gas production and refining, petrochemical and chemical processing, biochemical, pharmaceutical, pulp and paper manufacturing, power generation plants, and food and beverage. Pumps and compressors are critical and integral components of the process flow configuration to move oil, gas, and other fluids to specified destinations and at the desired pressure or flow rate.

1.2.1 Liquid Pumping

∆

An elemental liquid pumping process includes the liquid supply from the pump suction side and the liquid destination on the discharge side, as depicted in Fig. 1.5. The largest pumps are typically used in oil pipeline operations. For example, Fig. 1.6 illustrates the main oil line (MOL) in one of the Gulf countries. Around one million barrels of crude oil are transported daily from the interior to the coast. The MOL (size 38–42”) runs through mountainous terrain, reaching a “high point” of

Fig. 1.5 A simple pumping process

1.2 Applications of Pumps and Compressors

7

Fig. 1.6 Large pumps in pipeline operation

670 m above sea level, before arriving at the oil terminal, which is over 100 km away at the coast. Two boosting stations, equipped with pumps powered by gas turbines or electric motors, provide the necessary energy to move the oil over the mountain. The discharge pressure is at around 50 bar(g). The critical requirement is maintaining a minimum pressure at the “high point” to prevent a vacuum inside the pipeline that could cause it to collapse. The terminal operates at near-atmospheric pressure. Arriving pressure must be controlled, and excessive pressure must be avoided. In addition, large pressure fluctuations can cause uneven flow and excessive turbulence, leading to emulsion formation in crude oil with the risk of failing export requirements. Therefore, the reliable and stable operation of the booster pumps is crucial for successfully transporting the oil. A complex pumping process can involve multiple pumps operating in parallel or series and different modes. For instance, two machines operate in parallel to increase capacity or provide redundancy. Figure 1.7 shows a surface processing facility in

Fig. 1.7 A complete surface facility with pumps and compressors (reproduced, with permission, from Niu and Xiao (2022))

8

1 Introduction to Pumps and Compressors

upstream oil and gas production. Multi-phase fluid from wells is sent under pressure to the separators, where it is separated into gas, oil, and water, then transferred downstream via compressors and pumps for further processing or sales.

1.2.2 Gas Compression Compressors play a critical role in many sectors of industry. Bloch (2006) has provided a comprehensive list of compressor applications in the process industry. Some typical applications include wet gas compressors for FCCU, refrigerant compressors in liquefied natural gas (LNG), CO2 injection, booster compressors for gas pipelines, instrument air compressors, and vapor return compressors for LNG ship loading. An elemental gas compression system includes the gas source, a suction scrubber, a single-stage compressor, a discharge cooler, a discharge knockout drum, the recycle line and valve, and the destination of the gas, as shown in Fig. 1.8. 1. Gas source. The gas to be compressed can come from various sources, depending on the type of operation. For example, the gas supply is usually from upstream separators in a typical E&P facility and cracked gas in an ethylene plant. 2. Suction cooler, inter-stage cooler, and discharge cooler. As the gas is compressed to a higher pressure, its temperature increases simultaneously. For practical reasons such as metallurgy, lubrication, and efficiency, the discharge temperature must not exceed a specific limit, typically up to 150 ◦ C (Hanlon 2001). The gas must be cooled at appropriate points along the flow path before being sent downstream for further compression or processing. 3. Suction and discharge scrubber. Liquids, solids, and other contaminants can prove troublesome for the compressor operation and must be removed before entering the compressor. The suction/discharge scrubber serves this purpose; the entrained liquids/solids are “scrubbed” from the bottom.

Fig. 1.8 A typical gas compression process (reproduced, with permission, from Niu and Xiao (2022))

1.2 Applications of Pumps and Compressors

9

4. Driver system. The driver provides mechanical power to the compressor. The type of the driver depends on the power and torque requirements and can be a steam turbine, turbo expander, electric motor with fixed-speed drive, variable-speed gearbox (VSGB), or variable frequency drive (VFD). In most modern compressors, the driver is an electric motor. 5. Compressor. The compressor is the central component of the compression system. Each compressor operates within a specific operating range (compressor operating envelope). Within this range, the compressor receives energy from the driver. It then converts the energy to the gas’s potential energy (defined as the head or pressure) and kinetic energy (defined by flow rate). 6. Recycle line and recycle valve. When a centrifugal compressor’s throughput (also called the load or capacity) is lower than a specific limit due to low supply or demand, the compressor becomes starved, and backflow may result. This abnormal phenomenon is called compressor surge, characterized by rapid switching between backward and forward flow. Compressor surge could harm the compressor’s mechanical integrity and must be prevented. The standard solution to prevent surge is circulating a portion of the compressed gas back from the discharge side to the suction side of the concerned stage. Typically a special antisurge recycle valve is installed at each stage to adjust the amount of recycle flow. With an air compressor, because air is unlimited in supply and not harmful to the environment, it is more convenient to blow off part of the compressed air to the atmosphere at the discharge side instead of recycling it back to suction to re-compress. 7. Suction or discharge throttling valve. The throttling of the suction or discharge valve varies the system resistance and thus changes the split of the added energy between potential energy and kinetic energy. 8. Discharge check valves. Backflow is undesirable, especially in the case of an emergency shutdown. Check valves (non-return valves) are installed at the compressor discharge to prevent backflow. 9. Gas destination. Like the gas source, the back pressure at the gas destination also significantly impacts the compressor control strategy. Complex compression processes may involve multiple compressors working together to achieve a higher pressure (via serial arrangement) or more flow throughput (via parallel configuration). A compressor system with two compressors, each with two stages, is shown in Fig. 1.9. This 2 × 2 configuration is sufficiently representative to show the concept of a complex compression system and is also flexible enough for scaling up or down to accommodate different needs. It will be used as the process configuration in the later discussions. Machines operating in parallel share the same suction and discharge headers. As a result, all machines receive fluid from the same suction header, and all the running trains share the same pressure ratio. Figure 1.10 is an example of a depletion compression process. Gas wellhead pressure depletes over time, from 25 bar(g), 10 bar(g) to the eventual 3 bar(g) before permanent shut-in of the wells. Compressors are added in phases to cope

10

1 Introduction to Pumps and Compressors

Fig. 1.9 A compressor system with two compressors in parallel

Fig. 1.10 Multi-phase depletion compressors

with the decreasing pressures of the gas supply. The startup and operation of such a complex compressor network are quite challenging. Meanwhile, the many ways of configuring and operating the system provide opportunities for overall optimization. Figure 1.11 shows the process flow of a typical ethylene plant. A five-stage cracked gas compressor (CGC) and many pumps and other compressors move the cracked

1.3 Operation and Control of Pumps and Compressors

11

Fig. 1.11 A typical ethylene plant with compressors

gas and condensed liquids. The high compression ratio and wide variation in the cracked gas composition pose a considerable challenge to operation and control.

1.3 Operation and Control of Pumps and Compressors Pumps and compressors are crucial to the process operation, with primary concerns on the safe and efficient operation of both the process and equipment (Liptak 2006; King 2016; McMillan 1983; Watterson 2018).

1.3.1 Operating Requirements and Control Objectives The primary objective of pumps and compressors in an industrial setting is to safely and efficiently move the process fluid (liquid for pumps and gas for compressors) from one location to another as required by continuous process operation. A large pump or compressor is characterized by some unique properties: 1. Large capital investment. A large pump or compressor can easily cost millions of dollars to purchase and install.

12

1 Introduction to Pumps and Compressors

2. Critical to operation. The liquid pumping and gas compression system is essential to the operation. A trip or shutdown of a critical pump or compressor often significantly interrupts production, resulting in production loss or deferment. 3. High operating cost. Liquid pumping and gas compression constitute a considerable part of the operating cost. It is common to see compressors rated at over ten megawatts in the oil and gas industry.2 4. Maintenance intensive. Pumps and compressors are also maintenance-intensive and account for a considerable part of rotating equipment engineers’ maintenance effort. The rise in global energy consumption and environmental consciousness, coupled with the depletion of fossil fuel reserves, has led to a surge in demand for new compression systems. This demand is particularly evident in the increasing number of gas-to-liquids (GTL), coal-to-liquids (CTL), carbon capture and storage (CO2 injection), and integrated gasification combined cycle (IGCC) facilities, which rely heavily on extensive compression systems (Elliott and Bloch 2021; Shelley 2006). Minimal energy consumption, maximum throughput, and low maintenance cost have become the mandate. As a result, the efficient operation and reliable protection of pumps and compressors are critical factors in process control design and operation.

1.3.2 Overall Control Strategy A reliable process control solution helps achieve safe and efficient operation by the following means: 1. Regulate the process flow to maintain the desired pressure and capacity during normal operation. Due to inevitable disturbances and upsets, continuous adjustment of the process flow rate is required, even if the steady-state material balance is adequately satisfied. 2. Protect the process and equipment against unsafe and inefficient operation during abnormal situations. Many engineering limits and operational constraints, such as pressure, temperature, flow, and motor power, set the operation boundary of the machines. Protective control is provided to keep the operating point within the desired operating range. 3. Safeguard the process and machine against catastrophic failures. Although operators and automatic control are charged with keeping the process operation within the operating limits, the effectiveness of control and the speed of response may not be sufficient. The operating point may run away and go out of control. In this

2

For example, a 10-megawatt compressor consumes more than 80 million kWh of power (10.0 MW × 1000 kW/MW) × 24 h/day × 365 day/yr = 87,600,000 kWh or over 8 million dollars per year, assuming US$0.1/kWh for electricity.

1.3 Operation and Control of Pumps and Compressors

13

Fig. 1.12 Process automation system (PAS) (reproduced, with permission, from Niu and Xiao (2022))

case, the safeguarding system will proactively shut down3 the operation to avoid more severe consequences. 4. Transition between different operating modes. A machine can operate in different modes, and so is the process. The startup, shutdown, and on-stream modes are essential. Reduced-capacity operation (also known as the turndown mode) is commonplace. The transition from one mode to another can be associated with many risks and can be highly complex. Sequence and logic are the primary means for transitional control, but interaction with and support from the process control scheme are also critical. For a complex pumping or compression process, there are additional considerations on the overall optimality of operation. For instance, the flow and pressure distribution among multiple compressors can significantly affect operational efficiency, which can be improved by rationalized operation or optimized control. A plant automation system (PAS), typically a combination of distributed control systems (DCS), safety instrument systems (SIS), and fire and gas system (FGS), provides the infrastructure to implement the control solution. PAS typically consists of three subsystems, as illustrated in Fig. 1.12. 1. Distributed control system (DCS). A DCS is the core platform and operator interface for monitoring and control. The DCS system is typically also the human– machine interface (HMI) for all other subsystems. 2. Safety instrument system (SIS). SIS is typically a PLC-based system running condition-based logic and sequences. In case of an emergency, it proactively shuts down the process and equipment, isolates hydrocarbon inventories, and switches off the electric systems. 3

An emergency shutdown is very disruptive with high risks and should be avoided as much as possible.

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1 Introduction to Pumps and Compressors

3. Fire and gas system (FGS). The fire and gas system continuously monitors all plant areas for abnormal conditions such as a fire or combustible/toxic gas release via various fire and gas detection instruments. The system alerts the operator of imminent danger if a hazardous situation occurs. Depending upon the hazard level, the fire and gas system can also proactively shut down the process equipment and activate automatic fire fighting systems to prevent incident escalation.

1.3.3 Process Control Technologies Process control is a branch of automatic control vital to safe and efficient operation. The pervasive control technologies range from simple and complex PID control schemes to advanced control solutions. This section provides a highlight of the core concept and a summary of the prevalent process control technologies for pumps and compressors. For comprehensive discussions on process control, see King (2016), Niu and Xiao (2022), Smith (2010). Feedback control is one of the most commonly used mechanisms for automatic control, as shown in the block diagrams in Fig. 1.13. The basic principle of feedback control is Measure

→

Compare

→

Correct .

(1.1)

Manual control by the operator is the primitive form of feedback control. The operator monitors the value of the controlled variable, compares it with the desired value, and adjusts the manipulated variable (e.g., control valves) to keep the controlled variable at or around its target value. This checking and adjusting keep on as frequently as necessary. This measure-compare-correct process is highly tedious and prone to human errors. An automatic control solution replaces the operator to perform this repetitive work more reliably and efficiently. Therefore, operator control and automatic control are both feedback controls. They complement each other to achieve the same control objectives. A feedback control loop comprises five essential components, as illustrated in Fig. 1.13, namely, the process to be controlled (➀), measurements and feedback

Fig. 1.13 Closed-loop control (feedback control)

1.3 Operation and Control of Pumps and Compressors

15

mechanism (➁), final control element (➂), the control objective (➃), and the control algorithm (➄).

∆

∆

1. Process. A process refers to the physical plant or equipment to be controlled. Control is based on process dynamics, which is the transient behavior of a process variable responding to a change in another variable. The critical information required on the process is the dynamic cause-and-effect relationships between, and transient behaviors of, these variables (See Fig. 1.14 for an illustration of process dynamics and cause-and-effect relationship). 2. The measurement, monitoring, and feedback mechanism. The measurement provides a window into the process or equipment to provide an undistorted view of changes in the process variables. The availability and credibility of process measurements are crucial for process control. A process measurement typically includes a sensor and a transmitter, with the former providing the physical measurement and the latter transmitting the measurement value to the controller as feedback. The four conventional process variables are flow, pressure, level, and temperature. See Fig. 1.15a for an illustration of the flowmeter. For advanced control applications, inferential properties (soft sensors) are widely used for those properties that are not directly measurable or cannot be measured reliably. See Fig. 1.15b for an illustration of the surge indicator calculation that is discussed in detail in Sect. 5.3. 3. Final control elements (FCE). The final control element is a manipulatable device that can influence the process and cause the process output to change predictably. The control valve is the most common final control element, as shown in Fig. 1.16a. A control valve is also called a throttling valve to distinguish it from an on/off valve. The critical valve properties of concern to process control include the speed of response, valve characteristics (see Fig. 1.16b.), and positioning accuracy. Other final control elements such as electric current, motor speed, or switches are also commonly encountered.

Fig. 1.14 A process with noise and disturbance

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1 Introduction to Pumps and Compressors

Fig. 1.15 Process measurement components

Fig. 1.16 Valve characteristics

4. Control objectives. The control objectives serve the operating objectives and dictate what process variable is to control and at what value it should be controlled (see Fig. 1.17 for an illustration of operating point and operating envelope). 5. Control algorithm or logic. The control algorithm or logic calculates the control action to eliminate the control error and maintain the process value on the target. The controller can be a simple on/off control logic, a standalone PID controller with one control handle and one control target, or a complex control scheme consisting of multiple PID controllers. The selection of control algorithms depends on many factors, and the critical considerations include performance, reliability, and the life-cycle ownership cost.

1.3 Operation and Control of Pumps and Compressors

17

Fig. 1.17 Control objectives and constraints (reproduced, with permission, from Niu and Xiao (2022))

Fig. 1.18 On/off control and PID control

On/off control is the simplest controller and thus is also the least expensive in life-cycle ownership. The manipulated variable can assume just two values, e.g., open/close for a valve, on/off for a switch, or run/stop for a pump. Figure 1.18a shows an example of a simple on/off switching control, represented by LS, where S stands for switching, with an on/off valve LSV-101. On/off control is a reliable and cost-effective option for control problems where sloppy control performance is acceptable, such as with levels of large storage tanks, the temperature in room heating, and pressure in instrument air. The major downside

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1 Introduction to Pumps and Compressors

Fig. 1.19 Structure of a PID control loop

of an on/off control scheme is that it cannot provide the required granularity in control moves to maintain a tight setpoint. For example, a home A/C system usually has an air compressor with on/off control, which can only maintain the room temperature within a set range (e.g., ±1 ◦ C).4 The majority of industrial process control is by PID control loops. A PID controller, as shown in Fig. 1.19, offers three types of control actions: 1. Proportional action is a linear function of the control error e(t) and provides a quick initial response; For example, for temperature control, the control action for a 20 ◦ C control error is twice that for a 10 ◦ C error. However, proportional action requires a non-zero control error to sustain the control action. This non-zero control error results in a steady-state offset, a significant drawback of proportional control. 2. Integral action eliminates steady-state errors; The control action is proportional to the time integral of the control error. For example, for temperature control, as long as there is a difference between the actual temperature and the desired temperature, the integral action will continue changing the heat input in the direction of reducing the control error. 3. Derivative action provides anticipatory action for better disturbance rejection. It calculates the rate of change in the control error and asserts a control action proportional to it for quick response. However, noises and disturbances are prevalent in the process variables. The derivative action amplifies noises and may result in too aggressive control actions. For this reason, most controllers in the process industry are P or PI controllers. D action is rarely used or used with carefully designed signal filters. Most industrial control loops are simple PID control loops (Åström and Kumar 2014; Lee and Weekman 1976; Shinskey 2001; Smith 2010), also called standalone PID control loops. They typically consist of only one variable to control (the control target) and one variable to manipulate (the control handle). Complex control problems consist of multiple controlled and manipulated variables. These variables must be considered together due to the interactions among 4

Variable-frequency A/C system is becoming increasingly affordable and can provide better temperature control with less power consumption for improved comfort.

1.3 Operation and Control of Pumps and Compressors Table 1.2 Common complex control loops Single control target On/off control Simple PID control Protective control Split-range control Dual controller control Fan-out control Feedforward control

19

Multiple control targets Cascade control Ratio control Override control Selective control Decoupling control Model-based predictive control

them. A natural solution is to have multiple simple controllers working together to address the complexities. Table 1.2 lists the common process control loops by the input/output structure. Cascade control, split-range control, fan-out control, and override control are the most widely used complex control schemes in pump and compressor control. For more in-depth discussions, please refer to Niu and Xiao (2022), Smith (2010).

1.3.4 Monitoring and Safeguarding Performance monitoring is crucial to the pump and compressor system’s sustainable and efficient operation. Performance monitoring serves two primary users, the control room operators and the process control engineers. Pump and compressor vendors typically offer comprehensive monitoring tools to ensure that the mechanical integrity of the machine is monitored, abnormal conditions are reported, and the operators are alerted. However, they are much less interested in the overall condition of the process operation, which requires intimate knowledge of both the process and control. A process is designed to operate under different setpoints and limits, including regulatory control setpoint, protective control setpoint, alarm limits, and trip limits. If automatic control fails to maintain the control target, an alarm alerts the operator for manual intervention. If operator intervention fails to bring the operating point back to safety, instrumented safeguarding logic kicks in to shut down the operation. The different layers of control and protection are achieved by operating at different setpoints and limits in a staggered fashion, with the setpoints and alarm limits properly aligned and spaced to allow ample time for the next line of defense to respond. Figure 1.20 shows the distinct layers of safety protection in an operating plant. Process control is the first layer of protection against process fluctuations and upsets, followed by the safeguarding layer against unsafe operations. Close integration between process control and safeguarding is critical in an integrated design to avoid unnecessary process disruptions and shutdowns.

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1 Introduction to Pumps and Compressors

Fig. 1.20 Layers of process safety protections (reproduced, with permission, from Niu and Xiao (2022))

1.4 Practical Considerations The lifespan of rotating equipment is very long, typically spanning multiple decades. Many of them are required to operate 24/7 for several years nonstop. The design and control philosophy must consider this long lifespan and high up-time requirements.

1.4.1 Process-Centric Versus Equipment-Centric Solutions The operation and control of a piece of rotating equipment must be considered within the context of the process configuration. Rotating equipment is part of the process and must coordinate with other components, such as vessels, exchangers, furnaces, distillation columns, piping, and valves to meet the operating requirements. Together, they serve the overall process control objectives. For this reason, the process control

1.4 Practical Considerations

21

solution must be process-centric aiming at overall integrity and optimality, rather than an equipment-centric solution focusing on the equipment alone. A thorough understanding of both the process and equipment is essential. Equipment control is traditionally monopolized by equipment manufacturers or their affiliates/partners, emphasizing equipment safety and mechanical integrity rather than the overall process control performance. However, the equipment manufacturer is unlikely to have sufficient knowledge of the process operation or process control. It is challenging for them to design an equipment control scheme that seamlessly integrates into the overall process control solution that they are unfamiliar with. Process control engineers with a holistic view of the operating requirements are thus better suited for designing the equipment control solution as an integral part of the overall control solutions.

1.4.2 In-House Versus Third-Party Solutions The protective control of pumps and compressors has traditionally been using proprietary technology and dedicated hardware and software (Elliott and Bloch 2021, Chap. 13). The downside of this approach is the high cost of life-cycle ownership. Over-reliance on a single third party for hardware, software, and services can result in unnecessary service delays and functionality limitations. Compressor control solution providers do not have a competitive edge over mainstream control systems (DCS and PLC) vendors in providing a reliable and versatile control system infrastructure to support the control solutions.5 As technology advances, especially in the control systems hardware (DCS and PLC), compressor control solutions can now be implemented in standard control systems similar to other process control solutions. The entire process control solution, including equipment control, can be designed, implemented, operated, and maintained by competent in-house process control engineers and instrument technicians. The in-house solution has many advantages over the third-party solutions. Table 1.3 lists the advantages and disadvantages of the two types of solutions. It is encouraging that the number of solutions based on standard process control technology on open platforms is rapidly increasing (Zelenov 2013). Some commercial vendors have also started to offer solutions in standard control systems instead of their own (CCC 2021; Elliott and Bloch 2021; Vermillion et al. 2023). With sufficient knowledge and experience, process control engineers can take ownership of a large part, if not all, of the life-cycle activities, from design, implementation, operation, and maintenance.

5

The recent acquisition of Compressor Control Company (CCC) by Honeywell, announced on April 26, 2023, marks the beginning of the end of this proprietary black-box approach for compressor control (Honeywell 2023).

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1 Introduction to Pumps and Compressors

Table 1.3 Third-party solutions versus in-house solutions In-house solution Third-party solutions Objectives Philosophy Technology Architecture Infrastructure CAPEX OPEX Warranty Service Maintenance

Overall optimal operation “Process-Centric” Open, Transparent Layered approach Standard DCS/SIS, “White-Box” Existing DCS/SIS In-house support Via Standard DCS/SIS In-house support By In-house team

Surge prevention + Others “Compressor Centric” Vendor proprietary Proprietary, “One for All” Proprietary, “Black-Box” Vendor Hardware/Software Vendor service On proprietary hardware/Software Vendor/Third party Vendor service/Third party

1.5 Summary Pumps and compressors are essential equipment in the process industry. The significant investment, large energy consumption, and costly maintenance demand an effective and integrated solution to control, protect, and safeguard their operation. As part of the process flow configuration, the control solution for the equipment must be based on a holistic view of the entire process operation instead of the equipment in isolation, resulting in a process-centric solution instead of the traditional equipment-centric one.

References Åström KJ, Kumar PR (2014) Control: a perspective. Automatica 50(1):3–43 Bloch HP (2006) Compressors and modern process applications. Wiley Boyce MP (2003) Centrifugal compressors – a basic guide. PennWell Corporation, Tulsa, USA den Braembussche RV (2019) Design and analysis of centrifugal compressors. ASME CCC (2021) CCC and Yokogawa R&D Cooperation. Tech. rep., Compressor Control Company (CCC), https://www.cccglobal.com/wp-content/uploads/2022/10/CCC-andYokogawaRD-cooperation.pdf DOE (2001) Pump life cycle costs: a guide to LCC analysis for pumping systems. Tech. Rep. DOEGO-102001-1190, Hydraulic Institute, Euro-Pump, and the US Department of Energy’s Office of Industrial Technologies (OIT) DOE (2006) Improving pumping system performance — a sourcebook for industry. Tech. rep., US Department of Energy’s Industrial Technologies Program (ITP) and the Hydraulic Institute (HI) Elliott H, Bloch H (2021) Compressor technology advances — beyond 2020. Walter De Gruyter Forsthoffer MS (2017) More best practices for rotating equipment. Elsevier Inc Forsthoffer WE (2005a) Forsthoffer’s rotating equipment handbooks, vol. 2: pumps. Elsevier Ltd Forsthoffer WE (2005b) Forsthoffer’s rotating equipment handbooks, vol. 3: compressors. Elsevier Ltd Hanlon PC (2001) Compressor handbook, 2nd edn. McGraw-Hill

References

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Honeywell (2023) Honeywell to acquire compressor controls corporation, driving the energy transition through leading automation and controls portfolio. https://www.honeywell. com/us/en/press/2023/04/honeywellto-acquirecompressor-controls-corporationdrivingtheenergytransitionthrough-leading-automation-and-controls-portfolio King M (2016) Process control: a practical approach, 2nd edn. Wiley Lee W, Weekman VW (1976) Advanced control practice in the chemical industry. AICHE J 22(27) Liptak BG (2006) Process control and optimization, instrument engineers’ handbook, vol II, 4th edn. Taylor and Francis McMillan GK (1983) Centrifugal and axial compressor control. Instrument Society of America, http://compressorcontrolstudent.modelingandcontrol.com Niu S, Xiao D (2022) Process control – engineering analyses and best practices. Advances in industrial control. Springer Shelley S (2006) The challenge of mega syngas plants. Turbomach Int Mag 8–11 Shinskey F (2001) Process control: as taught vs. as practiced. Ind Eng Chem Res 41 Smith CL (2010) Advanced process control – beyond single-loop control. Wiley Stewart M (2019) Surface Production Operations, Volume IV: Pumps and Compressors. Elsevier Inc Stoffel B (2015) Assessing the energy efficiency of pumps and pump units. Elsevier Vermillion L, Gracia J, Ilchenko M (2023) Solutions spotlight: integrating process and turbomachinery control. Control Mag. https://www.controlglobal.com/podcasts/article/21546058/yokogawaelectric-corporation-solutionsspotlight-integrating-processand-turbomachinery-control Watterson JM (2018) A simple guide to understanding compressors. Momentum Press Zelenov A (2013) White paper – CCS implementation of surge prevention control system on yokogawa stardom PLC. Tech. rep, Continuous Control Solutions (CCS)

Chapter 2

Characteristics of Pumps and Compressors

Pumps and compressors operate very differently from static equipment like reactors and distillation columns. However, when it comes to process control, the information required for controlling rotating equipment is not vastly different from that of static equipment. The analytical approach also remains fairly similar. The key is to identify the manipulated and controlled variables, the causal relationships among these variables, and their transient behaviors. This chapter presents the characteristics of pumps and compressors from a process control perspective, with a focus on a unified approach to understanding machine behavior and extracting the necessary information for control. A basic understanding of thermodynamics is also helpful for applying fundamental principles and processes to analyze equipment characteristics.

2.1 Basic Properties of Fluids A fluid can exist in any of the three states: gas, liquid, or solid. The form and volume of fluid in the gas state can change under external influences, while the form and volume are both fixed in a solid state. In a liquid state, the form can change, but the volume cannot. Pumps deal with liquids, and compressors handle gases. There are numerous theories and physical laws describing gas and liquid properties. It is not the objective to provide systematic and in-depth coverage of the fluid properties in this book. Instead, a few fundamental concepts and core principles are presented here to help understand the behavior of liquid pumping and gas compression.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. S. Niu, Process Control for Pumps and Compressors, Advances in Industrial Control, https://doi.org/10.1007/978-3-031-43122-7_2

25

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2 Characteristics of Pumps and Compressors

Fig. 2.1 Conservation of mass

2.1.1 Basic Principles of Fluid Dynamics Fluid dynamics is also called hydrodynamics. It is the study of the movement of liquids and gases. Critical to the process analysis and control are the conservation laws and Bernoulli’s equation. The foundational axioms of fluid dynamics are conservation laws, specifically, the conservation of mass, momentum, and energy. Conservation of mass states that the mass in a control volume can neither be created nor destroyed. Its implication to pump and compressor operation is that the mass flow rate remains the same during pumping or compressing, while the volumetric flow rate may change with external conditions. In equation format: Fm = ρ1 A1 v1 = ρ2 A2 v2 = ρ1 Fv,1 = ρ2 Fv,2

(2.1)

where Fm is the mass flow rate, Fv is the volumetric flow rate, ρ is the fluid density, v is the flowing velocity, and A is the cross-sectional area. The subscripts “1” and “2” denote any two points along the flow path, e.g., a compressor’s suction and discharge side, as shown in Fig. 2.1. The conservation of momentum states that any change in the momentum of the fluid within a control volume is due to the net flow of momentum into the volume and the external forces acting on the fluid inside the volume. The change in momentum can be determined by the change in the product of mass and velocity or by the external force acting on the fluid and is reflected in the changes in velocity or flow direction inside the pump or compressor. The conservation of momentum governs the transfer of mechanical energy to potential energy at the tip of the impellers in centrifugal machines. Similarly, conservation of energy claims that energy can be converted from one form to another, but the total energy in a closed system remains constant. For pumps and compressors, energy is transferred from the external driver (e.g., an electric motor) to the fluid inside the machine as either potential energy (head or pressure) or kinetic energy.

2.1 Basic Properties of Fluids

27

Fig. 2.2 Bernoulli’s equation for flow

The primary interest with rotating machines is how energy is transferred and converted. For instance, an increase in the speed of the fluid coincides with a decrease in static pressure or a decrease in the fluid’s potential energy. The conservation laws can be summarized with Bernoulli’s Equation (Fig. 2.2), which relates the different forms of energy as follows1 : 1 ρ v2 + ρ g h 2 1 1 P1 + ρ1 v12 + ρ1 g h 1 = P2 + ρ2 v22 + ρ2 g h 2 , 2 2 W =P+

(2.2) (2.3)

where W is the energy added from the external source, v is the fluid velocity, P is the pressure, and h is the elevation.

2.1.2 Basic Principles of Thermodynamics Thermodynamics is a branch of physics that deals with heat, work, temperature, and their relation to energy and entropy. Classical thermodynamics is characterized by three fundamental laws, from the first to the third. The first law of thermodynamics states that the changes in the system’s internal energy follow the energy conservation laws when energy passes into or out of a system (as work, heat, or matter). The second law states that in a natural thermodynamic process, the sum of the entropy of the interacting thermodynamic systems never decreases. In other words, heat does not spontaneously pass from colder to warmer bodies. The third law states that a system’s entropy approaches a constant value as the temperature approaches absolute zero. The laws of thermodynamics govern the working of a compressor. The first law implies that the total energy remains constant. The external driver imparts energy onto the fluid inside the machine, and the energy is converted to potential and kinetic energies (and losses). The second law helps explain the different compression processes, where the inevitable heat loss in gas compression renders most compression processes irreversible.

1

Bernoulli’s equation is only strictly valid for incompressible fluid but can be modified to apply to compressible gas for compressor applications.

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2 Characteristics of Pumps and Compressors

The state of a fluid under a given set of physical conditions is described by state variables such as pressure, volume, temperature, or internal energy. The state variables can be related by a thermodynamic equation known as the equation of state, which describes the properties of both pure substances and mixtures in liquids, gases, and solid states. The general form of an equation of state may be written as f (P, V, T ) = 0,

(2.4)

where P is the pressure, V is the specific volume (volume per mole), and T is the temperature. Although the equation of state can be used to describe solids, liquids, and gases, it is most frequently used to describe gas properties. Gas can be characterized as ideal or real. The equation of state for an ideal gas, or the ideal gas law,2 relates the gas’s pressure, temperature, and volume as follows3 : PV =mRT f (P, V, T ) = P V − m R T = 0

Ideal gas law

(2.5)

Equation of state for an ideal gas,

(2.6)

where m is the number of moles of a substance, and R is the gas constant (R = 8.31446 m3 · Pa/K · mol). An ideal gas is convenient for analysis but exists only in theory. An empirical correction factor is applied to make the analyses valid when dealing with real gases. This correction factor is the gas compressibility Z , with Z = 1 for an ideal gas and Z < 1 for real gases.4 Subsequently, the ideal gas law is modified to include the compressibility factor as P v = Z R T.

(2.7)

The most crucial gas property concerning a compressor’s operation and control is the gas density ρ. The gas density is determined by the gas composition (molecular weight, compressibility, and ratio of specific heat) and the operating conditions (pressure and temperature) and can be represented as ⎛ ρ=

2

PM Z RT

kg ⎜ 3 kmol = ⎝kg/m = J K mol · K kPa

N kg ⎞ m2 kmol ⎟ , ⎠ N·m K mol · K

(2.8)

The equation of ideal gas law is based on the laws of Charles, Boyle, Gay-Lussac, and Avogadro. Petroleum engineers call the pressure, volume, and temperature the PVT properties, which describe the physical properties of reservoir fluids and variations in the volume and phase state that occurs during oil production. 4 Under extremely high pressure, the gas compressibility Z may exceed 1.0. 3

2.1 Basic Properties of Fluids

29

where M is the molecular weight of the gas. The density of a liquid is determined mainly by the type of liquid (molecular weight) and does not change markedly with pressure and temperature. The core difference between liquid pumping and gas compression is that gas is compressible while a liquid is incompressible. In other words, the density of a liquid can be assumed constant during pumping, while the density of gases decreases when compressed. Example 2.1 Gas density calculation. Figure 2.3 shows part of an orifice-based flowmeter datasheet. A flowmeter is a critical element in compressor control, requiring gas density as a crucial gas property for design or calibration. The operating condition and gas property are given by the datasheet as follows: Pressure: P = 23 bara = 23 × 100 kPa = 2, 300 kPa Temperature: T = 83.5 ◦ C = 83.5 + 273.15 K = 356.65 K Molecular Weight: M = 59.643 kg/kmol Compressibility: Z = 1.0. The gas density can be calculated and validated with Eq. 2.8: PM Z RT 2300 × 59.643 = 1.0 × 8.314 × 356.65 = 46.26 kg/m3 ,

ρ=

(2.9)

where R = 8.314 J/mol/K is the gas constant. The calculated gas density agrees with the value given in the datasheet.

2.1.3 Gas Compression Process The pressure and volume of a gas obey the following relationship when being compressed: P vn = const,

(2.10)

where P is the gas pressure, and v is the specific volume. The polytropic exponent n indicates the type of compression process. For instance, the condition of n = 0 represents an isobaric process, n = 1 for an isothermic process, and n = ∞ for an isochoric process. See Table 2.1 for a summary of all possible compression processes. An isobaric process does not cause pressure change; thus, no work is done. It is thus not much useful. On the other hand, an isochoric process maintains the volume

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2 Characteristics of Pumps and Compressors

Fig. 2.3 Gas density calculation in a flowmeter datasheet Table 2.1 Compression cycles Polytropic Exponent Process n n n n n

=0 =1 =κ ∈ (1, ∞) =∞

Equation

Isobaric p = const Isothermic p v = const Isentropic p v κ = const Polytropic p v n = const Isochoric (isometric) v = const

Description Constant Pressure Constant Temperature Reversible and Adiabatic Reversible but non-adiabatic Constant Volume

constant while working on the fluid, coinciding with the pumping of an incompressible liquid. The polytropic process is a generic term covering many compression processes. An isentropic process is an ideal compression process that only exists in theory. However, it is frequently used as a benchmark process to facilitate analysis. An isentropic compression process is both adiabatic and reversible (without heat loss). The polytropic exponent of an isentropic process equals the ratio of specific heat κ = C p /Cv , where C p is the specific heat under constant pressure, and Cv is the specific heat under constant volume. The ratios of specific heat for some common gases are given in Table 2.2. The process gas is usually a mixture of different pure

2.1 Basic Properties of Fluids

31

Table 2.2 Ratio of specific heat for some common gases Gas Air Hydrogen Nitrogen Oxygen Ammonia Methane Ethane Ethylene Acetylene Propane Carbon Dioxide Carbon Monoxide

Formula Mole Weight Cp Cv kg/kmol kg/(kg.K) KG/(kg.K) H2 N2 O2 NH3 CH4 C2 H6 C2 H4 C2 H2 C3 H8 CO CO2

28.96 2.016 28.02 32.00 17.03 16.04 30.07 28.05 26.04 44.10 28.01 44.01

1.01 14.32 1.04 0.91 2.19 2.22 1.75 1.53 1.69 1.67 0.84 1.02

0.72 10.16 0.74 0.66 1.66 1.70 1.48 1.23 1.37 1.48 0.60 0.72

κ 1.40 1.41 1.40 1.40 1.31 1.30 1.19 1.24 1.23 1.13 1.29 1.40

gases. It can be as “light” as hydrogen or as “heavy” as cracked gas. See Table 2.3 for some examples. When a gas is compressed, the gas properties can vary in response to changes in external conditions, such as pressure and temperature. Figure 2.4 illustrates a reciprocating compressor’s pressure and volume changes under different compression cycles.

2.1.4 Liquid Transport Process A liquid is usually assumed to have a constant density during the pumping process.5 Pumps work by the same principle as compressors, but the assumption of constant density makes the analysis and control much more straightforward. Although not precise in theory, the discussion of liquid pumping and gas compression can be unified by assuming that pumping an incompressible liquid can be treated as a polytropic compression process with n = ∞, i.e., an isochoric process that does not involve volume changes in the fluid, see Fig. 2.4. This book will focus primarily on the analysis and control of compressors. Once compressor operation and control are understood, most of the analysis can readily apply to pumps in a simplified form by forcing n = ∞.

5

All fluids are compressible to an extent; that is, changes in pressure or temperature cause changes in density. However, with liquid, the changes in pressure and temperature are sufficiently small that the changes in density are negligible. In this case, the flow can be modeled as an incompressible flow. Otherwise, the more general compressible flow equations must be used.

32

2 Characteristics of Pumps and Compressors

Table 2.3 Examples of process gas compositions Composition Argon Hydrogen Nitrogen Oxygen Carbon Dioxide Methane Acetylene Ethylene Ethane Propylene Propane Butene n-Butane i-Butane n-Pentane i-Pentane n-Hexane Others Total

Fig. 2.4 Compression cycles

Natural Gas Cracked Gas Hydrogen % % % Ar H2 N2 O2 CO2 CH4 C2 H2 C2 H4 C2 H6 C3 H6 C3 H8 C4 H8 C4 H10 C4 H10 C5 H12 C5 H12 C5 H12

Air % 0.9

1.05

18.0

78.1 20.9 0.03

1.06 90.00

5.37 1.70 0.33 0.27 0.09 0.06 0.07 100.0

99.0

0.1 52.6 14.1 8.3 3.7 1.9 0.6

0.7 100.0

1.00 0.07 100.0 100.0

2.2 Description of Pumps and Compressors

33

Fig. 2.5 Three basic variables for pump performance description

2.2 Description of Pumps and Compressors Pumps and compressors are machines that convert and transfer the mechanical energy from the driver to the potential and kinetic energies of the fluid. The general and fundamental principles of pumps and compressors can be found in, for instance, Bachus and Custodio (2003), Cumpsty (1989), Forsthoffer (2005), Elliott and Bloch (2021), Giampaob (2010), Gresh (2001), Watterson (2018), although much of the information is of no interest to process control. From a process control perspective, the primary concerns are the variables that describe the machine characteristics and the cause-and-effect relationships among them. These can be summarized as three variables, two curves, and one point, described with an invariant coordinate system.

2.2.1 Three Variables: Speed, Head, and Flow Pumps and compressors work on similar principles: the external driver, such as an electric motor and turbo expander, imparts energy to the fluid (gas or liquid) inside the machine. The energy is then converted to the fluid’s potential and kinetic energies, reflected by the increase in the head and flow. The energy transfer and conversion can be conveniently described with three basic variables: speed, head, and flow, as shown in Figs. 2.5 and 2.6 for pump and compressor, respectively. The speed indicates the amount of energy transferred to the fluid, while the head and flow reflect the split between the potential and kinetic energy added to the fluid. The characteristics of, and the relationship between, the three variables are critical in understanding and controlling pumps and compressors. For centrifugal machines, the impeller design determines the machine’s characteristics, and the relationships between the three variables (see Fig. 2.7) are complex. For reciprocating machines, on the other hand, the relationships among the three variables are more straightforward.

34

2 Characteristics of Pumps and Compressors

Fig. 2.6 Three basic variables for compressor performance description

Fig. 2.7 Impellers and diffusers in a centrifugal machine

Speed N The machine speed refers to the shaft speed measured in revolutions per minute (rpm) for a centrifugal machine or the frequency of piston strokes for a reciprocating machine (1/s). With a radius of r2 , the impeller tip speed U2 in a centrifugal machine (see Fig. 2.8) is related to the rotating speed N via U2 = N · r2 . For both centrifugal and reciprocating machines, the machine speed is an independent variable determined by the external driver and can be constant or varying, depending on the type of driver. Correspondingly, the machine can be operated in fixed-speed or variable-speed mode. Flow Fv For a centrifugal machine, the actual velocity that the fluid leaves the impeller is given by both the impeller tip speed U2 of the machine and the relative exit speed W2 of the fluid (see Fig. 2.8):

2.2 Description of Pumps and Compressors

35

Fig. 2.8 Three basic variables: head, flow, and speed

→

→

→

[Absolute Exit Velocity] V2 = [Speed] U2 + [Relative Velocity] W2 ,

(2.11)

The flow rate is the fluid volume measured in, e.g., cubic meters per hour (m3 /h) or gallons per minute (GPM): ⎧ ⎨[Volume Flow] = [Exit Area] × [Exit Speed] × 3, 600 ⎩F

v

(m 3 / h)

(m 2 )

(m/s)

(s/ h)

= A · V2 .

(2.12)

A reciprocating machine’s flow rate is the piston volume multiplied by the stroke frequency. That is [Volume Flow] = [Stoke Volume] × [Stroke Frequency] × 3, 600. (m 3 / h)

(m 3 )

(1/s)

(s/ h)

(2.13)

Head H The head H of a machine is the energy required to deliver one mass unit of the fluid at a given temperature from one energy level (e.g., suction pressure) to another (e.g., discharge pressure). The fluid can be liquid, gas, or even solid, depending on the conditions of the fluid at that time. Head as an energy variable has an engineer unit of kJ/kg. For legacy reasons, the pump head is typically represented as the height h of the liquid in meters or feet. The pump head can be intuitively interpreted as the maximum height that the pump, at a fixed speed, can raise the liquid to. A compressor works on gas that is much

36

2 Characteristics of Pumps and Compressors

Fig. 2.9 Head and pressure

“lighter” than liquid, so the concept of the head in terms of height is not as intuitive as the pump head. As a result, the compressor head is more commonly (and rightly) represented as energy, e.g., in kJ/kg. Head in elevation (meters) and energy (kJ/kg) can be confusing when pumps and compressors are discussed together. For example, ethylene can be in either liquid or gas form. If it is a liquid, a pump is needed to raise its pressure, and the pressure increase is usually represented as a head in meters or feet. If the condition renders the ethylene stream a vapor, then a compressor must be used to compress it to a higher pressure, and the pressure increase is measured as head in an energy unit such as kJ/kg. However, the two units can be readily converted between each other by multiplying with or dividing by the gravitational constant g = 9.81 m/s2 since they are both potential energies, as shown in Bernoulli’s equation (Eq. 2.3): H

(J/kg=m 2 /s 2 )

=

g · h,

(m/s 2 )

(m)

(2.14)

where h is the head in height (meters), and H is the head in energy unit (kJ/kg). See Fig. 2.9 for an illustration of the differences. For example, to pump water to a height of 10 m (h = 10 m), a head of H = g h = 9.81 × 10 = 98.1 J/kg is required, which is translated to a pressure of Pd − Ps = ρgh = ρ H = 1, 000 × 9.81 × 10 = 98, 100 Pascal, or 9.81 kPa, approximately 1 atmospheric pressure.6 In other words, the pump must generate 98.1 kPa of pressure to lift the water to 10 m high, equivalent to a head of 98.1 J/kg.

A rule of thumb is: 1 bar (1 bar = 100 kPa) or approximately one atmospheric pressure (1 atm ≈ 101.3 kPa) is roughly 10 m of water height, or 1 m of water generates roughly 10 kPa of pressure.

6

2.2 Description of Pumps and Compressors

37

A Mollier diagram that shows the relationship between pressure and energy at various temperatures can help understand the concept of the fluid head, which will not be explained in detail here.

2.2.2 Two Curves: Performance and Resistance Curves Pumps and compressors are part of the process flow configuration. The performance curve describes the head-flow relationship inside the pump or compressor, while the system resistance curve describes the pressure and flow profile in the process piping. The two curves together dictate how the machine operates. Equipment Performance Curves The performance curve is a graphical representation of the relationship between the three basic variables: head, flow, and speed, under the head-flow coordinate system. They are usually provided by the manufacturers to describe the flange-to-flange performance of the machine. See Fig. 2.10 for a comparison of the typical curves of centrifugal, axial, and reciprocating machines. Performance curves of centrifugal machines typically exhibit an inverse relationship for centrifugal machines (see the basic slope in Sect. 2.3.3 for a detailed explanation). At a constant speed, the head decreases as the flow increases. Axial machines behave similarly to centrifugal machines but have steeper performance

Fig. 2.10 Pump performance curve at constant speed

38

2 Characteristics of Pumps and Compressors

Fig. 2.11 Pump performance curves: fixed speed versus variable speed

curves.7 Nevertheless, unless mentioned otherwise, most discussions on centrifugal machines are also valid for axial machines. The performance of a reciprocating machine can be described with the same headflow coordinate system, but the head and flow relationship is drastically different. The flow rate is determined by the volume of the cylinder and remains almost8 constant if the stroking speed of the piston is kept constant. The head is determined mainly by the back pressure and motor power limit, independent of the flow. The resulting performance curve is close to a vertical line, as shown in Fig. 2.10. Depending on the driver system, a pump or compressor can operate at a fixed or variable speed. For example, a fixed-speed motor driving a compressor will result in a fixed-speed compressor. The same fixed-speed motor driving the same compressor through a variable-speed gearbox (VSGB) can achieve continuously varying speeds (within a reasonable range) and thus make the compressor a variable-speed compressor. The performance of a fixed-speed machine is described with only one curve (see Figs. 2.11a and 2.12a), while a variable-speed machine with multiple performance curves (see Figs. 2.11b and 2.12b). The speed change can be continuous9 or discrete, depending on the driver. The mechanical construction of the machine determines the performance curve. Once the machine is built, the curves remain unchanged, barring mechanical modifications, fouling, or wear and tear. The vendor-provided performance curves typically have additional performance information in addition to the head-flow relationship, such as head/efficiency/power against mass/volume flow. Typically the operating limits of the machine speed and flow rate are also shown on the performance curves. An example of pump 7

Steeper performance curves are better suited for constant-flow applications than for constantpressure applications (Liptak 2006). 8 The curve slightly bends to the left at high head values due to higher leakage and losses at higher pressures. 9 Even if the machine speed can vary continuously, the performance data (head-flow) are supplied at only a few typical speeds. Those in between can be readily inferred via interpolation.

2.2 Description of Pumps and Compressors

39

Fig. 2.12 Compressor performance curves: fixed speed versus variable speed

Fig. 2.13 Typical pump curves (reproduced, with permission, from Niu and Xiao (2022))

performance curves is provided in Fig. 2.13, while Fig. 2.14 is an example of compressor performance curves. Multiple machines can operate in parallel or series to meet higher demands on the flow or head. Machines share the same pressure ratio when operating in parallel and have the same (mass) flow rate when operating in series.10 Figure 2.15 illustrates the composite performance curves of two compressors in parallel and series. The same concept can be extended to pumps and reciprocating machines (Golden et al. 2002). A comparison of Fig. 2.11 with Figs. 2.12 and 2.13 with Fig. 2.14 reveals that the performance curves of centrifugal compressors and pumps are very similar. For this reason, we will treat compressors and pumps with a unified approach. Many discussions on compressors can be applied to pumps. On the other hand, there are 10

There may be liquid knockouts or side streams between compressor stages.

40

2 Characteristics of Pumps and Compressors

Fig. 2.14 Typical compressor curves

sufficient differences between the two types of machines, and separate discussions are offered as necessary. System Resistance Curves The performance curve defines the head-flow profile on the machine side, while the system resistance curve describes the pressure-flow profile on the process side. The term “system resistance” refers to the “resistance to flow,” caused by all the components in the flow line. The resistance curve defines how the pressure is affected by the flow-resisting components. Since the head and pressure ratio can be easily converted from one to another (see Sect. 2.2.4), the pressure and flow relationship can be plotted on the same head-flow

2.2 Description of Pumps and Compressors

41

Fig. 2.15 Composite performance curves

coordinate system as the performance curves. This representation shows a parabolic shape, as depicted in Fig. 2.16.11 Unlike the equipment performance curve, which is fixed once the machine is built, the resistance curve is determined by the process flow resistance components and can be adjusted by changing the flow resistance. Some components, such as piping and equipment, are fixed once the plant is built.12 In contrast, other components, like the control valves and inlet guide vanes, are meant to be manipulated and changed. Therefore, the resistance curve can be “moved” by adjusting the system resistance. There are several ways to adjust the system resistance, including: 1. Throttling the suction or discharge valve. Closing the discharge valve increases the system resistance, causing the resistance curves to move to the left. 11

The resistance curve is theoretical and imaginary, assuming ideal conditions. It is rarely exactly known in a practical setting. 12 The resistance from some flow components, such as filters and exchangers, may change with time due to fouling and aging.

42

2 Characteristics of Pumps and Compressors

Fig. 2.16 System resistance curve and process dynamics

Opening the valve decreases the system resistance, allowing more flow to pass through and causing the resistance curve to move to the right. See Fig. 2.16b. 2. Opening the recycle valve. Opening the recycle valve reduces the system resistance, allowing more flow to pass through the machine (but not necessarily to the downstream process). 3. Changing the back pressure. The source and destination pressures of the fluid can cause changes in system resistance, thus affecting the flow rate. Changing the system resistance is a primary means of compressor operation and control and will be discussed in detail in later chapters.

2.2.3 One Point: Operating Point The operating objective of a pump or compressor is to deliver the required flow at the desired head (or pressure). The head and flow constitute the operating point. The machine’s performance curves dictate where the operating point can be, while the resistance curves, imposed by the process, determine where the operating point should be. They jointly define where the operating point can operate and what trajectory the operating point can follow. The operating point can be viewed as the equilibrium between the energy required by the process and the energy produced by the machine. When a pump or compressor is connected to the process, the operation must meet the requirements of both. As a result, the actual operating point is always at the intersection of the performance and resistance curves. The performance curve remains unchanged once the machine is constructed, while the system resistance curve can shift left and right in response to resistance changes in the process components on the flow path. As a result, the operating point of a fixed-speed machine can only move along a single performance curve via resistance

2.2 Description of Pumps and Compressors

43

Fig. 2.17 Operating point on performance and resistance curves

changes (see Fig. 2.17a). The operating point of a variable-speed machine can move along both the resistance curve and the performance curve, responding to changes in the machine speed and system resistance. See Fig. 2.17b. Changing the machine speed and system resistance together can “move” the operating point to anywhere on the performance map (subject to constraints and limits). Due to the reverse relationship between the head and flow in the machine (described by the performance curve) and the direct relationship between the pressure and flow in the piping (described by the resistance curve), the operating point of a centrifugal machine is somewhat self-regulating. With a change in the head or flow, the operating point will be pulled in opposite directions because of the opposite signs of the slope of the two curves. The machine will eventually reach a new equilibrium and settle at a new operating point by itself, provided that the new point is still within the operating limits and constraints. The operating point is described by the three basic variables: speed, head, and flow. The three variables are correlated. Any two of them can fully define the operating point on the head-flow-speed performance map. On the other hand, the operating point can be “forced” to move to a new location by changing any one or two of the three basic variables using the available control handles. This basic principle of pump and compressor operation is discussed in detail in Chap. 3.

2.2.4 † Other Variables and Curves Several other variables supplement the description of machine performance. These variables will be used in various contexts in later chapters.

44

2 Characteristics of Pumps and Compressors

Power W Power is defined as work per unit of time, with a typical engineering unit of kilowatt (kW) or horsepower (hp). The power consumption for compressing a given gas flow can be calculated by integrating the volumetric flow over the pressure: 

d

W =

Fv d P,

(2.15)

s

where “s” means suction and “d” discharge. The gas law relates the pressure P and volume flow Fv of a polytropic process by Eq. 2.10 as n = const, P · Fvn = Ps · Fv,s

(2.16)

the gas power is then given by  W =

d

Fv d P s

 =

d

s



n Fv,s Ps P  d 1

dP

P− n d P s   n−1 Pd n n Ps · −1 . n−1 Ps

= Fv,s Psn = Fv,s

n1

1

(2.17)

A centrifugal pump can be treated as a special case with n = ∞ and Fv = Fv,s , which leads to   n−1 n→∞ Pd n n Ps −1 ≈ Fv,s · (Pd − Ps ) . (2.18) W = Fv,s · n−1 Ps Equation 2.18 is the same result as directly derived from Eq. 2.15 with a constant volumetric flow Fv independent of the pressure P. The power can refer to fluid power (hydraulic horsepower), shaft power (or brake horsepower), or motor power (or drive horsepower), depending on what losses are included in the calculation. Typically, [Motor Power] > [Shaft Power] > [Gas Power] [Shaft Power] = [Gas Power] + [Mechanical Losses].

(2.19) (2.20)

The gas power is the work done on the total flow, while the head is the work per unit of mass weight. From Eq. 2.17:

2.2 Description of Pumps and Compressors

Hp =

45

W Fm

  n−1 Pd n Fv,s n Ps = · −1 Fm n − 1 Ps   n−1 Pd n 1 n = Ps · −1 ρs n − 1 Ps   n−1 n Ps Pd n = −1 n − 1 ρs Ps   n−1 n Z s R Ts Pd n = −1 n−1 M Ps with: ρs =

(2.21)

Ps M . Z s R Ts

For isentropic compression, the polytropic component n in Eq. 2.21 is substituted with the isentropic component κ, which equals the ratio of specific heat of the gas κ = C p /Cv : Hisen

κ Z s R Ts = κ −1 M



Pd Ps

κ−1 κ

 −1 .

(2.22)

It is more accurate to use the average value (Z s + Z d )/2 in place of Z s . However, the compressibility Z s and Z d are functions of pressures and temperatures and cannot be measured directly. Fortunately, Z s and Z d remain reasonably constant within the operating range of most applications (Mirsky et al. 2012). Polytropic Efficiency η p The power calculated with Eq. 2.15 is the net power transferred to the fluid and is thus called the gas power in the case of gas compression. The power required is always greater than what is transferred to the fluid due to hydraulic inefficiencies, driver inefficiencies, and mechanical losses. The difference between the power delivered by the driver and the power received by the fluid is represented by the efficiency term η, a ratio of the ideal energy required to the actual energy delivered. The best efficiency point (BEP) is illustrated in Fig. 2.18. It is desirable to design or select the machine so that the normal operating point is at or near the best efficiency point.13

13

In many applications, the optimal operating point tends to be close to the operating limits. In the case of pumps and compressors, however, the primary operating limits are the surge points, which differ from the best efficiency point.

46

2 Characteristics of Pumps and Compressors

Fig. 2.18 Best efficiency point and efficiency ellipse

The efficiency decreases as the operating point moves away from the BEP. The constant efficiency line exhibits an elliptical shape, with its long axis approximately parallel to the constant-resistance line. Therefore, it is sometimes also called the efficiency ellipse. See Fig. 2.18. The precise calculation of the polytropic efficiency for real gas is complicated and requires equation of state (EOS) data. One practical approximation of the polytropic efficiency without elaborate EOS data is as follows: ηp =

Hp κ −1 = Hactual κ



n−1 , n

(2.23)

where κ is the ratio of specific heat (assuming to be known from gas analysis), and n is the polytropic exponent in Table 2.1. Equation 2.23 indicates that when the compression process approaches isentropic, with n approaches k, the polytropic efficiency η p approaches 100% (which is not achievable in reality). Pressure Ratio (Pd /Ps ) and Pressure Rise (Pd − Ps ) The fluid head is not directly measurable. In practice, the pressure ratio (Pd /Ps ) or pressure rise (Pd − Ps ) across the machine is usually used in place of the head for calculation.

2.2 Description of Pumps and Compressors

47

From Eq. 2.21, the pressure ratio is related to the head as follows: n n   n−1   n−1 n − 1 ρs n−1 M Pd = Hp + 1 = Hp + 1 . Ps n Ps n Z s R Ts

(2.24)

Pressure rise (Pd − Ps ) is another commonly used variable to describe energy. The pressure rise is related to the pressure ratio simply by Pd − Ps = Ps

Pd −1 . Ps

(2.25)

For centrifugal pumps, assuming an isochoric process with n = ∞, the pump head is given from Eqs. 2.21 and 2.24 as H=

Ps ρs



 Pd 1 −1 = (Pd − Ps ) Ps ρs

H Pd = ρs +1 Ps Ps Pd − Ps = ρs H = ρs g h,

(2.26) (2.27) (2.28)

where H is the head in kJ/kg, and h is the head in meters. Equation 2.28 is the same as Eq. 2.14. Polytropic Exponent n For a centrifugal compressor, the polytropic exponent n is a critical variable indicating the type of compression cycle the gas goes through (see Table 2.1) and thus is indispensable in most analyses and calculations. The exact value is determined by the machine’s mechanical construction and the gas’s physical property and is difficult to know. However, an approximate value can be calculated from the pressure and temperature of the gas before and after compression. Assume a polytropic compression process, with Ps and Ts the pressure and temperature at the suction side and Pd and Td the pressure and temperature at the discharge side. The polytropic exponent n is given in Eq. 2.10 as Pd Ps n= . Fv,s ln Fv,d ln

n n = Pd Fv,d Ps Fv,s

⇒

From the law of mass conservation, assuming Ms = Md , we have

(2.29)

48

2 Characteristics of Pumps and Compressors

Fm = ρs Fv,s = ρd Fv,d ⇒ Pd Md Fv,s ρd Pd Ts Z s Z d R Td = = ≈ . Ps Ms Fv,d ρs Ps Td Z d Z s R Ts

(2.30)

The polytropic exponent n is then given from Eq. 2.29 as

Pd Ps

. n= Pd Ts Z s ln · · Ps Td Z d

ln

(2.31)

The compressibility factor Z is introduced for real gases to account for the nonideal property, but the exact values are rarely available without rigorous state-ofequation calculation. The result of n from Eq. 2.31 is typically very unreliable. In practice, within the normal range of most applications, the value of Z does not change drastically from suction to discharge. Therefore, a constant Z d /Z s = 1 is acceptable. The polytropic exponent n is thus simplified to ln

n= ln

Pd Ps

Pd Ts · Ps Td

.

(2.32)

The polytropic exponent can also be computed from the polytropic efficiency η (if available) from Eq. 2.23 since polytropic efficiency is closely related to the type of compression cycle: n=

κ ηp . κ ηp − κ + 1

(2.33)

A related variable that is frequently used for convenience is the polytropic index σ derived from Eq. 2.32 (Mirsky et al. 2012):

Td n−1 Ts = . σ = Pd n ln Ps ln

(2.34)

2.3 Behaviors of Dynamic Machines

49

2.3 Behaviors of Dynamic Machines The dynamic behavior of the machine refers to the cause-and-effect relationships between, and the transient responses of, the machine variables, such as the head, flow, and speed, which profoundly impact the operation and control strategy. In addition, because the pumps and compressors are integral parts of the process flow system, the dynamics include both the machine and process dynamics. Therefore, it is crucial to understand the machine’s behavior in the process context (Boyce 1993, Gresh 2001). It is worth noting that the perspective and needs of a process control engineer differ significantly from that of a process engineer or equipment engineer, and the essential knowledge of the pump and compressor characteristics is thus also quite different.

2.3.1 Relationship Among Head, Flow, and Speed Inside a dynamic machine, the mechanical energy from the driver is transferred to the fluid and then converted to potential energy (as pressure increases) and kinetic energy (reflected by flow increases). The energy transfer and conversion can be conveniently described by the three basic variables: head, flow, and speed. Speed is an independent variable determined by the external driver system. Changes in machine speed can simultaneously affect the head and flow of the machine. However, the impact depends on whether the machine is reciprocating or centrifugal. For instance, the volumetric flow rate of a reciprocating machine is a function of the machine’s speed and is independent of the head. That is, a fixedspeed reciprocating machine will deliver a fixed volumetric flow rate regardless of the fluid type and pressure/temperature. In contrast, the volumetric flow of a fixed-speed centrifugal machine is determined by the machine’s speed and also the energy split between the potential (head) and kinetic (flow) energy. See Fig. 2.19 for a simple illustration of this cause-and-effect relationship.

Fig. 2.19 Cause-and-effect relationship among speed, head, and flow

50

2 Characteristics of Pumps and Compressors

The relationship between a centrifugal machine’s power, head, flow, and speed can be described by the so-called affinity laws, popularly known as the fan laws.14 The relationship among the variables can be expressed as: For a given centrifugal machine with a fixed-diameter impeller, the capacity will be directly proportional to the speed, the head will be directly proportional to the square of the speed, and the required power will be directly proportional to the cube of the speed.

The affinity laws indicate that if the machine speed changes, the flow, head, and power vary by the speed ratio’s first, second, and third power. In equation format: W2 = W1



N2 N1

3 ,

H2 = H1



N2 N1

2 ,

Fv,2 N2 = , Fv,1 N1

(2.35)

where W is the power, N is the speed, H is the head, and Fv is the volume flow rate. Subscripts “1 ” and “2 ” denote two operating points. In another format: Fv1 Fm1 N1 ∝ ∝ , Fv2 Fm2 N2

H p1 ∝ H p2



N1 N2

2 ,

W1 ∝ W2



N1 N2

3 .

(2.36)

A re-examination of Fig. 2.16 and Eq. 2.16 demonstrates the logic of this law. For example, if the speed of the dynamic machine is increased by 10% (i.e., N2 /N1 = 1.10), the changes in flow, head, and power are given by15 Volumetric flow increases by 10%: Fv,2 /Fv,1 = 1.10 Head increases by 21%: H2 /H1 = 1.12 = 1.21 Power consumption increases by 33%: W2 /W1 = 1.13 = 1.33. The effect of the affinity laws on flow, head, and power is illustrated in Fig. 2.20. Due to the different responses by head and power, many energy-saving opportunities exist to optimize the operation of a complex system consisting of multiple pumps or compressors. See Chap. 7 for some examples.

14

Note that the term “fan laws” is a misnomer. The term law means a principle proven to be true for all cases. Unlike other physical laws, fan laws are only an approximation with limitations. They are well applicable to low-head single-stage compressors, including fans and blowers. The accuracy can be significantly affected by many factors, such as the molecular weight of the gas, high discharge pressure, the backlean angle of the impellers, and the number of compression stages in the compressor (Brown 1991). 15 A common revamping activity for centrifugal machines is re-wheeling, which involves reducing the diameter of the impellers. A change in the impeller diameter has the same effect as a change in speed since the tip speed of the impeller is proportional to its diameter.

2.3 Behaviors of Dynamic Machines

51

Fig. 2.20 Flow, head, and power under affinity laws

2.3.2 † Suction and Discharge Relationship Many changes occur when the fluid travels from suction to discharge inside a pump or compressor. These changes are reflected in critical process variables such as head, flow, pressure, and temperature. By the law of conservation of mass, the mass flow rate remains the same from suction to discharge. The volumetric flow can also be assumed to be the same for pumps working on incompressible liquids since the density remains constant. For compressors handling compressible gas, however, a significant increase in density occurs during compression; thus, the volumetric flow rate becomes significantly lower from the suction to discharge, even though the mass flow remains the same. The changes are closely related to the gas property and operating condition: Fm = Fm,s = Fm,d = ρs Fv,s = ρd Fv,d Ps M 1 − n1 − n−1 Fv,d ρs Ps Td Pd Td Z s R Ts = = ≈ = = , Pd M Fv,s ρd Pd Ts Ps Ts Z d R Td

(2.37) (2.38)

where Z s = Z d is assumed, which is not exactly true but usually acceptable. The accurate profile of the compressibility value inside the compressor is challenging to obtain. A related flow definition is the standard flow rate, the volumetric flow rate at a standard condition of P0 = 101.3 kPa and T0 = 15 ◦ C = 288.15 K. The standard flow is a volumetric flow. However, it is the same concept as mass flow since the flow condition is fixed. When describing the processing capacity or calculating power consumption, it is customary to use either mass flow or standard flow since they are independent of the specific operating condition. See Niu and Xiao (2022) for the different types of flows.

52

2 Characteristics of Pumps and Compressors

The discharge pressure can be related to the suction pressure via the temperature ratio (see Eq. 2.10): Pd = Ps



Td Ts

n

n−1

.

(2.39)

The suction and discharge pressures can also be related via the polytropic head with Eq. 2.24: 

n  n−1 M n−1 Hp +1 n Z s R Ts   σ1 ρs = Ps · σ H p · +1 . Ps

Pd = Ps ·

(2.40)

The calculation of discharge pressure Pd from suction pressure Ps requires the value of the polytropic exponent n or polytropic index σ , which in turn requires the ratio of specific heat κ and efficiency η. As discussed later, the unavailability or inaccuracy in the polytropic index n is a significant challenge in compressor performance analysis and control design. An acceptable approximation is needed. For a centrifugal pump, assuming an isochoric process with n = ∞ (i.e., σ = 1), Eq. 2.40 reduces to

ρs +1 Pd = Ps · H Ps = Ps + ρs · H = Ps + ρs · g · h,

(2.41)

where h is the head in height. Equation 2.41 is the same as Bernoulli’s equation in Eq. 2.3, assuming the same flow velocity from suction to discharge. Pressure rise causes the temperature to increase. For centrifugal compressors, temperatures at the suction and discharge side are related by Td = Ts



Pd Ps

n−1 n

→

Td = Ts ·

Pd Ps

n−1 n

.

(2.42)

Example 2.2 Changes in pressure and temperature during centrifugal compression. For natural gas with n = 1.4, assuming a compression ratio of 3, the volumetric flow rate at discharge is given by Eq. 2.38 as Fv,d = Fv,s



Pd Ps

− n1

= 3− 1.4 = 0.456 = 45.6%, 1

(2.43)

2.3 Behaviors of Dynamic Machines

53

which is less than half of the suction flow rate, although the mass flow rate is the same. The primary concern for a higher compression ratio is the excessively high temperature at discharge which can cause damage to the device and piping. Typically the discharge temperature should not exceed 180 ◦ C (or 350 ◦ F). As shown in Eq. 2.42, discharge temperature increases with pressure, which is primarily caused by inlet temperature, compression ratio, and gas composition. Correspondingly, the most practical measures for limiting discharge temperature are providing adequate gas cooling and limiting the compressor ratio. Assume the suction temperature is at Ts = 60 ◦ C. A compression ratio of 3 will result in a discharge temperature as Td = Ts ·

Pd Ps

n−1 n

= (60 + 273.15) × (3)

1.4−1 1.4

= 456.0 K = 182.8 ◦ C.

(2.44)

If we would like to limit the discharge temperature to 150 ◦ C, the maximum compression ratio can be calculated from Eq. 2.39 as Pd = Ps



Td Ts

n

n−1

150 + 273.15 = 60 + 273.15 = 2.31.

1.4

1.4−1

(2.45)

2.3.3 ‡ Euler’s Equation and Slope of Performance Curve The machine’s performance is determined by its geometric construction, which is dictated by fundamental laws like Euler’s equation. The shape and slope of the performance curve are critical factors in assessing the machine performance, with a profound impact on the machine’s behavior, impacting its operation and control. Euler’s Equation The fluid energy, represented by the fluid head, can be calculated from the change in angular momentum of the fluid entering and exiting the impeller. Based on Newton’s third law of motion, the fluid’s rate of change in angular momentum equals the net torque imposed on the fluid by the rotor (Liptak 2006; Elliott and Bloch 2021):

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2 Characteristics of Pumps and Compressors

τ=

Fm (r1 V1u − r2 V2u ) , g

(2.46)

where τ is the shaft torque, Fm is the mass flow, V1u and V2u are the tangential components of the fluid velocity, r1 and r2 are the impeller-eye radii and outside diameter hub radius. g is the gravitational constant. The energy E transferred from the rotor to the fluid is thus given by E =τω Fm ω (r2 V2u − r1 V1u ) = g Fm = (U2 V2u − U1 V1u ) g with U1 = ω r1 , U2 = ω r2 ,

(2.47)

where U1 is the inlet tangential velocity, and U2 is the exit tangential velocity at the impeller outside diameter. Equation 2.47 is the basis of nearly all performance characteristics for all forms of turbo-machinery and is known as Euler’s Equation. It states that the energy transferred between the rotor and the fluid can be accounted for by the difference between the product U1 · V1u at the entry and the product U2 · V2u at the exit of the impeller. In other words, the rate of change in angular momentum of the fluid equals the net torque imposed on the fluid by the rotor. The head, defined as the energy produced per unit of mass flow, is given by H =−

1 E = (U2 V2u − U1 V1u ) . Fm g

(2.48)

Usually, the impeller is so designed that the fluid entry is axial, i.e., V1u = 0 and V1w = V1 (see Fig. 2.21), then Euler’s Equation would reduce to H=

1 U2 V2u . g

(2.49)

The head produced is a function of the impeller tip speed and the gas exit velocity relative to the blade, which is proportional to the volumetric flow rate. For an impeller with back lean angle β2 , the component of the fluid velocity V2u is given by V2u = U2 − V2w cot(β2 ),

(2.50)

therefore, H=

1 U2 (U2 − V2w cot(β2 )) , g

(2.51)

2.3 Behaviors of Dynamic Machines

55

where V2u is the exit velocity of the fluid and is related to the volumetric flow Fv,2 via V2w = Fv,2 /A2 , with A2 being the cross-sectional area at the outlet. We then have

1 Fv,2 H = U2 U2 − cos(β2 ) . g A2

(2.52)

This equation shows that at a constant speed, Euler’s head is a function of the volumetric flow rate and nothing else. In other words, for a given diameter impeller at a given speed, a fixed amount of energy (kJ/kg) is transferred to each mass unit of fluid, regardless of the density of the fluid. Note that if the backlean angle β2 = 90◦ , and cot β2 = cot 90◦ = 0, the head generated would be a function of the blade tip speed alone: H=

1 2 U . g 2

(2.53)

Basic Slope The performance curves we have shown so far all have a negative slope under the head-flow coordinate system, which is not always true. The slope of the curve is dictated by the underlining mechanical design and physical principles, with the impeller being the determining factor. Each centrifugal machine can have multiple sections, each section has multiple stages, and each stage has multiple impellers. An impeller consists of multiple rotating vanes to impart mechanical energy to the fluid. In theory, the performance curve is per impeller, and the curve differs from impeller to impeller. In practice, however, composite performance curves are generally provided for each stage. Because no heat is removed between impellers, the composite performance curves are acceptable as a good trade-off between complexity and accuracy. There are many different designs of impellers. One critical factor affecting the machine’s performance is the backlean angle β2 , as shown in Fig. 2.21a. This angle determines the slope of the performance curves. For different β2 values, the so-called basic slope, which is the ideal or theoretical slope of the head-flow relationship without considering any losses, is shown in Fig. 2.21b. For radial exit with β2 = 90◦ , the basic slope is zero, corresponding to a flat head-flow line. With a backlean angle β2 > 90◦ , the basic slope would be positive, indicating that more flow will generate more head. See Fig. 2.21b for an illustration. With a backward lean angle β2 < 90◦ , also called “back-sweeping,” the performance line between the head and flow has a negative slope, which indicates that the more flow through the machine, the less head it will generate. In addition, a smaller angle will result in steeper curves, and vice versa. This relationship can be revealed from the illustration in Fig. 2.22, where it is seen that more flow implies a higher relative speed from W2 to W2 . The absolute

exit speed moves from V2 to V2 , resulting in a smaller value in V2u . According to

56

2 Characteristics of Pumps and Compressors

Fig. 2.21 Impellers and Euler’s equation

Fig. 2.22 Reverse relationship between head and flow

Euler’s equation, the generated head is the product of the tip speed U2 , and the flow

. Therefore, a larger flow rate will produce a smaller head value of H component V2u at the same speed. See Fig. 2.22a. Similarly, less flow throughput implies a lower exit speed, and thus, a more prominent flow component for the head calculation. The result is a higher head with less flow, as shown in Fig. 2.22b. This phenomenon is as expected. With a fixed blade tip speed, the head is determined by the relative velocity of the gas. A higher flow implies a higher gas velocity

2.3 Behaviors of Dynamic Machines

57

Fig. 2.23 Reverse relationship between head and flow for radial blades

exiting the impeller. The higher the velocity, the less time the gas is in contact with the impeller blade and the less energy it will pick up from the blade. As a result, a lower pressure will be developed. Most centrifugal machines in the process industry choose backward-leaning blades (with β2 between 55 and 75◦ ) because their characteristic curves with a negative slope provide a better differential head and a wider stable range for process control (Boyce et al. 1983). For comparison, Fig. 2.23 shows the head and flow for impellers with radial exit. With β2 = 90◦ , the gas exits the impeller in the radial direction. The flow component V2u remains constant with changing flow velocities. Therefore, the head generated becomes a function of the tip speed only, unaffected by the flow. Actual Performance Curves In reality, there are inevitable aerodynamic and mechanical losses16 during the energy transfer from the rotor to the fluid, including, for instance, fluid separation from the blade surface causing a decrease in exit whirl velocity or slip, fluid-wall friction, and turbulence (Boyce et al. 1983). This separation of the fluid from the blade’s exit angle is called slip. As a result, the actual performance curve deviates significantly from the theoretical curves in Fig. 2.22, especially at both ends. It resembles what is illustrated in Fig. 2.24.

16

Mechanical losses affect the power input to the machine, but do not influence the shape of the head-flow curve.

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2 Characteristics of Pumps and Compressors

Fig. 2.24 “Basic slope” and performance curves

Moreover, the head/flow lines derived from the Euler equation assume that the fluid velocity is uniform across the impeller cross section and exits along a path guided by the blade’s exit angle. However, the fluid does not exit perfectly along the blade’s exit angle since flow separation between the fluid and the blade’s surface takes place long before the fluid exits. It is virtually impossible to know the exact shape of the actual performance curves. The qualitative description based on the manufacturer-provided performance curves is sufficient for most applications.

2.3.4 ‡ System Resistance and Slope of Resistance Curve The process around the pump and compressor comprises two parts: the suction system and the discharge system. The objective of the machine is to remove (or “pull”) the fluid from the suction vessels at the same rate as it enters that vessel. Similarly, the discharge system “pushes” the fluid against the discharge system resistance to the downstream operation to achieve the desired discharge pressure. The discharge head corresponds to the external energy required and is the net effect of the total resistance from both the discharge and suction systems. Figure 2.25 illustrates the resistance components of a simplistic singlestage single-train compression process, including ➀ piping, heat exchangers, filters/strainers, and non-return valves; ➁ control valves; ➂ back pressure; and the line-up of the flow path. The diffuser of the compressor is another major flow-resistant component. For the fluid to flow forward, a pressure gradient must exist. Assume any two points on the flow path, with pressure P1 and P2 , respectively (see Fig. 2.26a), and the flow resistance is lumped into a single component represented by an imaginary

2.3 Behaviors of Dynamic Machines

59

Fig. 2.25 System resistance and process flow components (reproduced, with permission, from Niu and Xiao (2022))

Fig. 2.26 Flow and system resistances

choke valve or equivalent orifice. The relationship between the flow rate and pressure gradient is given by  Fm = C ρ (P1 − P2 )

(2.54)

where Fm is the mass flow rate, and ρ is the fluid density. Flow constant C is a relative measure of the efficiency of the flow-resisting component between the two points on the flow path. To achieve a flow rate of Fm , the pressure difference between the two points must meet the following requirement: P2 − P1 =

1 Fm2 . C2 ρ

(2.55)

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2 Characteristics of Pumps and Compressors

In many operations, the pressure difference P1 − P2 is not large enough to produce the desired flow rate. For example, in an oil and gas processing facility, the fluid often must be processed and transferred from a lower pressure point to a higher pressure point, e.g., the main oil line in Fig. 1.6. The required pressure gradient is provided by a pump for liquid or a compressor for gas, as shown in Fig. 2.26b, where Ps and Pd are the suction and discharge pressures of the pump, respectively, with Pd > Ps . Assume that the suction and discharge systems are simplified into two equivalent choke valves for convenience of understanding. By conservation of mass (see Eq. 2.1), the pressure profile must meet the following requirements: ⎧ 1 ⎪ ⎪ ⎨ P1 − Ps = 2 C1 1 ⎪ ⎪ ⎩ Pd − P2 = 2 C2

Fm2 ρ1 Fm2 . ρ2

(2.56)

The pressure boost provided by the pump or compressor is a function of the source pressure P1 , the destination pressure P2 , the fluid density ρ, and the flow constants C: Pd − Ps =

1 1 + 2 2 C1 ρ1 C2 ρ2

Fm2 − (P1 − P2 ).

(2.57)

This relationship indicates that the pressure rise in the pump or compressor is approximately a quadratic function of the flow rate. The source and destination pressure affect the relationship via the P1 − P2 term. At the same time, the resistance changes in the flow components, such as the throttling valves, are reflected in the flow constant C1 and C2 in Eq. 2.57. For example, suppose a fluid with constant density ρ is transferred from one storage tank to another under atmospheric pressure (P1 = P2 ). In that case, the pump must provide the pressure gradient to overcome the flow resistance to produce the desired flow rate of Fm : Pd − Ps =

1 ρ



1 1 + 2 C12 C2

Fm2 .

(2.58)

The pressure rise generated by the pump is a quadratic function of the flow rate, similar to any flow component on the flow path shown in Eq. 2.55. The system resistance curve is a theoretical concept. If the back pressure remains constant and all valves (throttling and recycling) remain unchanged, the result is a constant-resistance curve. An example of a constant-resistance curve is an electric fan that draws air from the atmosphere and pushes the air to the atmosphere. Similarly, the resistance curve resembles one constant-resistance curve if the compressed gas is discharged to the main gas line of relatively infinite capacity. In practice, however, the system resistance rarely remains constant. There are almost always multiple factors affecting system resistance. As a result, the actual

2.4 Surge and Choke Phenomena

61

trajectory of the operating point is a combined effect. For instance, if the discharge gas is sent to a confined space like a storage tank, such as buffering tank of instrument air, the back pressure increases as more gas is received, the system resistance will increase with time, and the resistance curve on the performance map will shift to the left as the pressure increases. We will call the trajectory the actual-resistance curve17 to distinguish it from the constant-resistance curves.

2.4 Surge and Choke Phenomena The flow through a centrifugal machine has an inherent operating range. When the flow falls below a specific limit, the machine may go into surge, an unstable working condition. Centrifugal machines are also constrained by the maximum flow that they can deliver. The maximum flow is attained when the flow reaches the velocity of sound and is said to have choked.18 For centrifugal compressors, the choked flow limit is also called the stonewall.

2.4.1 Surge and Choke Points A surge in a centrifugal compressor is a result of flow separation from the flow surface caused by low gas velocity. It can occur anywhere on the flow path in the compressor. Centrifugal pumps experience the same separation phenomenon at low flows, causing the liquid to vaporize, resulting in cavitation. The surge point on the performance curve represents the minimum flow value for stable operation. At a flow rate below the stability limit, the head produced by the compressor cannot overcome the system resistance to maintain a forward flow, resulting in temporary backflow. This resistance is imposed by the process and is reflected by the pressure difference across the machine. The thrust reversal can lead to violent vibrations to cause mechanical damage to the machine. The surge point is located at the peak of the curve, as shown in Fig. 2.27a, and marks the head/flow condition where the surge phenomenon may start. To the right of the surge point, the slope of the performance curve is negative. The slope approaches zero as the operating point approaches the surge point. Over the surge point, the slope turns positive. 17

The trajectory of the operating point for a compressor sending gas to a confined space is also called the integrative resistance curve in some literature, e.g., Boyce et al. (1983), Kurz et al. (2016) since the pressure increases as more gas is brought in. 18 Choked flow at compressor discharge resembles critical flow through an orifice. When choked, the volumetric flow does not increase with pressure increases (the mass flow can still increase with √ higher pressure or higher gas density). The speed of sound at the inlet is given by s = gκ Z RTs where κ is the isentropic exponent, and Ts is the inlet temperature.

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2 Characteristics of Pumps and Compressors

Fig. 2.27 Slope of the performance curves

Similarly, as the operating point moves to the right, the performance curve becomes steeper (i.e., more negative slope). The performance curve becomes almost vertical after a certain point, and the head-producing capacity falls off rapidly, with low efficiency and unpredictable performance, thus deemed unsuitable for normal operation. The cutoff point for this low-efficiency operation is the stonewall point or choke point. Vendor-provided performance curves customarily only provide the segment that can be operated stably, i.e., from surge point to choke point. Therefore, on almost all commercially available performance curves, the surge point is on the extreme left, and the choke point is on the extreme right, see Fig. 2.27b. See also Fig. 2.14 for an example of vendor-provided performance curves. The positive slope on the head-flow coordinate system indicates resistance to flow, while a negative slope indicates the opposite. The system resistance curve always has a positive slope, while the slope of the performance curve can be positive or negative. When the operating point is to the right of the surge point, the negative slope of the performance curve and the positive slope of the resistance curve counteract each other and provide a self-regulating condition for the operating point to reach equilibrium by itself. Once the operating point moves left over the surge point, both the resistance and performance curves have positive slopes; the machine loses the energy to counter the system resistance. The operation quickly becomes unstable and is said to have entered a surge condition. The surge phenomenon results from the interaction between the compressor and the process. A compressor in surge fails to meet the operating requirements, and the rotor’s violent axial and radial movements can also cause severe damage to the machine. Potential initiators of surge include startup and shutdown, trips, severe turndown, fouling, blockage, or drastic changes in operating conditions such as molecular weight. Higher pressure and higher molecular weight applications can result in more significant damage from a surge. Low-density applications such as hydrogen can cause surge damages that may only be detectable until the equipment is

2.4 Surge and Choke Phenomena

63

Fig. 2.28 Compressor surge cycle (reproduced, with permission, from Niu and Xiao (2022))

disassembled. One of the most impressive examples of compressor surge is when the axial compressor on a jet engine goes into surge (Giampaob 2010). A surge can be a mild surge or a deep surge. With a deep surge, an insufficient head may cause the machine flow to reverse direction and flow backward. Once the sufficient volume is rebuilt, the flow changes direction and moves forward again. If the low-flow condition persists, the backflow will develop again, leading to rapid fluctuations in flow and pressure and violent vibrations in the machine and associated piping. Deep surges can reduce efficiency, create instability, and cause damage to seals, bearings, and impellers. An accumulated surge of over 30 min is detrimental to the components, with damage beyond acceptable levels (Day 2016; Hafaifa et al. 2014; Sundström et al. 2018). Surge is a high-speed phenomenon; the flow reversal can occur in sub-seconds. Figure 2.28 illustrates a typical surge cycle, where the cycle time is between 300 ms and 3 s: A → C: 20∼50 ms, D → E: 20∼120 ms, A → · · · → E: 300 ms ∼ 3 s (Mirsky et al. 2012). Surge and choke phenomena are consequences of extreme gas velocity in the machine. Surge is caused by low-flow turbulence, while choke is caused by highvelocity friction. They can occur in dynamic machines, including centrifugal and axial pumps and compressors (and blowers). However, there are no such concerns with reciprocating machines. An adequately specified compressor has its normal operating points near the best efficiency point (BEP), well above the minimum flow limit. In other words, a surge19 19

Stall is another terminology related to surge. Reduced flow through a centrifugal machine will increase the losses in its aerodynamic components, such as the diffuser and impeller, eventually causing the separation of the fluid from the flow surface. As a result, part of the fluid will not exit

64

2 Characteristics of Pumps and Compressors

is an abnormal phenomenon under abnormal operational conditions (Gravdahl and Egeland 1999; McMillan 1983; Hafaifa et al. 2014).

2.4.2 Surge Line and Choke Line For centrifugal machines operating at multiple speeds, connecting all the surge points at different machine speeds produces the surge line. Similarly, connecting all the choke points produces the stonewall line or choke line (Hafaifa et al. 2014). See Fig. 2.28. The surge and choke lines are the dividing lines between stable and unstable operating regions. The operation point is expected to be limited between the surge and choke lines for stable operation. The surge line is jagged due to errors and approximations in calculations or measurements. Although the jaggedness poses little challenge to human interpretation, automatic control requires a smooth line that can be represented with a simple mathematical formula, with the following two requirements: 1. A simple mathematical representation of the surge line that can be used by both human operation and real-time control. 2. The representation must be valid for all the desired operating scenarios with different pressure, temperature, and gas properties. These two questions are central to pump and compressor control. The answer to the first question is the so-called surge reference line, and the second is the concept of the invariant coordinate system; both are discussed in detail in Chap. 5. The different approaches to handling the above two questions mark the difference in the control solutions provided by all commercial control solutions, as discussed in later chapters.

2.5 Summary Pumps, compressors, fans, and blowers are prevalent rotating equipment in the process industry. They share many similarities in their working principles but differ in many details. Process control engineers view these machines differently from rotating equipment engineers or process engineers. Process control concerns mainly the process variables describing the behaviors of the machines, the cause-and-effect relationship among the variables, and the dynamic transient responses of these variables.

the machine. Stall is a precursor to surge, although sometimes used interchangeably (Sundström et al. 2018).

References

65

There are many commonalities in these machines’ dynamic analysis and control design from this perspective. The common characteristics can be extracted and visualized with three variables (head, flow, and speed), two curves (performance and resistance curves), and one point (the operating point). The three basic variables describe the machine’s characteristics. The two curves represent the cause-and-effect relationships among the variables. They form the basis for operation and control.

References Bachus L, Custodio A (2003) Know and understand centrifugal pumps. Elsevier, London Boyce MP (1993) Principles of operation and performance estimation of centrifugal compressors. In: Proceedings of the twenty-second turbomachinery symposium, College Station, Texas Boyce MP, Bohannan WR, Brown RN, Gaston JR, Meher-Homji C, Meier RH, Pobanz NE (1983) Tutorial session on practical approach to surge and surge control systems. In: Proceedings of the 12th turbomachinery symposium, College Station, Texas, USA Brown RN (1991) Fan laws, the use and limits in predicting centrifugal compressor off design performance. In: Proceedings of the 20th turbomachinery symposium, Texas A&M University. Turbomachinery Laboratories, pp 91–100 Cumpsty N (1989) Compressor aerodynamics. Longman Group UK Limited Day I (2016) Stall, surge, and 75 years of research. J Turbomach 138(1) Elliott H, Bloch H (2021) Compressor technology advances — beyond 2020. Walter De Gruyter Forsthoffer WE (2005) Forsthoffer’s rotating equipment handbooks, vol. 1: principles of rotating equipment. Elsevier Ltd Giampaob T (2010) Compressor handbook: principles and practice. The Fairmont Press Golden S, Fulton SA, Hanson DW (2002) Understanding centrifugal compressor performance in a connected process system. Petrol Technol Q Gravdahl JT, Egeland O (1999) Compressor surge and rotating stall – modeling and control. Springer, London Limited Gresh MT (2001) Compressor performance: aerodynamics for the user, 2nd edn. Butterworth Heinemann Hafaifa A, Rachid B, Mouloud G (2014) Modeling of surge phenomena in a centrifugal compressor: experimental analysis for control. Syst Sci Control Eng 2:632–641 Kurz R, White RC, Brun K, Winkelmann B (2016) Surge control and dynamic behavior for centrifugal gas compressors. In: Proceedings of Asia turbomachinery and pump symposium, Turbomachinery Laboratory, Singapore Liptak BG (2006) Process control and optimization, instrument engineers’ handbook, vol II, 4th edn. Taylor and Francis McMillan GK (1983) Centrifugal and axial compressor control. Instrument Society of America, http://compressorcontrolstudent.modelingandcontrol.com Mirsky S, Jacobson W, Tiscornia D, McWhirter J, Zaghloul M (2012) Development and design of anti-surge and performance control systems for centrifugal compressors. In: Proceedings of the forty-second turbomachinery symposium, Houston, Texas Niu S, Xiao D (2022) Process control – engineering analyses and best practices. Advances in industrial control. Springer Sundström E, Semlitsch B, Mihaescu M (2018) Generation mechanisms of rotating stall and surge in centrifugal compressors. Flow Turbul Combust 100(April):705–719 Watterson JM (2018) A simple guide to understanding compressors. Momentum Press

Chapter 3

Operating Requirements and Control Objectives

Pumps and compressors are indispensable components in the process industry. They play a vital role in maintaining the safety and efficiency of the overall operation. To achieve optimal performance, it is essential to have a clear understanding of the control targets and skillful use of the control handles. Equally important is a good understanding of the machine’s characteristics and dynamic behavior. This knowledge is vital in predicting how the machine will respond to changes in the process. Moreover, pumps and compressors are not standalone components; they are a part of a larger system. The process flow configuration dictates the higher level operating objectives and strategies. Therefore, it is crucial to comprehend the machine’s behavior within the process context to ensure it contributes to the overall efficiency of the process. By considering these factors, operators can ensure that pumps and compressors operate optimally, resulting in a safer and more efficient process. With the use of advanced technologies and control systems, pump and compressor operation has become more sophisticated, and the demand for skilled operators has increased. This chapter aims to provide readers with the necessary knowledge to operate these machines successfully.

3.1 Operating Objectives and Requirements Pumps and compressors are critical elements of a process flow configuration. For example, in the oil and gas processing facility illustrated in Fig. 3.1, the many pumps and compressors are responsible for continuously moving the liquid and gas to the specified location at the specified flow rate and the desired pressure. 1. Operating point. As discussed in Sect. 2.2.3, the actual operating point must meet the requirements of both the machines and the process. The machine characteristics dictate where the operating point is allowed, while the process requirements determine where the operating point is desired. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. S. Niu, Process Control for Pumps and Compressors, Advances in Industrial Control, https://doi.org/10.1007/978-3-031-43122-7_3

67

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3 Operating Requirements and Control Objectives

Fig. 3.1 A typical compression process for upstream E&P facility (reproduced, with permission, from Niu and Xiao (2022))

The operating point is typically specified as the operating pressure and flow rate. The objective is to keep the operating point at the desired location on the performance map. There are two scenarios in the daily operation of the machine: proactive adjustment of the operating point in response to operating needs and reactive adjustment to counter the effect of load disturbances and process upsets. When the operating point moves away from the desired location, it must be brought back by adjusting the available control handles (LeBleu Jr. and Perez 2014). 2. Operating envelope. The operating point must be kept inside the various limits and constraints imposed by both the machine and the process, i.e., the operating envelope. During process upsets, the operating point may approach or breach these limits, and immediate corrective actions are required to restore the operating point. The most common constraints include the minimum/maximum flow limits and minimum/maximum speed limits imposed by the machine, the power and torque limit imposed by the driver, and the pressure and temperature limits imposed by the piping and vessels. If the corrective actions are unsuccessful, the process operation may go out of control; the machine or the processing unit may need to be proactively shut down to avoid severe consequences. 3. Abnormal situation handling. A pump or compressor is expected to operate under various modes, including startup, normal operation, crippled operation, turndown operation, and shutdown, to name a few. Bringing the machine on-stream from shutdown condition is challenging with high risk and requires careful attention and extensive experience. Improper startup procedures can cause severe damage to the equipment. A partial shutdown of the operation is a common requirement that can occur intentionally by operating request or unintentionally due to an emergency. During a partial shutdown, the remaining units are expected to stay in operation, and the partially operating unit is said to be in crippled mode. The smooth transition to

3.2 Maintaining the Operating Point

69

crippled mode and back to normal mode is a significant challenge for operation and control. Standard operation procedures (SOP) are essential to ensure a safe shutdown with minimal disruptive effects. Automated startup and shutdown sequences have attracted much attention in practical applications due to their potential to improve operational safety and efficiency.

3.2 Maintaining the Operating Point Normal operation requires maintaining the operating point at the desired values to meet the quality and capacity requirements. The operating point typically refers to the head and capacity of the machine corresponding to the pressure and flow of the process. They are the control targets (dependent variables). The control handles, or independent variables, are the means to influence the control targets. The three types of control handle for a centrifugal compressor, include the machine speed (➀), system resistance (➂ and ➃), and recycling (➄), are shown in Fig. 3.2. An inlet guide vane (IGV, ➁) is another control handle for centrifugal compressors, but not as widely used.

3.2.1 Operating with Single Control Handle Most of the time, maintaining the operating point is to maintain the desired flow throughput, referred to as capacity. The basis of operation is the cause-and-effect relationships among the variables of interest, represented by the cause-and-effect table (CET) in Table 3.1, derived from the characteristics of pumps and compressors discussed in Chap. 2. The column on

Fig. 3.2 Control handles for centrifugal compressor control

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3 Operating Requirements and Control Objectives

Table 3.1 Cause-and-effect table (CET) for pumps and compressors Centrifugal Machine Control Handles Machine Speed ↑

Reciprocating Machine

Head 

Flow 

Head 

Flow 

System Resistance ↑ Recycling ↑

 

 

 

− 

Inlet Guide Vane ↑ Stroke Length ↑ Clearance Pocket ↑

 − −

 − −

−  

−  

the left lists the control handles, and the row on the top the control targets. The up arrow ↑ indicates a step change in the control handle, while the arrows  or  indicate the direction of the response of the control targets to the step change, assuming only one control handle changes at a time. All control handles in Table 3.1 may cause changes to the head and flow. Depending on whether the machine is centrifugal or reciprocating, the changes can be different. For instance, increasing machine speed will cause increases in head and flow for both types of machines. Increasing recycle will result in high flow and lower head. Changing system resistance affects both flow and head of a centrifugal machine, but only the head of a reciprocating machine. Inlet guide valve is specific to centrifugal compressors, while variable stroke length or clearance pockets are for reciprocating machines only.

Machine Speed Adjusting the machine speed to change machine flow is the most efficient approach. For instance, with performance curves illustrated in Figs. 3.3 (for centrifugal machines) and 3.4 (for reciprocating machines), capacity change from 20.0 kg/s to 15.0 kg/s can be achieved by reducing the compressor speed. The operating point moves from the current point A to the new operating point C, along the constantresistance curve, assuming all other control handles remain the same. Since the efficiency ellipse is roughly parallel to the constant-resistance curve, moving the operating point along the resistance curve does not significantly affect the operating efficiency.

System Resistance Most machines operate at a fixed speed. The operating point is maintained by adjusting the system resistance through a control valve on the machine suction or discharge. Changing the system resistance moves the operating point along the constant-speed line, illustrated by the trajectory from A to B in Fig. 3.3. Changing machine capacity by varying system resistance is less efficient than adjusting the speed because extra energy is needed to raise the pressure, which is to be

3.2 Maintaining the Operating Point

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Fig. 3.3 Capacity control with centrifugal machines

Fig. 3.4 Capacity control with reciprocating machines

killed downstream. Moreover, moving along the constant-speed performance curve causes the operating point to move away from the best efficiency point (BEP) (see Fig. 3.3). However, capacity change with a throttling valve is simple and reliable, with less capital investment and lower maintenance needs than variable-speed machines. Changing system resistance has an insignificant influence on the flow of a reciprocating machine, as shown by the steep slope of the performance curve in Fig. 3.4.

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The slope of the performance and resistance curves affects the easiness of operation and control. Once entering normal operation, a pump or compressor, whether centrifugal or reciprocating, is surprisingly reliable and tolerant within a specific range of operating conditions. However, the operation can be relatively less stable if both the performance and resistance curves are flat.

Recycling Operation with recycling is another approach to adjusting the operating point. Three flows are essential to understanding and operating pumps and compressors: the process flow, machine flow, and recycle flow, as shown in Fig. 3.5. The machine flow is the sum of the process flow and recycle flow: [Machine Flow] = [Process Flow] + [Recycle Flow] Fs = F1 + Fr .

(3.1)

The machine does not know, nor does it care, whether the flow into the machine comes from the process or recycle line. For this reason, capacity adjustment can be achieved by directly recycling a portion of the flow at the discharge side back to the suction side, thus maintaining the desired flow rate through the machine while reducing the flow from the process. The effect of recycling is illustrated in Figs. 3.3 and 3.4 with lines A → D. At the same machine speed and pressure ratio, the machine flow remains at 20.0 kg/s. A recycle flow of 5.0 kg/s displaces the process flow and allows the process to turndown to 15.0 kg/s. In extreme cases, such as during startup, the machine flow can be entirely from the recycle flow with zero process flow (forward flow)! See Fig. 3.6 for an illustration. The recycling operation wastes energy to re-pressurize the recycled fluid, thus inefficient. For this reason, capacity change with recycling is typically reserved as a last resort for achieving capacity turndown beyond the minimum flow limit of the machine, e.g., during startup and crippled operation. Nevertheless, recycling is

Fig. 3.5 Three flows in pumps and compressors

3.2 Maintaining the Operating Point

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Fig. 3.6 Process flow, machine flow, and recycle flow

simple and reliable, and thus often used in many simple applications. For instance, recycling is the preferred control strategy for reciprocating compressors due to its simplicity. For air compressors, bleeding the air into the atmosphere is typically used, similar to recycling in terms of efficiency.

Inlet Guide Vane Moving the operating point by adjusting the inlet guide vane (IGV) works differently than changing speed, resistance, or recycling. From a process control standpoint, a compressor with IGV can be viewed as having a variable geometry. Changing the entry angle of the guide vane effectively changes the performance curve, which indirectly causes the operating point to move. For instance, assume that the compressor operates at 100% speed (of fixed speed). Reducing the guide vane angle causes the operating point to move along line ➀ while reducing the speed makes the operating point move along line ➁, as shown in Fig. 3.7.

3.2.2 Operation with Multiple Control Handles Practical applications often require both the flow and head to be maintained on target. Since flow and head are separate control targets, they require two independent control handles, usually the compressor speed and system resistance. Figure 3.8 illustrates how the machine speed and throttling valve work together to maintain the head and flow on target. Suppose the head is to be kept constant while the machine speed is reduced. The operating point would move in the direction of A → C, which would cause the head to decrease. The discharge valve will then be throttled to increase the resistance. The increased resistance will cause the head to return to the target value (Point B). Speed reduction and valve throttling together will eventually move the operating point to D. The actual trajectory from A to D

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Fig. 3.7 Capacity control with inlet guide vane

Fig. 3.8 Capacity control with centrifugal machines

may differ depending on how quickly the speed is reduced and how fast the valve is throttled. Example 3.1 Operation of a hairdryer. Consider a two-speed hair dryer in Fig. 3.9a. A hairdryer is an air blower and can be treated as a low-pressure air compressor.

3.2 Maintaining the Operating Point

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Fig. 3.9 A two-speed hair dryer

The two-speed option provides discrete speed changes for capacity control. The concentrator increases the system resistance to increase the exit speed of the warm air. With the two-speed switch and the detachable concentrator, the hairdryer has four possible operating points, as shown in Table 3.2 and Fig. 3.9b. When the hair dryer is at the lower speed and without the concentrator, the operating point is at A. Switching to the higher speed moves the operating point to B along the system resistance line. Attaching the concentrator increases the outlet resistance and forces the operating point to move from B to D along the constant-speed line. See Table 3.3 for a summary. If the dryer is switched to the lower speed and the concentrator is removed simultaneously, the operating point would move from D to A. Whether this move is through B or C depends on which action is taken earlier and which response is faster: the speed switch or concentrator removal. If both the speed and the resistance could change continuously, then the trajectory from D to A would take any path between D → C → A and D → B → A, similar to that in Fig. 3.8. Table 3.2 Operating points of a hairdryer

Concentrator OFF

Concentrator ON

A B

C D

Low Speed High Speed

Table 3.3 Cause-and-effect table for a hairdryer Control handle

Method

Machine speed Switch to higher speed System resistance Add concentrator Machine speed Switch to lower speed System resistance Remove concentrator

Operating point A⇒B B⇒D D⇒C C⇒A

Flow

Head

More Higher Less Higher Less Lower More Lower

Power More Less Less More

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3.2.3 † Capacity Turndown Capacity is a different name for flow throughput. Two types of capacities concern us: the process capacity, i.e., process flow, and the machine capacity, i.e., the machine flow. The process flow is the control target at the process level, and the machine flow is the control target at the machine level. These two flows are not always the same since the machine flow has a turndown limit while the process flow does not. In case of conflict, the target at the process level takes precedence over the target at the machine level (except for protective actions), and additional handles must be used to meet the process level requirements. For centrifugal machines, the machine flow can be influenced by any of the control handles shown in Fig. 3.3. For instance, process flow turndown can start with reducing the process and machine flows in tandem. After the machine flow reaches its minimum flow limit, recycle flow is introduced to continue reducing the process flow while maintaining the machine flow at the minimum flow limit. This two-step turndown is illustrated in Fig. 3.10. From Point A to B is via valve throttling, and from B to B is via recycling. Similarly, from A to C is by reducing the speed, and from C to C is via recycling. With both machine speed and throttling valve changing simultaneously, the operating point can be moved from A to D , after which recycling is introduced to move the operating point from D to D. The amount of recycling (the difference between F2 and F3) in these scenarios is significantly different. It is also possible to move the operating point from A to D by recycling only. However, this is inefficient due to the unnecessarily large recycle flow.

'

'

'

Fig. 3.10 Flow turndown below surge limit

3.3 Protecting the Operating Envelope

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Table 3.4 Flow turndown in a centrifugal machine Process Flow Machine Flow Recycle Flow Point A Point B , C , D Point B, C, D

F1 F2 F3

F1 F2 F2

0 0 F2-F3

In other words, the capacity turndown can be achieved by any of the three types of control handles (speed, resistance, and recycling) before reaching the minimum flow limit. After that, recycling is the only control handle for further turndown. The flow values at various points are illustrated in Table 3.4. This minimum flow limit, or surge point, can be visualized on the performance map and easily followed by a human. However, for automated flow control, the minimum flow limit must be represented in a machine-understandable format suitable for online implementation, such as a mathematical formula or look-up table. This quantitation of the performance curve is the main topic of control design in Chap. 5.

3.3 Protecting the Operating Envelope Disturbances and abnormal conditions are inevitable in actual operation. Responding to abnormal situations is more critical and challenging than normal operations since operational safety is at stake. Keeping the operating point inside the operating envelope is compulsory.

3.3.1 Operation Under Abnormal Operating Conditions Typical process conditions that may drive the operating point to an inefficient or unsafe region include process upsets, equipment failures, instrument malfunctions, and turndown operation. As shown in Fig. 3.11, the operating envelope (shaded area) is defined by various limits and constraints imposed by both the machine and the process, such as minimum and maximum speed, minimum flow (surge) and maximum flow (choke), motor power, pressure and temperature, and gearbox torque. The minimum flow limit is crucial for centrifugal machines, and over-pressure for reciprocating machines. Operational safety requires that the machine operation not violate the operating limits. At the same time, operational efficiency demands that the machine be allowed to operate as close as possible to the limits for maximum operating range. For instance, minimizing recycle flow through better control significantly contributes to energy efficiency because recycling is highly inefficient. However, excessive recycling, common in many operating plants, is a huge energy waste.

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Fig. 3.11 Compressor operating point and envelope

The process operating constraints vary with the actual process flow configuration. For instance, process piping and equipment all have pressure and temperature ratings that must not be exceeded, especially in reciprocating machines where the back pressure determines the discharge pressure and is limited only by the power supply from the driver. Low pressure at the suction side of a reciprocating pump may violate the net suction pressure head required (NSPHR) and should be monitored and avoided. On the machine side, pumps and compressors have inherent design limits. For instance, a centrifugal machine is designed to operate within the rotation speed range. Below the minimum speed, the machine may become unstable, while operating at too high a speed may also put the mechanical integrity at risk. The typical operating range is between 70% and 105% of the design speed. Enforcing the speed limits is straightforward by adequately monitoring and limiting the rotating speed. The surging phenomenon is a common threat to all centrifugal and axial machines, which can potentially cause severe mechanical damage.1 Surge is caused by insufficient flow through the machine, commonly occurring during initial startup, severe turndown, or significant load disturbances.

1

On the other hand, some machines, usually smaller ones, can operate for long periods with intermittent or continuous light surges without mechanical harm, although with significant impairment of aerodynamic performance.

3.3 Protecting the Operating Envelope

79

Fig. 3.12 Compressor stonewall

When the machine flow approaches the minimum stable flow limit,2 the recycle valve should be opened to send a portion of the fluid at the discharge side back to the suction via the recycle line to maintain the machine flow above the limit. In the actual operation, the main challenge is getting real-time information on the minimum allowable flow limit, which varies with speed and inlet condition. Too much flow through a centrifugal pump or compressor is also a concern. As the discharge flow approaches sonic speed, the flow can no longer increase. The machine is said to have reached the “choked” condition, or stonewall, as shown in Fig. 3.12. The choke phenomenon is not as threatening as a surge but can still cause serious operational problems such as vibration and extremely low efficiency. If a centrifugal machine is prone to approaching the choke line often, it may be necessary to limit the machine flow. A restrictive orifice or throttling valve can be installed on the discharge line to limit the flow. The challenge for choke prevention is knowing where the choke line is in relation to the current operating point, the same as surge prevention. The driver for a pump or compressor is typically an electric motor or a gas turbine. The motor can have a fixed-speed drive (FSD) or variable frequency drive (VFD). 2

Centrifugal pump operation has three minimum flow limits: minimum continuous thermal flow (MCTF), intermittent minimum flow, and minimum continuous stable flow (MCSF). By minimum flow, we typically refer to the minimum continuous stable flow (MSCF). MCSF ranges from roughly 10% to 80% of the best efficiency point flow depending on pump size and type, operating speed, impeller suction geometry, liquid density, and other factors. The operation of centrifugal pumps below their minimum flow requirements is the primary cause of premature pump failure. Hydraulic instability occurs at low flows and can cause a surge, cavitation, and excessive vibration in the pump. The extent and type of damage to the pump depend on how long the low-flow persists and the magnitude of the generated forces and vibrations.

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Fig. 3.13 Flow through an orifice plate

A fixed-speed motor can also be equipped with a variable-speed gearbox (VSGB) to achieve variable-speed operation. These machines and devices have operating constraints, such as electric current, power, and torque, that should not be violated.

3.3.2 ‡ Flow in System Resistance Components A pump or compressor is connected to a suction and a discharge system; both can be viewed as flow-resisting virtual orifices or choke valves. The machine “pulls” fluid from the suction system and then “pushes” it through the discharge system to reach downstream operation. From the process point of view, the pressure versus flow behavior can be interpreted as a flow through a series of flow resistance components (Fig. 2.25a). A flow through a contraction in the piping results in a pressure drop, which exhibits a quadratic function of the flow rate (Cunningham 1951; ISO-5167 2003). For example, the pressure drop P across a standard orifice (Fig. 3.13) is proportional to the squared flow rate Fv2 :  Fv = C P/ρ, P = ρ

Fv2 . C2

(3.2) (3.3)

C is a flow coefficient that remains a constant once the orifice plate is constructed.3 The pressure drop across a valve exhibits similar behavior, except that the flow coefficient C varies with the valve opening. 3

A carefully designed and constructed orifice plate is an inexpensive and reliable flow measurement device. See Sect. 6.2.4.

3.3 Protecting the Operating Envelope

81

In general, this quadratic relationship exists for all the components in the flow line, including filters, strainers, coolers, and control valves. Each component has the same mass flow but a different flow coefficient C. The flow through an orifice becomes unstable when the flow rate falls below a specific limit. A typical range is 10:1 in terms of differential pressure across the orifice. For this reason, an orifice-based flowmeter√loses its accuracy at approximately 10% of the maximum DP value or one-third ( 10 : 1 = 3.16 : 1 ≈ 3 : 1) of the maximum flow rate, as shown in Fig. 3.13b. The surge and choke phenomena share many similarities with flow through a valve or orifice. A compressor in stonewall operation is like an orifice with a critical flow (Boyce et al. 1983). The choked flow through an orifice defines the maximum flow, with the turndown limit at approximately 1/3 of the maximum flow. Coincidentally, a centrifugal machine suffers from the surge problem at approximately 1/3 of the maximum flow rate, defined by the choke flow, similar to an orifice plate. The pressure difference Pd − Ps between the suction and discharge is defined by the pressure rise across the impeller, and the pressure drop across the diffuser. The former is a function of machine speed and flow rate, while the latter is determined by the flow rate only. The fluid inside the machine reaches the maximum speed at the tip of the impeller with the highest energy at the entrance of the diffuser (Fig. 2.7). A pressure drop occurs when the gas goes through the diffuser. The pressure difference and the flow rate through the compressor have a relationship similar to that of an orifice (see Eq. 3.3):  (3.4) Fv ∝ C (Pd − Ps )/ρ Pd − Ps ∝ Fm2 ∝ Fv2 .

(3.5)

This analogy is made more prominent by flipping the X and Y axes of the flow versus DP relationship in Fig. 3.13b. Assume Pmax is the pressure at the blade tip. The relationship between the pressure drop (Pmax − P) and the flow in Fig. 3.14a is similar to the head-flow relationship in the compressor performance curve in

Fig. 3.14 DP versus flow in an orifice plate and head versus flow in a compressor

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Fig. 3.14b. This similarity helps explain and understand the performance and resistance curves discussed in Sect. 2.2 and the surge indicators in Sect. 5.3. This relationship agrees with Eq. 2.57. In other words, the pressure rise in the compressor is roughly a function of the square of the machine speed, which in turn is proportional to the machine flow, per fan laws (Boyce et al. 1983). As a result, this pressure difference across the compressor is roughly proportional to the pressure drop across an orifice on the same flow path: Pd − Ps ∝ P.

(3.6)

This conclusion is extremely qualitative and has included many approximations. Nevertheless, this simplified relationship had been the basis for many early anti-surge control solutions (Boyce et al. 1983; Liptak 2006; Staroselsky and Ladin 1979; White 1972).

3.4 Transitioning Between Operating Modes Process operation can have many different operating modes. Transitioning from one mode to another poses unique challenges, sometimes with severe risks. A safe and smooth transition is compulsory, requiring a good understanding of the startup/shutdown sequence and the transitional behavior of the machine. For example, the startup and shutdown of rotating equipment are routine operations that are complicated and potentially risky. Damages to pumps and compressors most often occur during startup or emergency shutdown.

3.4.1 Startup of Centrifugal Machines The startup can be cold or hot. For example, for the two-train compressor system in Fig. 1.9, if both trains are started from a shutdown condition, it is a cold startup, which is characterized by low pressures at both the suction and discharge headers. On the other hand, assume train 1 is in normal operation, and train 2 is in shutdown mode. When train 2 starts to join the first train, it is a hot startup. During a hot startup, pressure headers at suction and discharge are also established by the running machines. The electric current required during startup can be several times higher than keeping the machine running at the normal operating condition. The heat generated during startup can be significantly higher than normal since the heat generated is proportional to the current squared (I 2 R). The startup of a centrifugal pump or compressor is a complex sequence. The machine starts with the downstream block valve closed and the recycle valve fully opened. Once the machine is started, the fluid quickly fills the recycle line; the

3.4 Transitioning Between Operating Modes

83

operation enters total-recycle mode. Depending on the recycle piping and valve size, the operating point will typically be on the far right side of the performance curve. As more process flow enters the machine, the discharge pressure (thus the head) builds up. For a hot startup, such as a machine joining an established header, the block valve would be opened as soon as the discharge pressure is higher than the downstream line pressure, and thus the transition is bumpless. However, the downstream may be a long empty pipeline with virtually zero pressure during a cold startup. The discharge pressure remains very low until the pipeline is filled with liquid. If the block valve (an on/off valve!) is suddenly opened with virtually zero resistance to flow, the operating point would abruptly move beyond the end-of-curve and trip the machine. Example 3.2 Cold start of an injection pump. Deep water disposal (DWD) is an integral part of a surface facility to inject the produced water (after treatment) back into the underground reservoir. As shown in Fig. 3.1, the pump discharge connects via a long pipeline to the deep disposal wells. One particular challenge for a cold startup is the need for initial system resistance. As the motor starts, the operating point rapidly moves to the far right on the performance curve due to the low system resistance (low head) from downstream. The high flow rate quickly overwhelms the motor and trips the motor by high power or vibration. The solution is to artificially create the required system resistance during a cold startup. Two popular designs are as follows: 1. Discharge throttling valve. If available, the discharge control valve for capacity control can create the initial system resistance during startup with the valve initially closed. Once the pump reaches full recycle mode, the valve can be manually and slowly opened to build up the back pressure in the downstream pipeline. See the piping configuration in Fig. 3.15a. 2. A discharge control valve is typically not installed for a variable-speed pumping process. Even if available, the control valve may not be rated for the type of high-pressure drop across the valve in high-pressure pumping applications. For this scenario, a working example is to utilize two block valves in parallel, one large and one small. See Fig. 3.15b. At the initial phase of the startup, the large valve is closed, with only the small valve open. The small valve provides enough

Fig. 3.15 Pump startup with a throttling valve

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3 Operating Requirements and Control Objectives

Fig. 3.16 Trajectory of operating point during cold startup

resistance to keep the pump running to prime the pipeline. Once the back pressure in the pipeline reaches an acceptable level, the large valve opens. The startup sequence is responsible for the opening and closing of the valves. Example 3.3 Startup procedure of a centrifugal machine. The startup of a large compressor is very challenging. Figure 3.16 shows the trajectory of the operating point during a cold start of a produced gas compressor (PGC). The suction and discharge header pressures are both under pressure control, and thus, the pressure ratio is nearly constant. 1. Initial ramp-up of machine speed: ➀ → ➁. The machine starts with the recycle valve fully open. It first rapidly ramps the machine speed to above the minimum stable speed with the compressor in total-recycle mode. The operating point quickly moves to the far right to the valve capacity limit. The flow increases as the pressure inside the circuit builds up (variable resistance curve). The discharge pressure increases as more gases are brought in but are still below the discharge header pressure, and thus the non-return valve is still closed, with no process flow (i.e., forward flow) going downstream. The compressor flow equals the recycle flow. 2. Establishment of forward flow: ➁ → ➂. After the machine exceeds the minimum stable speed, continue ramping up the machine speed but at a much slower pace for stability reasons. At the same time, the recycle valve is slowly closed to build up the discharge pressure. Once the discharge pressure is above the discharge header pressure, the non-return valve opens, and the gas starts to move forward. As the recycle valve slowly closes, the operating point moves to and stabilizes at point ➂.

3.4 Transitioning Between Operating Modes

85

3. Normal operation: ➂ → ➃. The operating points move between point ➂ and ➃ during normal operation, responding to the changes in capacity demand. The trajectory is approximately flat with a constant-pressure ratio since the suction and discharge pressures are both under control. The compressor speed is adjusted to maintain the desired capacity (compared to the trajectory in Fig. 3.8). 4. Shutdown: ➃ → ➄. A controlled shutdown starts by reducing the compressor speed and opening recycle, which brings the operating point to the origin ➀. The trajectory of the operating point for a fixed-speed compressor is different but can be similarly analyzed based on what has been discussed in this section. Chapter 5 will provide more detailed discussions on the startup sequences.

3.4.2 Shutdown of Centrifugal Machines Machine shutdown is the process of bringing the head and flow to zero. Shutdowns can either be controlled (scheduled) or uncontrolled (emergency). A scheduled shutdown follows the standard operating procedure (SOP). The machine speed is slowly reduced to the minimum stable speed before cutting off the power supply. This procedure ensures that the operating point reaches the origin following a steady and controlled path, such as ➀ in Fig. 3.17. An emergency shutdown is a disruptive process and poses many challenges to equipment safety, with surge being one of the main risks. During an emergency shutdown, the fuel supply to the gas turbine or electricity to the motor is cut off instantly, causing the compressor to coast down on inertia. Since the drop in the head (or compression ratio) is proportional to the square of the machine speed, and the

Fig. 3.17 Trajectory of operating point during shutdown

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3 Operating Requirements and Control Objectives

downstream and upstream piping imposes the pressure difference across the machine, the compressor may enter a surge condition if the pressure cannot be relieved quickly by the recycle valve. The decrease in the head may be faster or slower than the reduction in the flow, depending on the machine configuration and process flow condition. Thus, the trajectory from the current operating point to the origin may exhibit significant variations, as shown in Fig. 3.17. It is nearly impossible to know the exact trajectory since the shutdown happens extremely fast4 and is influenced by many factors unless a highfidelity rigorous dynamic simulation is conducted. The primary concern is whether the operating point would move too far to the left of the surge line and stay there for too long during the shutdown for the machine to enter a deep surge, as shown by line ➁ in Fig. 3.17. A typical and acceptable trajectory is similar to line ➂. The most critical consideration is that the accumulated gas in the surge volume must be minimized in the process design to increase the speed of response. For instance, the recycle line’s take-off should be before the discharge cooler. Otherwise, hot or cold bypass lines may need to be added.

3.4.3 † Crippled Operation A complex process configuration often comprises multiple pumps or compressors. It is common to run into a situation where a part of the operation goes down, and the remaining unit is expected to stay in operation, leading to the so-called crippled mode operation (partial shutdown). Like an emergency shutdown, the safe and smooth transition to crippled mode can be very complicated and disruptive. Consider the two parallel compressors in Fig. 3.18. Assume that the second compressor is tripped to a shutdown. What would happen to the first compressor, and how is it expected to respond to this abrupt change without tripping itself? When the second train is tripped to shutdown, the process flow shared by the two compressor trains is now forced through the first train alone, causing the suction header pressure to increase. The higher suction pressure will demand a quick increase in the machine speed. With proper responses by the operator or control scheme, the first train may react fast enough to survive the disruption. Eventually, the operating point will settle at a higher flow rate to accommodate the entire flow. Otherwise, the first train may trip as well.

4

Extremely high-speed data recorder is in increasing use to record data during a shutdown for post-incident analysis.

3.5 Summary

87

Fig. 3.18 Process flow of a 2 × 2 compressor network

3.5 Summary The operation of pumps and compressors is challenging. The goal is to achieve safe and efficient operation, and the operation is based on a sound understanding of the critical process variables such as speed, flow, and head, the familiarity of the dynamic cause-and-effect relationships between the key variables, which are discussed in Chap. 2. These are also the basis for automatic control to be discussed in later chapters since process control is to automate manual operations. The tasks of pump and compressor operation typically include: • maintaining the operating point in terms of flow and head, • protecting the operating envelope by observing both process constraints and machine limits, and • ensuring a safe and smooth transition between the different operating modes. The operation of complex systems involving multiple machines is even more challenging due to the infinite possibilities of process flow configuration. It is impossible to be familiar with all the variations. Instead, applying the basic concepts and principles to analyze and guide the operation is more effective and efficient.

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References Boyce MP, Bohannan WR, Brown RN, Gaston JR, Meher-Homji C, Meier RH, Pobanz NE (1983) Tutorial session on practical approach to surge and surge control systems. In: Proceedings of the 12th turbomachinery symposium. College Station, Texas, USA Cunningham RG (1951) Orifice meters with supercritical compressible flow. Trans ASME 73:625–638 ISO-5167 (2003) Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full, 2nd edn. ISO LeBleu Jr J, Perez R (2014) Operator’s guide to rotating equipment—-An introduction to rotating equipment construction, operating principles, troubleshooting, and best practices. AuthorHouse Liptak BG (2006) Process control and optimization, instrument engineers’ handbook, vol 2, 4th edn. Taylor and Francis Niu S, Xiao D (2022) Process control—engineering analyses and best practices. Advances in industrial control. Springer Staroselsky N, Ladin L (1979) Improved surge control for centrifugal compressors. Chemical Engineering, pp 175–184 White MH (1972) Surge control for centrifugal compressors. Chemical Engineering, pp 54–62

Chapter 4

Overall Control Strategy

Rotating equipment are complex machines with extremely fast responses. Achieving safe and efficient operation through manual control (Chap. 3) is nearly impossible. Unscheduled shutdowns of these machines can result in significant interruptions to production, reduced capacity, and equipment damage. Therefore, automated control solutions are necessary to ensure reliable operation and protect the equipment. Since process requirements vary across applications, there is no universally applicable control design. A sound control solution is based on a holistic view of the process operations and follows a process-centric approach that includes machine control as an integral part. A structured approach and proven methodology are advised to analyze the process flow, extract the cause-and-effect relationship, and design the control solution.

4.1 Overall Control Strategy Rotating equipment is instrumental to the safe and efficient operation of any industrial processes, similar to static equipment such as chemical reactors or distillation columns (Bahadori 2016; Borremans 2019; Giampaob 2010; Lieberman and Lieberman 2014; McMillan 1983). They deserve the same attention and treatment in the overall process control design as received by static equipment.

4.1.1 General Control Philosophy Equipment control has traditionally been the responsibility of equipment manufacturers or their affiliated/certified partners. The focus is primarily on the safe operation of the equipment and much less on the efficient operation of the entire process. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. S. Niu, Process Control for Pumps and Compressors, Advances in Industrial Control, https://doi.org/10.1007/978-3-031-43122-7_4

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The equipment control solution is usually designed and implemented with proprietary technology, hardware, and software, separately from the overall process control solution. Consequently, equipment control is often treated as a black-box component of the process control solution in both design and operation. This equipment-centric design is usually poorly integrated with process control for overall optimality. Due to its black-box implementation, it is also a maintenance nightmare (Botros et al. 2016). On the contrary, a control strategy based on a holistic view of the process flow configurations has a much higher chance of reaching overall optimality than piecemeal control designs (Kurz and Brun 2017). From the process control perspective, a pump or compressor is no more complex than a distillation column or chemical reactor. Both can be analyzed by following the same standard analytic procedures, designed with the same control methodologies, and controlled with the same standard process control technologies we already possess (Niu and Xiao 2022). Equipment control is an integral part of process control. The process and equipment must be treated as a single integrated system when designing the optimal control solutions. A flawed process control strategy may fail to maintain the proper material balance and causes oscillations in the unit operation, making equipment control more challenging. When this happens, even a perfectly working equipment control solution may fail to deliver the desired performance. Another perception is that pumps and compressors are high-speed rotating equipment and require high-speed hardware and software to support the control solution. As computer technology advances, the same speed that could only be offered by proprietary hardware and software is now achievable with standard control systems such as most DCS and PLC systems (Elliott and Bloch 2021; Honeywell 2023; Vermillion et al. 2023). The standard control system infrastructure has the advantage of established reliability, rich functionality, and complete transparency.

4.1.2 Overall Control Objectives The operating objectives dictate the control objectives. Generally speaking, the overall control objective is to achieve safe and efficient operation, which can be summarized as controlling one point, protecting two envelopes, as well as ensuring smooth transitions between different operating modes: 1. Control the operating point. The pressure and flow define the operating point, dictated by the machine’s performance curve and the process’s resistance curve. Continuous regulatory control keeps the operating point on the target. 2. Protect the operating envelope. Design limits and operating constraints imposed by both the process and machine constitute the operating envelope. The operating point should be allowed to move close to the operating envelope for maximum operating range. At the same time, the protective control functions prevent the

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operating point from moving outside the operating envelope for safety and efficiency. 3. Safeguard the safety envelope. Even the protective control functions may fail during a major process upset or device failure, and the operating point may move out of the safety envelope. The instrumented safeguarding logic will initiate a proactive shutdown to avoid severe damage. Typical trip events include vibration, surge, and high pressure. 4. Ensure smooth mode transitions. There are various operating modes in practical applications, such as shutdown mode, normal operating mode, turndown mode, and crippled mode. It is crucial to maintain safety and efficiency when the operation transits from one mode to another.

4.1.3 Layered and Integrated Design A sound control design follows a layered yet integrated approach, with normal regulatory control, protective overriding control, and instrumented safeguarding as the three lines of defense against abnormal situations. See Fig. 4.1 and compare with 1.20.

Fig. 4.1 Layers of process safety protections for pumps and compressors

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1. Normal regulatory control, such as capacity control, continuously executes to maintain the operating point on the target. It serves as the first line of defense against abnormal conditions and reduces the probability of machine surges. 2. Protective overriding control like anti-surge control keeps the operating point inside the operating envelope. Protective control remains dormant during normal operating conditions and becomes active only when the operating point moves outside the operating envelope. It serves as the second line of defense against abnormal conditions. Anti-surge control is the most crucial protective control for a centrifugal machine. 3. Safeguarding logic, such as anti-surge trip logic, monitors the operating point against the safety envelope and proactively shuts the operation down if the safety limits are violated. Anti-surge trip logic provides the third line of defense against potentially damaging events like surge. It is crucial to distinguish between normal regulatory control and protective overriding control in control design. Normal regulatory control is responsible for the continuous and smooth operation of the entire process to maintain the desired material and energy balance. Protective overriding control focuses more on localized protection of a specific process area or equipment against abnormal operating conditions. Complex control solutions can also become much easier to apprehend or design by separating regulatory and protective control. There are many significant advantages to this layered design. For example, the control solution is unaffected by a single mode failure. The multiple lines of defense against abnormal conditions provide more refined control action. Each layer can be tuned separately with different levels of aggressiveness based on the urgency of action.

4.1.4 Migration from Proprietary to Open-Platform Solutions Many vendor-provided solutions are based on proprietary hardware and software that is too difficult or costly to support the layered design in Fig. 4.1. Many reported failures with third-party solutions are with the hardware/software infrastructure (e.g., with the computer motherboard) rather than the control solutions itself. Proprietary hardware and software are becoming a liability that can no longer compete with the full-featured and field-proven DCS and SIS control systems that have already existed and have been running the entire plant. The use of proprietary hardware and software for control solutions is becoming increasingly difficult to justify. Specifically, the equipment control, particularly antisurge control, is shifting toward open solutions that rely on standard hardware and software (CCC 2021; Elliott and Bloch 2021; Honeywell 2023; Vermillion et al. 2023; Zelenov 2013). The control solution can now be designed with existing process control technologies we have all been familiar with, following the same standard methodology and procedure as we do with other process control solutions. Moreover,

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the control solution is implemented on standard hardware and software in the existing control systems we have been using. They can be operated and maintained like other process control solutions in the control system. This paradigm shift has a long-term impact on control and operation. The new paradigm enables the control strategy to base on a holistic view of the process and equipment with equipment control as an integral part of the overall control strategy, focusing on the overall control optimality. At the same time, this new paradigm shift demands increased knowledge of the machine characteristics and control strategy by process control engineers and operation personnel.

4.2 Regulatory Control: Capacity Control Normal regulatory control typically includes quality control and capacity control. Quality control is an operating requirement at the process level and is usually not a main consideration for pump and compressor operation. Capacity control is thus the primary requirement for normal regulatory control (Giampaob 2010). In practical operations, fluctuations and disturbances are inevitable. The operating point must be regulated by continuously adjusting the process flow rate. Capacity control is thus a regulatory control action to maintain the material balance between supply and demand. The improved stability of the plant operation through capacity control also benefits the protective control loops (e.g., anti-surge control) and safeguarding functions (e.g., anti-surge trip). We will explain the general capacity control strategy by examining the five essential components of a feedback control loop one by one within the context of capacity control.

4.2.1 Capacity Control Objectives The pumps and compressors provide the energy for the fluid to flow forward by overcoming the resistance created by the piping, fitting, and other static equipment. Automatic control ensures the process gas flows to the right place at the desired pressure and flow rate. The primary objective of capacity control is thus to keep the operating point at the desired pressure and flow, dictated by the material balance at the process level (see Fig. 4.2). A secondary control objective is optimizing the operation to achieve the best efficiency, especially when multiple pumps or compressors are involved. All pumps and compressors should have their best efficiency points (BEP) aligned with the normal operating condition for best efficiency, which translates to maximum energy savings.

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Fig. 4.2 Compressor operating point

4.2.2 Process Dynamics and Cause-and-Effect Relationships Process dynamics, including the supply-and-demand model, cause-and-effect relationship, and transient response behavior, are the basis of design for capacity control. The supply-and-demand model dictates whether the operation is supply driven (“supply pushing”) or demand driven (“demand pulling”). In a supply-driven operation, the upstream operation dictates the flow rate. The fluctuations in the supplyand-demand balance propagate forward along the process flow path. In contrast, the process flow throughput is dictated by downstream demand in a demand-driven operation, and the fluctuations in demand propagate backward to upstream. Supply driven : fluid supplied by upstream = fluid pushed to downstream Demand driven : fluid demanded by downstream = fluid pulled from upstream. The supply-driven and demand-driven operations often require drastically different capacity control designs. A systematic supply-and-demand analysis is thus essential in complex process design before starting control design or troubleshooting. The cause-and-effect analysis starts with defining the key process variables. The controlled variables in pump and compressor operation are typically the head and flow and can be influenced by machine speed, system resistance, and recycling. Speed

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Table 4.1 Cause-and-effect table for pump and compressor operation Control Handles Machine Speed ↑ System Resistance ↑ Recycle ↑

Centrifugal Machine Head Flow      

Reciprocating Machine Head Flow    −  

is an independent variable that directly impacts the head and flow. System resistance and recycling affect the head and flow more complexly. The cause-and-effect relationships are summarized in the cause-and-effect table (CET) (see Table 4.1). The CET helps determine the targets to be controlled (controlled variables), the control handles to be manipulated (manipulated variables), and the control strategy to follow for meeting the control targets with the available control handles. The transient behavior between the variables is another critical factor to consider in the control design since some variables can change extremely rapidly, requiring a similar response speed from the controller.

4.2.3 Process Measurements and Controlled Variables The control target for capacity control is the desired flow rate amid supply-anddemand fluctuations. The imbalance between supply and demand is caused by flow changes and is reflected by the variations in gas pressure or liquid level. The pressure or level will increase if the incoming flow exceeds the outgoing flow. Conversely, the pressure or level will decrease if the outflow exceeds the inflow. Instead of directly and explicitly controlling the flow rate, regulating the pressure or level is more reliable and convenient for capacity control. Thus the pressure and level are the controlled variables and essential process measurements. Multiple relay points are needed to propagate the supply-and-demand balance forward along the process flow path. At selected control points (or relay points), the pressure and level are indicators of the inventory level in the system. Any imbalance in supply and demand is reflected in the changes in pressure (for gas) or level (for liquid). At each relay point, the pressure is maintained by adjusting the incoming or outgoing flow rate. The typical pressure measurements around a compressor are the suction header pressure P1 and discharge header pressure P2 . See Fig. 4.3. If the gas supply increases, the pressure P1 increases. A pressure controller speeds up the machine to maintain the target pressure. Higher speed causes the discharge pressure to increase, which

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Fig. 4.3 Control target and handles for centrifugal compressor control

in turn triggers the discharge pressure controller to force more flow downstream to bring the discharge pressure back on target. The pressures at the key relay points are also the required process measurements.

4.2.4 Final Control Elements and Manipulated Variables The final control elements (FCE) include the three major types of control handles for compressor capacity control: the rotating speed, system resistance, and recycle flow, as shown in the cause-and-effect table in Table 4.1. A list of the most common control handles are as follows: 1. On/off switch. Switching the machine on and off to control the capacity is surprisingly common, especially with reciprocating machines. On/off control is a powerful and economical solution for process operations if the machine has high starting reliability and can accept slack control performance. Many small-capacity machines often operate on an on/off basis. For instance, a jockey pump is designed to start and stop frequently; the home A/C unit is based on on/off control; and an operating plant’s nitrogen gas or instrument air compressor is switched on and off to maintain the gas supply pressure within the desired range in a storage vessel. 2. Rotation speed. A pump or compressor can operate at different speeds by design. Changing the machine speed is an energy-efficient way to achieve the desired pressure or flow. The variable-speed capability is usually provided by a variablefrequency drive (VFD), variable-speed gearbox (VSGB), or gas expander. 3. Inlet guide vane (IGV). Centrifugal compressors can be equipped with adjustable inlet guide vanes (IGV) on the inlet. The inlet guide vanes pre-rotate the gas stream relative to the impeller rotation and effectively change the performance curve. It is another efficient way of changing the compressor capacity.

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Table 4.2 Typical control handles for pump and compressor operation Control Handles Machine Speed Inlet guide Vane Throttling Valve Stroke length Suction Unloading Recycle Valve

Centrifugal Machine Pump Compressor x x➀ x➁ x x ➂, ➃

x

x➄

Reciprocating Machine Pump Compressor x x x x x x

x x x x

4. Throttling valves. The most common approach for capacity control for centrifugal machines is changing the system resistance via control valves at either the suction or discharge. Throttling the flow increases the pressure ratio that the compressor “sees,” indicating the system resistance that the machine must overcome. 5. Recycle valve. Recycling a portion of the high-pressure fluid from the discharge back to the suction side is a simple but inefficient way of adjusting the flow through the machine (Kurz et al. 2016). 6. Blow-down. Discharging a portion of compressed air into the atmosphere is prevalent for air compressor control. For a centrifugal compressor, the location of the potential control handles is illustrated in Fig. 4.3. Their applicability is summarized in Table 4.2, with the circled number corresponding to the control handles in Fig. 4.3. Some control handles are mutually exclusive and will not be installed/used on the same machine. For instance, a fixed-speed centrifugal machine typically depends on the suction or discharge throttling valve to adjust the capacity, but not both. The throttling valve is typically unnecessary if the machine has a variable-speed driver. If installed, the throttling valve is always at the discharge side for a centrifugal pump due to the requirement of net suction pressure head (NSPHR). However, for a centrifugal compressor, the throttling valve is preferably at the suction but can also be on the discharge.1 Varying the machine speed for capacity control is more efficient than valve throttling, which in turn is more efficient than recycling, as illustrated in Fig. 3.3.

1

Surge calculation is typically based on suction flow. If discharge flow is provided, it must be converted to suction flow in the calculation. This conversion requires the polytropic exponent or efficiency and thus makes an invariant coordinate less “invariant.” See Chap. 5.

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Table 4.3 Typical control strategies for pump and compressor operation Centrifugal Machine Pump Compressor Fixed-Speed Valve Throttling + Recycle Variable-Speed Speed + Recycle

Reciprocating Machine Pump Compressor Recycle Speed

4.2.5 Capacity Control Algorithms Capacity control is typically based on standard PID controllers. Depending on the process flow configuration, the control scheme can be as simple as a single standalone PID controller; it can also be very elaborated, comprising multiple PID controllers, sequences, and logic. Even with the same controlled and manipulated variables, the control strategy can vary significantly depending on the supply-and-demand model and the cause-and-effect relationship.

Supply-Driven and Demand-Driven Control Process engineering design ensures the steady-state supply-and-demand balance for material and energy.2 However, supply and demand are never precisely balanced in a dynamic operating environment due to fluctuations, or swings, in the supply or demand: Swing = Supply − Demand.

(4.1)

Process design typically includes built-in buffering capacity or surge volume, such as “line-packing”3 for gas and surge tanks for liquid. However, the inherent surge volume is limited. Swing streams or swing capacity often need to be explicitly provided in the design to “absorb” the sustained imbalance in supply and demand. The imbalance between supply and demand is reflected in pressure (for gas operation) or level changes (for liquid operation) at selected control points. For this reason, capacity control is typically achieved indirectly via pressure or level control rather than direct flow control. There are many variations in control design due to different process configurations and personal preferences, including supply- versus demand-driven operation, variable versus fixed-speed drive, and reciprocating versus centrifugal machine. The typical control strategies are summarized in Table 4.3. 2

A persistent imbalance in steady-state supply and demand is a flaw in process design, often resulting in continuous flaring in gas operations or overflow in liquid operations. Flaring used to be a simple and popular “solution” to the material imbalance in gas plants but is no more viable due to more stringent environmental regulations. 3 Line-packing refers to the transient condition where more gas is fed to the piping that is taken out, usually leading to increased pressure.

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The process capacity control determines the machine capacity control as part of the overall process control strategy, where the supply-and-demand relationship is the critical consideration. The supply and demand can be affected by any components along the material flow path, including recycles and loop-backs. Hence, capacity control must be considered within the overall process configuration based on a holistic view of the complete process flow path. An operation can be supply driven or demand driven, requiring significantly different control strategies (Liptak 2006; Niu and Xiao 2022). For supply-driven operations, the process flow capacity is typically maintained by controlling the header pressure at the compressor suction or the tank level at the pump suction. Suppose there is more supply than the current capacity. The suction pressure or tank level will rise, and the pressure or level controller will increase the machine speed or open the control valve to increase the throughput. The downstream operation must have the swing capacity and swing-control mechanism to absorb the fluctuations in the flow. See Fig. 4.4a for an illustration. On the other hand, the discharge pressure is typically controlled for demanddriven operation. When the demand increases, the discharge pressure will decrease. The pressure controller at the discharge header will increase the machine speed or open the discharge control valve to increase the throughput. Swing capacity and swing control must exist upstream of the machine to accommodate the changes in demand. See Fig. 4.4b. The same supply-and-demand analysis for centrifugal machines applies to reciprocating machines. For example, an ordinarily supply-driven control is typically via pressure control at the suction side (see Fig. 4.5a), while a demand-driven control is via pressure control on the discharge side (see Fig. 4.5b). Capacity control of reciprocating machines is achieved predominately with recycling. Recycling is simple and reliable but inefficient, a price to pay for a simple control solution. Example 4.1 Overall control strategy for an upstream production facility. Figure 1.7 illustrates a complete surface processing facility for oil-and-gas production from the wellhead to the final sales point. Multi-phase fluids from the production wells are

Fig. 4.4 Supply-driven versus demand-driven control

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Fig. 4.5 Capacity control of reciprocating machines

Fig. 4.6 Overall control strategy for a general E and P process, supply driven (reproduced, with permission, from Niu and Xiao (2022))

sent to the separators to be separated into gas, oil, and water, which are then sent to the respective processing units with the help of pumps and compressors. The operating objective is to maximize oil production; therefore, the production rate from the wells determines the overall throughput (capacity), and the operation is supply driven. The supply-driven control design is illustrated in Fig. 4.6. The gas processing unit compresses the gas to the desired pressure and sends the gas to downstream users ➁, following a supply-driven propagation. Similarly, the oil ➂ and water ➃ processing units are also supply driven. Assume the consumers of the produced gas have decided to dictate the gas flow rate based on their actual needs. The gas processing unit then becomes demand driven. The change in demand propagates back to the separator and the wells. The well production must be able to adjust production rate to adapt to the changes. This reversal from supply-driven to demand-driven operation requires a significant modification in the process or control design. The re-designed overall control strategy

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Fig. 4.7 Overall control strategy for a general E and P process, demand driven (reproduced, with permission, from Niu and Xiao (2022))

Fig. 4.8 Supply-driven control, speed versus throttling valve

is shown in Fig. 4.7, with the stream ➁ being demand driven and the stream ➀ a swing.

Fixed-Speed Versus Variable-Speed Control Capacity control is typically achieved via speed change for variable-speed machines or a throttling valve for fixed-speed machines, as shown in Fig. 4.8. A fixed-speed machine is considerably cheaper in procurement, installation, and maintenance than a variable-speed machine. However, the operation is less energy efficient due to the throttling waste, and the overall operating cost can be significantly higher in the long run. Moreover, a fixed-speed machine may require a larger capacity motor to cope with the initial surge in electric current. On the contrary, variable-speed compressors are more efficient than fixed-speed ones, leading to significant energy savings, but investing in and maintaining a variable-speed driver is considerably more costly, except for the inherently variable-

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Fig. 4.9 Capacity turndown, fixed speed versus variable speed (reproduced, with permission, from Niu and Xiao (2022))

speed turbo expanders. In addition, the variable-speed driver as another system (usually without backup) adds complexity to operation and vulnerability to failures. Variable-speed control favors compressors with steep resistance curves, such as pipeline compressors, while the throttling valve is more appropriate for relatively flat resistance curves, such as off-gas compressors.

Split-Range Control for Turndown Operation Operations require that the process flow be able to vary between zero and maximum flow. However, centrifugal machines have a minimum flow limit imposed by the surge phenomena. When the machine flow reaches the minimum flow limit, the recycle flow must be introduced to keep the machine flow above the minimum flow limit while reducing the process flow. Combining the machine and recycle flow to turn down the process flow constitutes a split-range control arrangement (King 2016; Niu and Xiao 2022). The machine flow as the primary control handle reduces the process flow to the minimum flow limit; the recycle flow is then introduced to reduce the process flow further to 0. The split-range operation is illustrated in Fig. 4.9a. The machine flow is the sum of the process and recycle flow (Fig. 3.5). The minimum flow limit is different at different speeds. Recycling can start at any operating point. Recycling early provides more surge margin, but unnecessarily wastes energy. On the other hand, introducing recycling too late can result in operating too close to the surge line. See Fig. 4.9b. There are other standalone regulatory control loops for rotating machines. For example, temperature controllers at suction, discharge, and inter-stage coolers are

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Fig. 4.10 Compressor operating envelope

required to maintain the gas temperature4 to avoid excessively high discharge temperatures. The scrubbers are typically on level control (on/off control or regular PID control) to prevent liquid carry-over or gas carry-under. These standalone control schemes are straightforward and will not be discussed further in this book (See Fig. 4.10 for an illustration of the operating envelope).

4.3 Protective Control: Anti-surge Control The regulatory control discussed above assumes normal stable operating conditions. In other words, normal regulatory control aims to maintain the operating point on the target for stable operation. It is not designed and configured to respond swiftly and decisively to prevent the operating point from moving away from the normal operating region in case of a sudden process upset, which is inevitable in practical applications. For this reason, protective control is provided to prevent the machine from violating these operating limits. Protective control works separately from normal regulatory control. If the normal regulatory control fails to hold the setpoint, the 4

In addition to the influence on gas temperature, the cooler will also cause a pressure drop of 35 to 70 kPa (Campbell 2004).

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protective controller responds quickly and aggressively to bring the operating point back inside the operating envelope (Botros et al. 2015; Kurz et al. 2016; Majumdar 1999; Niu and Xiao 2022; Mirsky et al. 2012). Protective controls are also based on feedback principles. We will examine the five essential components of feedback control loops one by one within the context of protective control design.

4.3.1 Protective Control Objectives Protective overriding control aims to keep the operating point inside the operating envelope to avoid unstable or inefficient operations. Meanwhile, they should allow the operating point to run close to the limits to maximize the operating region. Protective control is thus a trade-off between safe operation and maximum operating range. Pumps and compressors are designed to raise the pressure of the fluid to the desired value, overcoming resistance from the piping, vessels, and equipment, which all have design limits. The requirements of the process and the machine jointly determine the operating envelope. On the process side, the pressures and temperatures must be maintained within the design limits to protect the vessels and piping. While on the machine side, the operation of centrifugal machines must stay clear from surge and choke conditions. There may be other limits and constraints requiring additional protective controllers. For instance, a high limit on motor current typically exists for the safe operation of the motor. In the case of a variable-speed operation via a variable-speed gearbox, the gearbox typically has a constraint on the torque. The typical protective control requirements are listed in Table 4.4. However, the actual implementation varies from application to application, depending on the specific process flow configuration; not all are required.

Table 4.4 Typical requirements and means of protective control Limits and Constraints

Centrifugal Machine Pump Compressor

Reciprocating Machine Pump Compressor

Minimum Flow Recycle Flow Control Anti-surge Control − Maximum Flow End-of-Curve Control Anti-choke Control − Minimum Speed Speed Control Maximum Speed Speed Control Discharge Pressure Discharge Pressure Control Discharge Temperature Discharge Temperature Control Motor Power Motor Power Control Gearbox Torque Gearbox Torque Control

− −

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Table 4.5 Cause-and-effect table for protective control Centrifugal Machine Reciprocating Machine Pressure Ratio Machine Surge Margin Pressure Ratio Machine Flow Flow Machine Speed ↑      System Resistance ↑     − Recycle ↑      Control Handles

4.3.2 Process Dynamics for Operating Envelope Protective control is based on the process and equipment dynamics discussed in Chap. 2. The dynamic characteristics of the machine near or at the operating envelope, especially the dynamic cause-and-effect relationship between the control targets and control handle near the surge line, are of primary interest, see Table 4.5 for the cause-and-effect table. Surge is the primary concern in a centrifugal machine’s operation. A surge occurs when the machine flow (actual flow through the machine) is below the minimum flow rate required by the centrifugal machine, e.g., due to low process flow (net forward flow). Since the machine flow is the sum of the process and recycle flow, as illustrated in Fig. 3.5, recycling is the most effective way to influence the machine flow. Other means of influencing the machine flow include changing the machine speed and varying the system resistance, but their impact is slower and less direct. The choke phenomenon is not as damaging as surge and can be prevented by discharge flow throttling or speed reduction. In addition to surge and choke, the pumping and compression operation raises the fluid pressure, accompanied by temperature rise. Protecting both the equipment and piping against high pressure and temperature is compulsory.

4.3.3 Measurements and Controlled Variables The objective of protective control is to keep the operating point away from the limits and constraints imposed by the operation envelope, which requires reliable measurements to indicate the real-time location of the operating point relative to each operating limit. Some variables can be directly measured online, while others can only be indirectly inferred from other variables based on engineering insight. 1. Machine flow. Fast and reliable flow measurement is the most important requirement for compressor and pump operation and control. A DP-based orifice plate is typically used for flow measurement because of its simplicity, reliability, and fast response.

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2.

3. 4.

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The DP value is also a required measurement by most surge indicator calculations, as shown in Chap. 5. Pressure and temperature. Fast and reliable measurements of the pressure and temperature at various points are also essential for protecting the machine and piping. Machine speed. Reliable speed measurement must be available to ensure the machine does not operate outside of the stable speed range. Motor power. The motor power or current must not exceed its maximum operating limit. The motor power can be measured online or calculated from real-time electric current and voltage measurements. Gearbox torque limit. In the case of a variable-speed operation via a variablespeed gearbox, the maximum torque limit must not be exceeded. Reliable online measurement or calculation of the gearbox torque is needed protecting the gearbox.

Surge avoidance is the most critical requirement for protective control. The primary challenge is detecting when a surge is likely to occur and how much recycle flow is needed to avert the surge. A surge indicator is typically used as the controlled variable. The surge indicator is not a variable that can be directly measured online. It is usually calculated indirectly from other online measurements, such as flow and pressure, based on engineering insight into the machine’s behavior. This type of calculation is called inferential property or soft sensor, which is widely used in process control. Its calculation can be rather involved and is thus deferred to Chap. 5. Another approach to detecting surge conditions is monitoring the rate of change in selected process variables such as machine flow, pressure, or temperature (Elliott and Bloch 2021). For example, a rapid decrease in discharge pressure or an increase in suction temperature may indicate an ominous surge. Although adding rate-ofchange-based protection can potentially increase reliability, the actual definition of the surge signature and selection of the detection threshold can be quite tricky and can result in many nuisance alarms or trips if not configured properly. Motor power can be an inferential property as well. The motor driving the pump or compressor has a rated limit on its power or electric current. A protective control loop on the motor power can prevent the motor from unnecessary trips or damages. The power consumption can be measured directly with a watt-meter. It can also be calculated from online measurements of the electric voltage and current as follows, assuming three-phase A/C power: √ 3 × Current × Voltage × [Power Factor] Preal . [Power Factor] = Papparent [Motor Power] =

(4.2) (4.3)

The correct location of the flow and pressure meters contributes to the reliability of measurements. For example, the flow transmitters should be placed above the

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orifice plates with the minimum length of impulse lines to reduce response time. The impulse lines should be self-draining to avoid liquid entrapment. Redundant measurements are often pursued to improve the reliability of control and safeguarding in some mission-critical applications. For control, three measurements with a mid-of-three filter can considerably increase the measurement reliability. For safeguarding, two-out-of-two (2oo2) or two-out-of-three (2oo3) voting logic can improve the reliability and reduce nuisance trips.

4.3.4 Recycle Valve and Manipulated Variables Protective overriding control shares control handles with the normal regulatory control. Based on the cause-and-effect table (CET) in Table 4.5, the three types of control handles, including the machine speed, throttling valve, and recycle valve, can all impact the surge margin. One significant difference among them, however, is the speed of response. The recycle valve can affect the surge margin much faster than the machine speed and throttling valve. Therefore, the protective control loops, such as anti-surge control and discharge pressure control, use the recycle flow as the primary control handle. A dedicated recycle valve is recommended for each pump or each stage of a compressor,5 with the size, response time, and characteristics as the most concerned specifications. 1. Valve size. The recycle valve is the most important control handle serving multiple purposes, including surge control, capacity control, and machine startup. Therefore, an adequate size is crucial. Too small a valve does not provide sufficient flow capacity to quickly empty the fluid entrapped in the surge volume (or discharge volume) in case of a surge. Process engineers often habitually overspecify the recycle valve for added assurance.6 An oversized valve increases the

5

In some older designs, a common anti-surge recycle line and valve may be shared by multiple stages. The recycle line draws from the discharge of the last stage and ties in at the suction of the first stage. This practice is discouraged because each stage has different characteristics and surge margins. If a composite performance curve is used for anti-surge control design, the inter-stage coolers significantly increase the uncertainties of the performance curves and negatively affect the control performance. In addition, the large pressure drop across the recycle valve may result in a drastic temperature decrease due to the Joule–Thomson effect. If the temperature downstream of the values goes below freezing, ice may form and block the recycle line. 6 Typically, for large centrifugal compressors, a comprehensive dynamic simulation must be carried out by the manufacturer to predict the operating point trajectory during emergency shutdown and recommend the size and response time of the recycle valve. If it is deemed to be beyond the capacity of the recycle valve to prevent surge during a shutdown, a second recycle line with an on/off valve may be needed.

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Fig. 4.11 Sizing of recycle valve

cost and also unnecessarily increases the response time, inadvertently affecting the control performance. The recommended size for the recycle valve is to have a maximum flow rate of 1.8 to 2.2 times the surge flow rate at the corresponding speed, as shown by line ➁ in Fig. 4.11. 2. Speed of response. The surge cycle is extremely fast, typically between tens of milliseconds to a few seconds. The response of the anti-surge control loop must be similarly fast to respond to the abnormal condition. Since the recycle valve has the longest response time among all the components in a closed control loop, selecting the recycle valve is thus of critical importance. A fast-responding valve can become very expensive, so it is always a trade-off between the cost and performance when deciding on the suitable valve for the job. A rule of thumb in the industry is that in case of a surge, the valve should be able to open fully from a closed position in less than two seconds. In addition to selecting the proper valve, the piping configuration can help reduce the response time. For instance, the surge volume of a centrifugal compressor is defined as the gas volume between the non-return valves and the recycle valve (Fig. 4.12). Once the valve is open, the accumulated gas inside this surge volume must pass through the recycle valve as quickly as possible to reduce the discharge pressure.7 Otherwise, a low flow and high head across the compressor may drive the compressor into a surge. A solenoid valve is usually added to the anti-surge control valve for emergency shutdown (ESD) actions. Once the solenoid is de-energized, the fail-open recy-

7

The minimum surge volume requirement also implies that the recycle line off-take should generally be upstream of the discharge cooler (hot recycle) rather than downstream.

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Fig. 4.12 Recycle surge volume

cle valve quickly opens and reaches its fully open position within two seconds, propelled by the force of the spring. 3. Valve characteristics. A fast-open characteristic is preferred by protective control for its fast response but is not ideal for capacity control that demands smooth control performance. The valve characteristics designated by manufacturers are based on a fixed pressure across the valve and are called the inherent characteristics or simply the manufacturer’s characteristics. When installed, the pressure across the valve is typically not fixed. The pressure decreases as the valve opens. As a result, a linear characteristic behaves more like a fast-open characteristic when installed. The characteristics under actual operating conditions are called the installed characteristics. To obtain fast-open installed characteristics, linear inherent characteristics are normally required. For reciprocating machines, there is no concern about surge. The recycle valve is used for capacity control and discharge pressure protective control. The sizing of the valve should match the operating range of the process flow.

4.3.5 Protective Control Algorithms Protective control is typically based on standard feedback control schemes, such as on/off control and PID control. It remains dormant during normal operations and “kicks in” only when the operation runs into abnormal operating conditions. For centrifugal machines, minimum flow control is the primary requirement for

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Fig. 4.13 Auxiliary performance lines for centrifugal machine control

protective controls, also called anti-surge control in centrifugal compressor operation and minimum recycle flow control in centrifugal pump operation. Figure 4.13 summarizes the performance lines for controlling and safeguarding centrifugal pumps and compressors.8 These lines use a surge indicator called the antisurge parameter (ASP) to indicate the surge margin, with a value from 0 to 100% (The surge indicator and anti-surge parameter are discussed in detail in Chap. 5). These lines will be frequently referenced when discussing control strategy and functional design. • Surge line. Connecting all the surge points at all machine speeds produces a line that marks the boundary between the stable operating region (to the right of the surge line) and the unstable surge zone (to the left of the surge line). • Surge reference line (SRL). The surge line is a jagged line connecting all the surge points. For the convenience of presentation and analysis, a smooth line with a simple mathematical representation is desired in place of the jagged surge line. This smooth line is called the surge reference line and typically takes the form of a straight or parabolic line. The surge reference line is so defined that all operating points to the left of the surge reference line are considered in the surge zone. The surge reference line is set to ASP = 30%. • Surge control line (SCL). The compressor is always operated a little distance from the surge line for safety. This line is called the surge control line, typically 10% (of flow) from the surge reference line at ASP = 33%.

8

Reciprocating machines work differently, and the performance lines are much simpler.

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• Capacity control line (CCL). Compressor capacity control requires that the operating point be further away from the surge reference line, typically 20% (by flow) at ASP = 36%. This control line is called the capacity control line. • Surge trip line (STL). The surge trip line defines the point at which the machine is considered in a severe surge state and must be shut down. This line is typically set halfway between the origin and the surge reference line, at ASP = 15%. • Flow transmitter line. The flow transmitter lines show the minimum and maximum flow lines corresponding to the 100% flow transmitter measurement range and the 30% flow turndown. The flow transmitter must provide reliable flow measurements for the full operating range. • Maximum flow line for recycle valve. The flow through the recycle valve can be shown on the same diagram as the performance curve. When the recycle valve is fully open, the pressure ratio versus flow rate is represented as a line similar to the system resistance or surge reference lines. Note that the recycle flow is very complex and depends on many factors; therefore, the line in Fig. 4.13 only illustrates the concept. • Choke line or stonewall. The choke line represents the maximum achievable flow through the machine. The line is approximately at ASP≈ 100%. The anti-surge control is a standard protective PID control, with the process value being the ASP value. Anti-choke control, if implemented, uses the same ASP value as controller input (PV) via an anti-choke controller. Because the stable operating range of the centrifugal machine is from approximately 30% to 100% in terms of ASP value, the anti-surge control keeps the ASP value above 33%, and a dedicated anti-choke controller keeps the ASP value below 100%. As rotating equipment raises the pressure and temperature, it is also essential to protect the vessels, piping, and equipment against excessively high pressures and temperatures.9 These protective controllers are standard protective PID controllers and are generally straightforward. They are not discussed in detail here.

4.4 Control Integration and Optimization A complete control solution for a process with pumps and compressors typically includes one or more functionalities listed in Fig. 4.14. Normal regulatory control and protective overriding control interact and potentially interfere with each other and must work together to achieve better performance.

9

An increase in head or pressure ratio implies an increase in discharge pressure, a decrease in suction, or both. Therefore, protection against low suction pressure may be needed if the discharge pressure is limited or controlled.

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Fig. 4.14 Overall control strategy for pumps and compressors

4.4.1 Sequential Control: Mode Transition A machine can operate in different modes, so is the process. Normal operation is one operating mode. Shutdown mode is another. The reduced-capacity operation, known as the turndown mode, is also pervasive. The transition from one mode to another is associated with many risks, and a safe and smooth transition is compulsory but rather complex. For instance, the startup requirements and procedure can differ significantly with the machine type and process configuration, affected by factors such as the machine speed, the position of the recycle valve, and the throttling valves. Sequence and logic are the primary means for managing the mode transition. The startup sequence also depends on a reliably functioning process control scheme (regulatory and protective control) to ensure the transition starts and ends in safe conditions. A typical startup sequence from a practical application is provided in Chap. 8.

4.4.2 Instrumented Safeguarding Against Failures During normal operations, the pump or compressor is operated under regulatory control (e.g., capacity control) and protected by overriding control (e.g., minimum flow control or anti-surge control). They serve as the first two lines of defense against abnormal operations. In severe operating conditions, such as a major process upset,

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the capacity and protective control may both fail to keep the machine inside the desired operating envelope. In this case, the anti-surge trip mechanism kicks in to proactively shut down the operation to avoid potentially severe damage to the machine. For centrifugal compressors, the anti-surge trip is based on the same surge margin calculation as in anti-surge control. An anti-surge parameter value below the surge trip limit (see surge trip line in Fig. 4.13) is considered a surge condition and triggers a proactive shutdown of the compressor or the affected unit. For reliability, the control and safeguarding functions require two separate and independent sets of measurements and execution logic implemented in two segregated systems, e.g., DCS and SIS. For critical operations such as liquidized natural gas (LNG), redundant measurements with a voting mechanism are often implemented.

4.4.3 Online Performance Monitoring Compressor performance monitoring is a crucial aspect of the long-term sustainable operation of the control solution. Compressor vendors typically offer comprehensive monitoring tools to ensure that the mechanical integrity of the machine is monitored and abnormal conditions are detected to avoid catastrophic failures; however, they are less interested or competent in monitoring process safety and operational efficiency. Process control plays a key role in monitoring the process and control performance. The display of the compressor map on the operator screen and the current realtime operating point provides a visual cue of the status and health condition of the compressor control system. Continuous calculation and monitoring of the compressor’s key performance indicators (KPI) and timely reporting of abnormal performance conditions are proactive means of performance assurance for the process control solution. Chapter 8 provides detailed discussions and some examples of performance monitoring.

4.4.4 † Integration of Capacity and Anti-surge Control The capacity of a centrifugal machine can be controlled by changing the machine speed, varying the system resistance, or introducing recycling. As shown in Fig. 4.15, the capacity can be turned down from F1 to F2 by moving the operating point from A to C through speed reduction, from A to B through throttling the suction/discharge valve, or from A to D through recycling. The operating point can be moved from A to anywhere on the map with flow F2 by combining all three control handles. However, it is important to note that the three types of control handles differ significantly in operating efficiency. The most efficient is adjusting the machine speed, which forces the operating point to move along the constant-resistance line, roughly parallel to the constant-efficiency lines (A to C). Valve throttling wastes

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Fig. 4.15 Compressor control as multivariable control with interactions

energy because it increases the discharge pressure and then kills it at the valve. Besides, it moves the operating point along the constant-speed lines (A to B) and away from the best efficiency point (BEP), resulting in less efficient operation. Recycling (A to D) is the least efficient due to the re-circulation and re-pressurization of the fluid. When multiple control handles are available, the most efficient ones should be utilized before using the less efficient ones. An undesired scenario is running the machine with maximum recycling while simultaneously throttling the control valve or increasing the speed. For instance, as shown in Fig. 4.16, to bring the flow from the current operating point A to the desired turndown flow, the recycle flow can be introduced as early as point ➀ or as late as point ➄. The amount of recycling is significantly different, so is the efficiency. A straightforward solution integrating the capacity control and anti-surge control is to bring the process flow from point A to point ➂; the anti-surge controller then kicks in and aggressively opens the recycle valve to maintain the compressor flow at point ➂ while the process flow continues to decrease. The abrupt transition from smooth capacity control to aggressive anti-surge control when the ASP value crosses the surge control line can potentially cause unacceptable operational disruptions. An improved solution for integration between capacity control and anti-surge control is shown in Fig. 4.17. When the process flow decreases during a smooth turndown operation, the operating point at A moves left under capacity control to reach point ➁, which is on the capacity control line (CCL). As a split-range control, the capacity control then opens the recycle to further decrease the process flow (see Fig. 4.5 for the split-range configuration). The machine flow remains at point ➁, and the capacity controller determines the amount of recycling. The anti-surge control

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Fig. 4.16 Unintegrated capacity control and anti-surge control

Fig. 4.17 Integrated capacity control and anti-surge control

would not be activated unless the capacity control fails, and the machine flow moves to the right of point ➂. When the process flow recovers, the recycle flow will be reduced first. The capacity controller provides smooth capacity control during normal operation with a split-range logic. Only when the capacity control is not fast enough will anti-

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surge control temporarily come to the rescue as the second line of defense against the potential surge. However, both actions manipulate the same anti-surge control valve but with different levels of aggressiveness in response. See Sect. 7.1 for a design example. Integration between speed and recycling may not always be desirable, depending on the steepness of performance curves and control trajectory. Similarly, variablespeed drive (VSD) may not always be justifiable considering the costly investment of a VFD motor or variable-speed gearbox (VSGB).

4.4.5 ‡ Load Balancing and Optimization Multiple machines operating in parallel share the same head or pressure ratio, while machines operating in series share the same mass flow. Due to these inherent constraints, the actual split of flows between each parallel train and the pressure profile around each compressor stage can significantly impact the overall operating efficiency and energy consumption (Jacobson et al. 2016; Nägeli et al. 1973).

Load-Balancing Among Parallel Compressors Based on the affinity laws, power consumption increases by a cubic function of machine flow, whereas head (compression ratio) increases by a quadratic function of flow. Due to these differences in pressure and power response to flow, there are optimal points for flow distribution (parallel operation) and pressure profile (serial operation) that result in the highest power efficiency. See Fig. 4.18. The load-sharing strategy aims to maximize the operating efficiency of a multicompressor network by optimally distributing the throughput among the multiple machines and stages. Load sharing is achieved via load-balancing control, which includes load-balancing control among multiple compressor trains (train balancing) and among the multiple stages (stage balancing). The load of a centrifugal machine typically refers to the machine flow. However, forcing machines of different design to run at the same flow rate will not result in the best efficiency. Figure 4.19 shows the performance curves of two machines on the same head versus flow coordinate. The two machines have significantly different capacities. Forcing them to run at the same flow rate can cause unnecessary early recycling, resulting in a narrower operating range. Surge prevention has a higher priority than operating efficiency, and balancing on flow will not lead to the same surge margin during turndown. Therefore, load balancing based on surge margin makes more sense than using flow rate or rotating speed. Balancing on surge margin, all stages of the compressors will operate at the same surge margin (ASP value) during severe turndown operations. On the performance map, all pumps or compressors stages will maintain the same distance to surge,

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Fig. 4.18 Load balancing improves energy efficiency

Fig. 4.19 Load balancing among parallel compressors

resulting in minimum recycle flows and thus maximum efficiency. The total power consumption can be considerably reduced. Load balancing can be achieved by introducing a load controller for each train. These load controllers receive the same surge margin request from the capacity controller as the control target and manipulate the machine speed or throttling valve to achieve the requested surge margin. For example, the two machines (A and B)

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Fig. 4.20 Load balancing among compressor stages

in Fig. 4.19 will maintain the same surge margin (A1–A2 and B1–B2) under very different flow rates (see Points A1 and B1). Section 7.2 presents a typical control design for load-balancing control among different trains.

Load Balancing Among Multiple Stages For multi-stage compressors on a common shaft, all stages will operate at the same speed. During severe turndown operations, a conventional capacity control design forces all the recycle valves to open by the same amount as soon as any stage approaches surge, even though some stages still have a healthy safety margin. Figure 4.20 shows the performance curves of two machines A and B. To turn down the machine flow,10 machine A will run into surge condition first and open the recycle to reach point A2, with a recycle flow of A1–A2. However, Machine B has ample surge margin to reach point B1 before needing to recycle. In practice, the different stage will not approach the surge line simultaneously. Introducing the same amount of recycling as requested by Machine A (via the same valve opening) unnecessarily wastes energy. The improved strategy for capacity control among stages is to recycle only when the machine reaches the surge limit at each stage. That is, each stage will start recycling independently of each other and only when necessary. There are different 10

Here, we use mass flow to illustrate the concept. All the stages share the same mass flow but may have different surge margins.

References

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ways of achieving this load-balancing control. A simple approach is calculating the difference between the stages in real time. The surge margin of each stage is individually adjusted by padding the surge margin with the difference between this stage and the stage with the worst-case scenario. The opening of the recycle valve is thus delayed until the adjusted surge margin reaches the surge limit. A typical design is provided later in Sect. 7.2.

4.5 Summary The pump and compressor control objective is maintaining one point and protecting two envelopes. The one point is the operating point, and the two envelopes are the operating and safety envelopes. The head and flow of the machine determine the operating point. The operating envelope is defined by the limits and constraints imposed by both the machine and the process. The safety envelope is defined by the various design limits and safety constraints. The control solution is typically implemented in a layered approach, including regulatory control for maintaining operating points, protective overriding control for maintaining the operating envelope, and instrumented safeguarding for guarding the safety envelope. Together, they form the three lines of defense against abnormal situations with increasingly aggressive and disruptive responses. The capacity control design is based on the supply-and-demand model and the cause-and-effect relationship of the entire process and can be rather complex. A welldesigned capacity control scheme can maintain the operating point at any desired point within the operating envelope with carefully selected control handles, including the machine speed, system resistance, and recycling. Protective control is mainly concerned with surge avoidance. Surge is caused by low flow through the machine and is prevented by recycling a portion of the flow from discharge to suction to keep the machine flow above the minimum flow limit. The primary challenge for control is that the minimum flow limit varies with the machine speed and inlet condition and must be constantly re-calculated in real time. Sequential control deals with the transition between operating modes, including automated startup and shutdown. A safe and smooth transition is compulsory.

References Bahadori A (2016) Essentials of oil and gas utilities process design, equipment, and operations. Elsevier Inc Borremans M (2019) Pumps and compressors. John Wiley & Sons Ltd Botros K, Hill S, Grose J (2015) A new approach to designing centrifugal compressor surge control systems. In: 44th turbomachinery and 31st pump symposia. Houston, TX Botros K, Grose J, Hills S (2016) Centrifugal compressor surge control systems–fundamentals of a good design. In: Asia turbomachinery and pump symposium. Singapore

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Campbell J (2004) Gas conditioning and processing-the equipment modules, vol 2, 8th edn. John M, Campbell and Company CCC (2021) CCC and yokogawa R&D cooperation. Tech. rep., Compressor Control Company (CCC). https://www.cccglobal.com/wp-content/uploads/2022/10/CCC-andYokogawaRD-cooperation.pdf Elliott H, Bloch H (2021) Compressor technology advances—beyond 2020. Walter De Gruyter Giampaob T (2010) Compressor handbook: Principles and practice. The Fairmont Press Honeywell (2023) Honeywell to acquire compressor controls corporation, driving the energy transition through leading automation and controls portfolio. https://www.honeywell. com/us/en/press/2023/04/honeywellto-acquirecompressor-controls-corporationdrivingtheenergytransitionthrough-leading-automation-and-controls-portfolio Jacobson W, Staroselsky S, Zaghloul M, McWirter J, Tolmatsky M (2016) Compressor load-sharing control and surge detection techniques. In: Proceedings of the 45th turbomachinery and 32nd pump symposia. Houston King M (2016) Process control: a practical approach, 2nd edn. Wiley Kurz R, Brun K (2017) Process control for compression systems. In: Proceedings of ASME turbo expo 2017: Turbomachinery technical conference and exposition. Charlotte, USA Kurz R, White RC, Brun K, Winkelmann B (2016) Surge control and dynamic behavior for centrifugal gas compressors. In: Proceedings of asia turbomachinery and pump symposium. Turbomachinery Laboratory, Singapore Lieberman NP, Lieberman ET (2014) A working guide to process equipment, 4th edn. McGraw-Hill Education Liptak BG (2006) Process control and optimization, instrument engineers’ handbook, vol II, 4th edn. Taylor and Francis Majumdar K (1999) Understand centrifugal compressor, equipment interaction. Hydrocarbon processing, pp 55–66 McMillan GK (1983) Centrifugal and axial compressor control. Instrument society of America. http://compressorcontrolstudent.modelingandcontrol.com Mirsky S, Jacobson W, Tiscornia D, McWhirter J, Zaghloul M (2012) Development and design of anti-surge and performance control systems for centrifugal compressors. In: Proceedings of the forty-second turbomachinery symposium. Houston, Texas Nägeli JP, Spechtenhauser A, Aicher W (1973) Turbomachinary in base load natural gas liquidification plants. In: Proceedings of the 12th world gas conference. Nice, France Niu S, Xiao D (2022) Process control—engineering analyses and best practices. Advances in industrial control. Springer Vermillion L, Gracia J, Ilchenko M (2023) Solutions spotlight: Integrating process and turbomachinery control. Control magazine. https://www.controlglobal.com/podcasts/article/21546058/ yokogawa-electric-corporation-solutionsspotlight-integrating-processand-turbomachinerycontrol Zelenov A (2013) White paper-CCS implementation of surge prevention control system on yokogawa stardom PLC. Tech. rep, Continuous Control Solutions (CCS)

Chapter 5

Invariant Coordinates and Surge Indicators

So far, the description and analysis of pumps and compressors are all based on a qualitative understanding of the head, flow, and speed relationship under a headflow coordinate system. This coordinate system has many distinct advantages for conceptual understanding and theoretic analysis and has been the de facto standard of describing machine performance. However, a primary drawback is that the head and flow are not directly measurable and thus unavailable for real-time operation and control. The actual coordinate system in practical applications must be based on process measurements available in real time. Data availability is the major factor that divides practical implementation from theoretical analysis, leading to different coordinate systems used in theory and practice. This chapter explains the concept of invariant coordinates and their significance for real-time control. It then shows the different ways of defining and calculating the surge indicators, which are the basis for capacity control and anti-surge control for practical applications discussed in Chaps. 6 and 7.

5.1 Inlet Conditions and Invariant Coordinate Systems A pump or compressor is expected to work under various operating scenarios, including different types of gases and varying pressures and temperatures. The different operating scenarios significantly impact the machine outlet condition and the operation and control.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. S. Niu, Process Control for Pumps and Compressors, Advances in Industrial Control, https://doi.org/10.1007/978-3-031-43122-7_5

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5.1.1 API Datasheet for Compressor When specifying the requirements of a centrifugal compressor, the process engineer defines the expected machine behavior with the compressor datasheet. This design datasheet is typically based on API Standard 617 and is thus also called the API datasheet. The API datasheet specifies the expected head and flow under different operating scenarios, e.g., summer and winter conditions and light and heavy gases. The typical data set must include the following: • The gas property: molecular weight Mw , compressibility Z s , and the ratio of specific heat κs . • The suction condition: pressure Ps and temperature Ts . • The expected discharge condition in terms of the head/efficiency (H p /η p ) or pressure/temperature (Pd /Td ), and the desired flow rate (mass flow Fm , standard flow F0 , or volumetric flow Fv,s ). Table 5.1 shows the API datasheet of five of the 13 different scenarios for a singlestage compressor. When plotted under the head and flow coordinate system, the design conditions of all the 13 operating scenarios in this example are shown in Fig. 5.1.

Table 5.1 Compressor API datasheet Variable

Unit

Case A Case B Case D Turndown

Suction Pressure Suction Temperature Molecular Weight Ratio of Specific Heat Compressibility Speed Polytropic Head Polytropic Efficiency Suction Volumetric Flow Mass Flow Standard Flow Power Discharge Pressure Discharge Temperature Ratio of Specific Heat Compressibility Certified

bar(a) ◦C kg/kmol rpm kJ/kg % m3 /hr kg/s MMSCFD kW bar(a) ◦C -

65.8 16.30 201.9 1.622 0.809 12,900 45,075 82.3 3,013 57.10 204.4 3,191 101.5 51.4 1.621 0.831

65.8 16.50 20.21 1.615 0.817 12,982 45,542 82.3 3,043 57.10 204.2 3,224 101.5 52.1 1.615 0.840 Yes

65.8 13.50 19.19 1.638 0.829 13,148 46,692 82.5 2,897 51.40 193.6 3,070 101.5 49.5 1.580 0.852

N2

65.8 5.00 21.70 30.0 19.72 28.1 1.584 1.408 0.830 1.000 12,761 14,160 48,239 55,411 81.1 81.8 2,358 3,239 41.76 5.00 153.1 12.90 2,549 364 101.5 8.7 58.0 96.0 1.561 1407 0.852 1.000

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Fig. 5.1 Compressor design conditions

Although the mass flow through the machine is constant following the law of mass conservation, the volumetric flow is heavily affected by the suction condition, defined as the pressure Ps , temperature Ts , gas molecular weight M, and gas compressibility Z s . This suction condition is called the inlet condition. The data that define the inlet conditions are shown in the top 5 rows in Table 5.1. The compressor manufacturer designs the impellers based on the API datasheet, with the predicted characteristics of the machine described with the performance curves (see Fig. 5.2), along with the design points. The machine’s operating envelope is expected to align with the desired operating envelope of the process.1 For this reason, the API datasheet can be deemed as the control objectives for the compressor control. The compressor manufacturer typically endorses a certified point (also called the guaranteed point). As discussed later, this certified point is often used as the reference condition in process control design. For this compressor, case B is the scenario with performance guaranteed by the compressor manufacturer, as shown in Table 5.1.

5.1.2 † Impact of Inlet Conditions A compressor is expected to work under a wide range of operating scenarios or inlet conditions. For a centrifugal compressor, the performance curves are always tied to a specific inlet condition since the inlet condition significantly impacts the machine’s 1

Many times, compromises must be made to fill the gap between the desire of the process engineers and the practicality of machine characteristics.

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Fig. 5.2 Operating scenarios on performance map

performance. For example, an ethylene plant’s cracked gas compressor (CGC) (see Fig. 1.11) compresses the off-gas from the cracking furnace. Depending on the market demand, the cracking severity is frequently adjusted to meet the required yields of ethylene, propylene, butene, and butadiene. The variation in the composition of the cracked gas is a change in the inlet condition that poses a significant challenge to the operation and control of the cracked gas compressor. The characteristics of a centrifugal machine are to increase the energy by working on the fluid with blades; anything that can affect the fluid velocity or density at the tip of the blades can impact the head generated or the flow produced. Most challenges in analysis and design are in handling the variations in inlet conditions. An example of the different scenarios is given in Fig. 5.2, where all the 13 scenarios in this example can be visualized selectively or collectively by selecting the scenarios of interest from the list of scenarios in the companion software tool CPACS. From Euler’s equation in Sect. 2.3.3, the head is a function of the volumetric flow and rotating speed. Although the changes in inlet conditions do not affect the head/flow relationship, they significantly impact most other variables and relationships. Table 5.2 shows the cause-and-effect relationship of the inlet condition with a few key variables, assuming the volume flow rate remains constant. The most prominent relationship is with inlet gas density. Higher molecular weight, higher pressure, and lower temperature can all result in a higher density. A higher gas density implies lower flow resistance, thus a higher mass flow and compression ratio, resulting in an energy split favoring kinetic energy (flow) over potential energy (head). For this reason, it is often said that a heavier fluid (gas or liquid) is “easier” to pump or compress, whereas “easier” means less power consumption to reach the same pressure ratio. This behavior is illustrated in Fig. 5.3. The operating point moves toward the bottom left as the gas molecular weight decreases (“lighter gas,” Case A –5% MW) and moves toward the top right as the molecular weight becomes higher (“heavier gas,” case A +5% MW). The shift of the operating point with a

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Table 5.2 Changes in inlet conditions with constant volumetric flow Head Mass Flow Pressure Ratio Gas Power H Fm Pd /Ps W Suction Pressure Suction Temperature Molecular Weight Compressibility

Ps Ts M Z

↑ ↑ ↑ ↑

-

   

  

   

Gas Density

ρs ↑

-







Fig. 5.3 Impact of gas molecular weight

molecular weight roughly follows a parabolic line, similar to the constant-resistance curve. Similarly, it is “easier” for the same pump or compressor to operate in a Winter environment than in Summer. In other words, winter operation has a lower “load” on the machine than in Summer for the same throughput because of cooler weather.2 The impact of the inlet condition can be expressed in equation format and has been briefly discussed in Chap. 2. The relevant equations are collected and reproduced here for the convenience of reference:

2

For this reason, controlling or limiting the suction temperature is compulsory. For compressor operation, suction and discharge coolers are essential to maintaining the temperature.

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Hp Pd Ps Fm W ρs

   n−1  σ  Pd Pd n n Z s R Ts 1 Ps = −1 = −1 n−1 M Ps σ ρs Ps n   n−1   σ1 M n−1 ρs Hp = +1 = σ Hp + 1 n Z s R Ts Ps Fv,s = ρs · Fv,s , Fv = ρs  σ  σ   Pd Pd Fm Ps Ps = Fm · H p = − 1 = Fv,s · −1 ρs σ Ps σ Ps Ps M = . Z s R Ts

(5.1)

(5.2) (5.3) (5.4) (5.5)

For example, based on Eq. 5.1, increased compression ratio Pd /Ps , decreased molecular weight M (“lighter” gas), or higher suction temperature Ts all cause a higher head H p to be produced. At a constant speed, a higher head is traded with a lower flow. The relationship between polytropic head and volumetric flow does not change with inlet conditions. Even though the inlet conditions are rather different, especially in the nitrogen case, all the operating points fall on the nine speed lines, as shown in Fig. 5.2. The surge points line up nicely to divide the performance map into two distinct operating regions, the stable region to the right and the unstable region to the left. On the other hand, the relationship between the polytropic head and the mass flow is drastically different with the inlet condition, as shown in Fig. 5.4. The surge points are so scattered that no common feasible region can be defined on the performance map under this polytropic head versus mass flow coordinate. The relationships between other variables can be visualized similarly with the CPACS tool by selecting the interested variable from the Y-Axis and X-Axis lists.

Fig. 5.4 Polytropic head versus mass flow

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Fig. 5.5 Polytropic head versus volumetric flow, an invariant coordinate

The degree of scatteredness of the surge lines is significantly different under the different Y-axis and X-axis choices.

5.1.3 Invariant Coordinate All the performance curves and maps discussed so far are based on the head versus flow coordinate system. The prominent advantage of the head versus flow coordinate is that at a constant speed, the head is a function of the flow alone and is unaffected by the type of gas, pressure, or temperature. On the performance map, the variations in inlet conditions do not significantly affect the shape of the performance curves, including the surge and choke points. As a result, all operating points fall nicely on the individual speed lines, with insignificant deviations3 ; see Fig. 5.5. The surge lines under the different inlet conditions converge to a narrow band. The head versus flow coordinate is thus called an invariant coordinate, i.e., invariant to the inlet conditions (Batson 1996; Bloch 2006; Mirsky et al. 2012). If the most conservative surge lines are based to derive a reference line representing all the required operating scenarios, then there will be no significant loss in the operating range for any individual scenario. Therefore, the control design based on invariant coordinates remains valid for all inlet conditions. In contrast, with a coordinate system such as polytropic head versus mass flow, as shown in Fig. 5.4, the scenario with nitrogen gas has a much different inlet condition than the process gas and thus has drastically different performance curves. 3

The deviation becomes more prominent at higher flow or pressure.

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It is impossible to find a surge reference line to represent all the scenarios without significantly reducing the operating ranges of some operating scenarios. This polytropic head versus mass flow relationship is said to vary with the inlet conditions and is thus a non-invariant coordinate system. Most commercial control designs vary primarily in their choice of invariant coordinate (Hafaifa et al. 2014).

5.2 Equivalent Coordinates Polytropic head versus volumetric flow is an invariant coordinate, thus the coordinate of choice for conceptual understanding and theoretical analysis. However, in practice, neither head nor flow is directly measurable for online applications; nor can they be calculated online because the fluid density ρ that they depend on is not directly measurable. Online control and monitoring must be based on an alternative coordinate system, with the head and flow replaced by online measurements (Batson 1996).

5.2.1 † Alternative Variables for Polytropic Head The performance map’s ordinate axis represents the fluid’s energy, with the fluid head as the default variable. In addition to the head, the fluid energy can also be represented by pressure in the form of reduced head, pressure ratio, or pressure rise, as summarized in Table 5.3. The variables in pump operation (by assuming n = ∞) are listed together for comparison and completeness. The reduced head Hreduced is defined as the polytropic head, “reduced” by the influence of suction pressure and gas density (Ps /ρs ):

Table 5.3 Potential variables for Y-axis in alternative coordinate system Energy Type Centrifugal Compressors Polytropic Head Hp  σ  1 Ps Pd Polytropic Head −1 σ ρs P s  1 Pd σ Reduced Head −1 σ Ps Pd Pressure Ratio Ps Pressure Rise Pd − Ps

Centrifugal Pumps H   Ps Pd 1 −1 = [Pd − Ps ] ρs Ps ρs Pd −1 Ps Pd Ps Pd − Ps

5.2 Equivalent Coordinates

Hp =

1 Ps  σ ρs



Pd Ps

129

σ

 −1

⇒

Hreduced =

1 σ



Pd Ps

σ

 −1 .

(5.6)

The reduced head is a popular alternative to the polytropic head. It is used directly or indirectly by most commercial anti-surge control solutions (Giampaob 2010; Mirsky et al. 2012). Pressure ratio Pd /Ps is the ratio between the (absolute) discharge pressure and the (absolute) suction pressure. Since the pressures are directly available as online measurements, the pressure ratio is the preferred alternative variable to the polytropic head. Pressure rise Pd − Ps is similar to pressure ratio, and is preferred in pump control.

5.2.2 † Alternative Variables for Volumetric Flow The flow through a compressor is usually measured with a DP-based flowmeter, such as an orifice plate or Venturi tube. The volumetric flow Fv is calculated from the differential pressure P across the device as  Fv = C

P . ρ

(5.7)

Although the differential pressure P can be measured online, the fluid density ρ cannot. Alternative flow representations must be used for online applications, typically based on P. The common candidates include the reduced and equivalent flows, as summarized in Table 5.4. The reduced flow is similar to the reduced head. It is derived by removing the same term Ps /ρs as in Eq. 5.6:

Table 5.4 Potential variables for X-axis in alternative coordinate systems Flow Type Centrifugal Compressor Centrifugal Pump Fv Fv P P Volumetric Flow C C ρ ρ √ √ Mass Flow C ρ P C ρ P Differential Pressure P P P P Reduced Flow Ps Ps P P Reduced Flow Squared Ps Ps Equivalent Flow Fe Fe

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5 Invariant Coordinates and Surge Indicators

 Fv,s = C

P =C ρs



Ps P  ρ  s Ps

 ⇒

Freduced =

Ps . Ps

(5.8)

A related variable is the reduced flow squared: 2 Reduced Flow Squared = Freduced =

Ps . Ps

(5.9)

The parabolic relationship between the reduced head and reduced flow becomes linear with reduced flow squared. The theoretical SRL becomes a straight line instead of parabolic. The downside of using reduced flow squared is that the relationship is no longer between head and flow, but between head and P. The reduced flow squared is no longer a flow, and has no clear physical meaning in its value and engineering unit. The preferred alternative is the equivalent flow, a reduced flow scaled with the measurement range of the suction pressure, gas density, and mass flow. Suppose the flowmeter produces a flow of Fm,r with a differential pressure of Pr at the design condition of Pr . The equivalent flow under the actual suction condition of Ps and from the actual DP of Ps is given by 

Ps,r

Freduced Pr   Ps,r P = Fm,r . Ps Pr

Fe = Fm,r

(5.10)

Unlike the reduced flow, the equivalent flow has the same engineering unit and measurement range as the actual flow.4 It equals the true flow when the operating condition matches the calibration condition of the flowmeter.5

5.2.3 † Equivalent Coordinate Systems With the alternative variables for head and flow listed in Tables 5.3 and 5.4, the possible choices for alternative coordinates are shown in Table 5.5. Evidently, not all combinations are suitable for practical applications, as demonstrated in Fig. 5.4. The head versus flow is called an invariant coordinate because the head and flow relationship does not change with inlet conditions. The relationship remains 4

Caution should be taken that the equivalent flow is the uncompensated flow. It is different from the true flow. See Niu and Xiao (2022) for discussions on mass flow, volumetric flow, actual flow, standard flow, and flow compensation. 5 The so-called equivalent speed adjusts the speed for the inlet condition changes. All the points with the same speed line up on the same equivalent-speed line rather than the actual-speed line.

5.2 Equivalent Coordinates

131

Table 5.5 Potential variables for describing head versus flow characteristics

invariant if both head and flow are scaled by the same value as in Eqs. 5.6 and 5.8. The resulting coordinate system is deemed invariant as well. We will call it the equivalent coordinate system. All equivalent coordinate systems are marked with “≡” in Table 5.5. Further simplification needs to exclude the σ term from the calculation, which introduces further approximation. However, because the variation in σ is relatively small and slow, the additional approximation introduced is usually within an acceptable range. The resulting coordinate systems are regarded as almost invariant to inlet conditions and are marked with “≈” in Table 5.5. All the equivalent coordinate systems marked with ≡ or ≈ in Table 5.5 are being in use in practical applications. However, due to approximations and errors, an invariant coordinate system is not truly invariant to inlet conditions. Similarly, an equivalent coordinate is not truly equivalent in the strict sense. Determining which one to use is always a trade-off between complexity and accuracy. Example 5.1 Performance map under equivalent coordinate systems. With the compressor data in Fig. 5.2, the performance map can be plotted by selecting the Y-axis and X-axis from the drop-down lists in the CPACS tool. The different performance maps are shown in Fig. 5.6. Figure 5.6a shows the performance map under the polytropic head versus volumetric flow coordinate system. Since the polytropic head is a fixed function of the volumetric flow under a constant speed, unaffected by changes in inlet conditions, all the operating points collapse nicely on the nine speed lines. All the surge points line up neatly along a common surge line. Figure 5.6b shows the performance map under the reduced head versus reduced flow coordinate system. The performance curves are also invariant to inlet conditions. However, they no longer align with the specific speeds since the variations in density have caused the lines to shift. The shift is along the constant-resistance line in the direction of speed change and does not affect the accuracy in indicating the division between the stable and unstable regions.

132

5 Invariant Coordinates and Surge Indicators

Fig. 5.6 Performance curves under equivalent coordinate systems

Similarly, if the pressure ratio is plotted against the equivalent flow, the performance map would appear as in Fig. 5.6c. The surge points also line up nicely despite the different inlet conditions but with a shift along the resistance line. Pressure rise (Pd − Ps ) versus flowmeter P is a primitive coordinate used by some early commercial service providers. It has the advantage of simplicity, where only two differential pressure measurements, one across the compressor and the other across the flowmeter, are required. However, its deviation from the true invariant coordinate (head versus flow) is often too significant to be reliable. Figure 5.6d shows the equivalency where it is seen that the surge points can still be treated as on the same line even though the performance curves with the nitrogen case have shifted drastically toward the origin (due to low pressure and flow). Anti-surge control is a significant part of process control for pumps and compressors. The significance of choosing invariant coordinates for practical applications, especially anti-surge control, will be explained later.

5.3 Surge Reference Line and Surge Indicators Surge is an abnormal condition that must be avoided. However, to prevent the machine from entering surge, the prerequisite is knowing the location of the surge limit and the current operating point in relation to the surge limit, in real-time quantitative terms.

5.3 Surge Reference Line and Surge Indicators

133

5.3.1 Surge Reference Line The surge line is the dividing line between each operating scenario’s stable and unstable operating regions. It is a jagged line due to errors and approximations in calculation or measurements. The complexity of the shape depends on many factors, with inter-stage cooling being a primary one. For instance, a composite surge line for a multi-stage compressor can be a complex curve containing multiple breakpoints, making the surge line deviate significantly from the expected parabolic line (see Fig. 2.15) because of the heat removal by the inter-stage cooler. Although a jagged line poses little challenge to human interpretation, automated operation and control require a simple and smooth line. This smooth line is the surge reference line (SRL), also called the surge limit line (SLL) (Mirsky et al. 2012). See Fig. 5.7 for an illustration of the surge line and the surge reference line. Each operating scenario (or case) has a separate surge line (see Fig. 5.5). The operating point is expected to stay a safe distance from the surge lines under all operating scenarios. The surge reference line is thus dictated by the worst-case scenario, and must be on the left side of all surge points. The invariant coordinate allows one surge reference line to represent all the scenarios without significantly compromising the feasible operating range. There are many ways of defining the surge reference line. All definitions of the surge reference line are approximations only since the exact form of the surge line is never known. One common approach is based on the affinity laws (Eq. 2.36). Assume everything remains constant. Changing the machine speed causes the operating point to move along the constant-resistance curve. The ratio of head change

Fig. 5.7 Surge line and surge reference line

134

5 Invariant Coordinates and Surge Indicators

Fig. 5.8 Surge reference line: flow versus flow squared

is a quadratic function of the flow ratio for any two points on the constant-resistance curve6 :   H p,2 Fv,2 2 ≈ , (5.11) H p,1 Fv,1 where H p,2 and H p,1 are the polytropic head of two arbitrary points along a system resistance line; Fv,2 and Fv,1 are the corresponding volumetric flows. Equation 5.11 represents a linear function between head H p and flow Fv2 , with slope S: H p = S · Fv2 ,

(5.12)

which is parabolic under the head (H p ) versus flow (Fv ) coordinate (Hafaifa et al. 2014). The relationship between the head and reduced flow squared (Fv2 ) becomes a straight line,7 stretching from the origin through the operating point, with slope S, as shown in Fig. 5.8b: S=

Hp , Fv2

(5.13)

and S is thus an angular measure of the location of the operating point in an x-ycoordinate. Figure 5.9 shows the constant-slope line on the performance map of a centrifugal compressor for any operating point. Each operating point on the performance map falls on an imaginary line with its slope given by Eq. 5.13.

6

This quadratic function is an approximation. It shows an increasing deviation and non-linearity as the compression ratio increases. 7 A straight line can be assumed as long as the deviation from fan laws is insignificant and the gas composition remains relatively constant (Mirsky et al. 2012).

5.3 Surge Reference Line and Surge Indicators

135

Fig. 5.9 Slope of the operating point versus the slope of the surge reference line

The surge reference line (SRL) is the most conservative constant-slope line with all the surge points on the left of it. By definition, all points on the SRL have the same slope. Let us define this slope as Sr =

H p,r , 2 Fv,r

(5.14)

where H p,r and Fv,r are the head and flow of a selected surge point (a reference point). The constant-slope SRL coincides with the constant-resistance line since they follow the same DP versus flow relationship. The location of the operating point in relation to the surge reference line is indicated as follows: ⎧ ⎪ ⎨= Sr on the surge reference line S < Sr on the right of the surge reference line (5.15) ⎪ ⎩ > Sr on the left of the surge reference line, where Sr is the slope of the SRL. To ensure all the surge points stay on the left of the SRL, the surge point (H p,r ,Fv,r ) selected for SRL calculation in Eq. 5.14 must be the most conservative one. The accuracy of the SRL determines how safely the compressor can operate. Its accuracy also impacts the size of the operating envelope.

5.3.2 Surge Indicators The SRL provides the basis for calculating the surge margin, defined in terms of the current flow Fv in relation to the surge flow Fv,r :

136

5 Invariant Coordinates and Surge Indicators

Surge Margin =

Fv − Fv,r · 100% . Fv,r

(5.16)

In other words, a 10% surge margin leads to 10% =

Fv − Fv,r · 100% Fv,r

⇒

Fv = (1 + 10%) · Fv,r .

(5.17)

The SRL by itself is not a convenient surge indicator for practical applications. A more intuitive variable is preferred for implementation and interpretation. This variable is the surge indicator, a real-time indication of the surge margin. With the surge reference line defined in Eq. 5.12, the surge indicator can be defined as the ratio between the slope of the surge reference line Sr and the slope of the current operating point S (Giampaob 2010; Mirsky et al. 2012): SI =

Sr . S

(5.18)

The value of SI indicates the location of the current operating point as follows: ⎧ ⎪ ⎨= 1.0 on the surge reference line SI > 1.0 on the right of the surge reference line ⎪ ⎩ < 1.0 on the left of the surge reference line.

(5.19)

Most anti-surge control technologies on the market are based on this concept but differ in implementation. With the slope definition in Eq. 5.13, the surge indicator for any operating point on the performance map is given by Sr S  Hp H p,r = 2 Fv,r Fv2 2  Hp Fv = Fv,r H p,r

SI =

=C

Fv2 , Hp

(5.20)

where C is a coefficient that lumps all the constant values. Since there is only one unknown coefficient, one surge point from the offline performance data is sufficient to determine its value, e.g., with the most conservative surge point on the head-flow performance map, similar to the calculation in Eq. 5.14. Once the C coefficient is known, the real-time SI value of any operating point can be calculated with the head H p and flow value Fv , if available online.

5.3 Surge Reference Line and Surge Indicators

137

Surge Indicator Based on Reduced Head and Flow The practical issue with Eq. 5.20 is that the head H p and flow Fv are not directly available online, but the pressures and orifice DP values are. Therefore, the head and flow need to be calculated from the pressure ratio Pd /Ps across the compressor and the differential pressure P across the flow-measuring orifice, given by ⎧  σ  Pd 1 Ps ⎪ ⎪ ⎪Hp = −1 ⎨ σ ρs Ps ⎪ P ⎪ 2 ⎪ . ⎩ Fv = C 2 ρs

(5.21)

With Eq. 5.21, the SI calculation is transformed to a function of the pressure ratio and flowmeter DP: SI = C1

Fv2 Hp

 2 P C2 ρ  s σ  = C1 Pd 1 Ps −1 σ ρs Ps P Ps  = C   Pd σ 1 −1 σ Ps =C

2 Freduced , Hreduced

(5.22)

(5.23)

where C is a coefficient that lumps all the individual constant terms ( C1 and C2 ) in Eq. 5.22. The denominator is “reduced” to the reduced head (Eq. 5.6) and the numerator to the reduced flow (Eq. 5.8). The surge indicator can be directly calculated using the reduced head and reduced flow with Eq. 5.22. It can also be calculated indirectly from the head and flow with Eq. 5.20, with the head and flow back-calculated from the reduced head and reduced flow with 5.21 first. Equation 5.22 is the generic formula from which most anti-surge control technologies are derived. This coordinate is made popular by the Compressor Control Company (CCC), one of the key providers of compressor control solutions and services (Bloch 2006; Honeywell 2023; Mirsky et al. 2012).8 However, many bells and whistles are added to enhance the control performance in the CCC solutions. 8

CCC was acquired by the DCS vendor Honeywell in April 2023.

138

5 Invariant Coordinates and Surge Indicators

The Swiss-army-knife design style for its software makes its solution extraordinarily versatile and, at the same time, very complicated. Due to its large install base (over 14,000 applications per Honeywell 2023), it is beneficial to understand this coordinate system to support the operation and migration of the existing CCC applications efficiently. One convenient feature is that an offset B is added as the control margin in the actual applications to define a new controlled variable DEV. The control objective in the CCC solution is thus to keep the DEV value above zero: ⎧ ⎪ ⎨= 0.0, on control line DEV = SI − 1 − B1 > 0.0, above control setpoint ⎪ ⎩ < 0.0, below control setpoint.

(5.24)

Under the reduced coordinate of Hr versus Fr2 , the surge reference line represented by the basic SI formula in Eq. 5.22 is a straight line from the origin, going through the selected surge point. There is one single constant C to be determined from the performance data, requiring a minimum of one surge point. The manufacturerprovided performance curves typically have multiple speed lines and, thus, multiple surge points. Due to non-linearities and measurement errors, all the surge points will not produce the same C-values. A simple approach is taking the most conservative point to calculate the C-value but will result in large inaccessible regions. The CCC solution uses ad hoc characterizers to modify the slope calculation to approximate the surge line more closely for improved accuracy: f 2 (Z 2 ) f 3 (Z 3 ) f 1 (Hreduced ) Ps P f 1 (Hreduced ) = K · f 2 (Z 2 ) f 3 (Z 3 ) · P/Ps f 1 (Hreduced ) = K · f 2 (Z 2 ) f 3 (Z 3 ) · . 2 Freduced

Ss = K ·

(5.25)

The characterizers f 1 , f 2 , and f 3 improve the curve fitting to the surge points to arrive at a non-straight surge limit line, which provides a better fit to the jagged surge lines to accommodate practical uncertainties in the data.

Surge Indicator Based on Pressure Ratio and Equivalent Flow API 670 (API 2014) recommends calculating the surge indicator with flow, pressure, and temperature (Elliott and Bloch 2021), similar to Eq. 5.22. However, the polytropic index σ is a function of temperature, and the temperature measurement is typically not fast and reliable enough for online calculation. The dependence on σ can be removed without detrimental impact on the invariance property of the coordinate system to inlet conditions. Taylor’s expansion is one way of approximation:

5.3 Surge Reference Line and Surge Indicators

1 σ



Pd Ps

σ

   2  3  Pd Pd Pd + C2 − 1 ≈ C0 + C1 + C3 + ··· . Ps Ps Ps

139

(5.26)

The generic SI formula based on the reduced head versus reduced flow in Eq. 5.22 becomes9 : SI = C

2 Freduced Hreduced

=

 C0 + C1

Pd Ps



P/Ps .  2  3 Pd Pd + C2 + C3 + ··· Ps Ps

(5.27)

To further facilitate the understanding, the equivalent flow Fe is used in place of the reduced flow in the numerator (see Table 5.4). The SI formula thus becomes 

2 Freduced Hreduced Freduced =C √ Hreduced

SI =

C

=



C0 + C1  with Fe = Fm,r

Ps,r Ps



Pd Ps 

Fe × 100%  2  3 Pd Pd + C2 + C3 + ··· Ps Ps

P , Pr

(5.28)

(5.29)

where Ps,r , Fm,r , and Ps,r are the pressure, flow, and DP at the flowmeter design or calibration condition. With the square root, the numerator is transformed from quadratic to linear in relation to the volumetric flow. This transformation allows for a more intuitive interpretation of the surge indicator, which can now be viewed as a function of the flow, proportionately scaled by a function of the pressure ratio. Anti-surge control, in turn, becomes a matter of minimum flow control, consistent with pump operation. Assuming that the surge reference line is assigned a value of 30%, the stonewall will have a SI value of approximately 100%, owing to the 1/3 turndown ratio from the

9

There are many variations in simplifications. One variation is the same formula in Eq. 5.27 but without the square root. Removing the square root in Eq. 5.27 still results in a valid (and popular) ASP formula but tends to be less intuitive since the formula becomes a function of DP instead of flow.

140

5 Invariant Coordinates and Surge Indicators

stonewall to the surge point (see Sect. 3.2.3). In other words, the range of the surge indicator is from zero to the stonewall (0∼100%), with the surge point at 30%.10 From now on, the surge indicator (SI) in Fig. 5.28 will be called the anti-surge parameter (ASP), with a re-defined range of 0 to 100%. The location of the operating point can be indicated with ASP as follows: ⎧ < 30% ⎪ ⎪ ⎪ ⎨= 30% ASP ⎪ > 30% ⎪ ⎪ ⎩ ≈ 100%

on the left of the surge reference line on the surge reference line (minimum stable flow) on the right of the surge reference line near the choke line (maximum flow).

(5.30)

The coefficients C0 , . . . , C3 are determined offline during control design with the pressure and DP data of the surge points on the performance curves. The number of coefficients to use is determined by the level of irregularity of the surge line, thus the accuracy of the approximation.

Surge Indicator Based Directly on Orifice DP The simplest solution requires one coefficient C0 and is based on two differential pressures, one across the compressor and one across the flowmeter (orifice). If the polytropic index σ remains constant and the polytropic head H p is not excessively high, the ASP formula can be simplified from Eq. 5.28 as follows: ASP1 = 



C0

Fe

or,

 Pd −1 Ps

√ P . ASP1 = C √ Pd − Ps

(5.31)

An example of the SRL with a single coefficient is shown in Fig. 5.10a. The ASP formula with two coefficients (C0 and C1 ) provides the best trade-off between accuracy and simplicity and is sufficient for most applications:  Fe

ASP2 = Pd C0 + C1 Ps

or,

ASP2 =

P . C1 Pd + C0 Ps

(5.32)

An example of the SRL with two coefficients is shown in Fig. 5.10b. A formula with three or more coefficients is used for compressors with performance curves that significantly deviate from the parabolic shape. The more coefficients are used, the better fit can be achieved, and the less operating area is wasted 10

The stonewall is usually provided with less precision and is of less interest than surge point, we simply set the surge reference line (SRL) at 30%, with the stonewall being roughly at 100%.

5.3 Surge Reference Line and Surge Indicators

141

(see the shaded areas). Examples of SRL with three and four coefficients are shown in Fig. 5.10c and d. However, more parameters also mean higher complexity. It is thus a trade-off between performance and complexity.

Surge Indicators for Pump Minimum Flow Control In pump operation, the fluid is incompressible liquid with a constant density. The equivalent flow is simplified to a mass or volume flow assumed to be directly measurable. The single-coefficient ASP formula is derived from Eq. 5.31 as ⎧ Fm ⎪ ⎪ C√ , ⎪ ⎪ ⎪ P d − Ps ⎪ ⎪ ⎪ ⎨ Fv , ASP1 = C √ ⎪ Pd − Ps ⎪ ⎪ ⎪ ⎪ ⎪ P ⎪ ⎪ C , ⎩ Pd − Ps

with mass flow measurement with volumetric flow measurements with DP measurements.

Fig. 5.10 Surge reference lines with one to four parameters

(5.33)

142

5 Invariant Coordinates and Surge Indicators

Generally speaking, the pump curves are much better-behaved than compressor curves, as shown in Fig. 5.8, where the surge line closely resembles a parabolic line (or straight line in head versus flow-squared coordinate). As a result, this singlecoefficient formula is sufficient for most pump control applications. However, if it does not, the ASP formula with two coefficients can be used, simplified from Eq. 5.32: ⎧ Fm ⎪ ⎪ , ⎪√ ⎪ ⎪ C P 0 s + C 1 Pd ⎪ ⎪ ⎪ ⎨ Fs , ASP2 = √ ⎪ C0 Ps + C1 Pd ⎪ ⎪ ⎪ ⎪ ⎪ P ⎪ ⎪ ⎩ C0 Ps + C1 Pd

with mass flow measurement with volumetric flow measurements

(5.34)

with DP measurements.

5.4 Calculation of Anti-surge Parameters The anti-surge parameter (ASP) provides a convenient indication of the location of the operating point in relation to the surge limit. When the operating point is below the ASP control setpoint, the anti-surge control opens the recycle valve to recirculate a calculated flow from the discharge side to the suction. The surge control line (SCL) is the actual control line by adding a sufficient control margin to the SRL (Giampaob 2010; Mirsky et al. 2012). With the SRL at 30%, the SCL is typically set to 33%, which is 10% away from the SRL (30%×(1 + 10%) = 33%, see Fig. 4.13). An insufficient surge margin can put the compressor into a surge; an excessively conservative surge margin can result in unnecessary recycling and energy waste (Elliott and Bloch 2021). We will conclude this chapter with a practical example to demonstrate the concept and calculation of the surge indicator. The example consists of a small subset of data from an actual compressor control application; therefore, it is possible to complete the calculation with pencil and paper. The full data set is overwhelmingly large for manual calculation, requiring a dedicated software tool to facilitate the calculation. See Chaps. 6 and Appendix A for a demonstration of the work process of anti-surge parameter calculation using the companion software tool CPACS. Example 5.2 Calculation of anti-surge parameter. The first step in anti-surge parameter calculation is collecting all the relevant performance data into a spreadsheet. The required data include the compressor performance data and the flowmeter data from the respective manufacturers. For this example, the performance curves under head versus flow coordinate are shown in Fig. 5.11, which must be digitized as the first step. The manufacturer-supplied data may not be in the desired format or engineering units as needed in real-time operation. Careful attention is needed to identify and

5.4 Calculation of Anti-surge Parameters

143

Fig. 5.11 Compressor performance curve

transform the data. Ensuring that the engineering units used during design match the engineering units during operation for all the variables is crucial. The minimal data set is collected and shown in Table 5.6. The second column is the minimum flowmeter data extracted from the flowmeter datasheet. The surge points are shown in the second section of the table, corresponding to the 8 points marked as 1 to 8 in Fig. 5.11. The actual measurement data from incipient surge tests (see Sect. 8.3.1) are included in the table to show the difference between the offline data during design and online data during operation.

Table 5.6 Example: compressor performance data

144

5 Invariant Coordinates and Surge Indicators

The objective is to determine the coefficients C0 , C1 , C2 , . . . in the ASP formula in Eq. 5.28, which requires the pressure ratio (Pd /Ps ) and the equivalent flow (Fe ). The pressure ratio is the ratio between the discharge and suction pressure (absolute), and the calculation is thus trivial. Calculating the equivalent flow, Fe , requires the flowmeter’s DP value (P). The flowmeter data provides the vital link between offline design data and online measurement through the flow coefficient C, which can be calculated as follows: Ps M 5.11 × 100 × 21.81 = 4.06 kg/m3 = Z s R Ts 0.99 × 8.314 × (60.00 + 273.15) 23.50 Fm =√ = 4.41. C=√ Ps ρs 7 × 4.06

ρs =

(5.35) (5.36)

Since the flow coefficient C remains unchanged for any fluid once the orifice is built, the P value can be calculated from the given mass flow rate Fm and the gas density ρ in Table 5.6 for all the operating points, even though they have different operating conditions or gas properties:

Fm = C ρ P

→

P =

1 Fm2 . C2 ρ

(5.37)

Once all the surge points are identified, the gas density ρ and the differential pressure (P) for each point are then calculated. These values are used to calculate the pressure ratio and equivalent flow, which are presented in the final two rows of Table 5.7:

Table 5.7 Example: compressor performance data, with compression ratio and equivalent flow

5.4 Calculation of Anti-surge Parameters

⎧ ⎪ ⎪ Pd ⎨ Ps ⎪ ⎪ ⎩ Fe

145

= Pd /Ps P Ps,r = Fm,r . Pr Ps

(5.38)

With the pressure ratio (Pd /Ps ) and equivalent flow (Fe ) available, the coefficients of the ASP formula are calculated by fitting the data to the following equations, which is rearranged from Eq. 5.28:  Fe2 ⇐ C0 + C1

Pd Ps



 + C2

Pd Ps

2

 + C3

Pd Ps

3 .

(5.39)

The ASP calculation becomes a curve-fitting problem with a polynomial equation: J = min







C0 ,C1 ,...

Fe2

− C0 + C1



Pd Ps



 + C2

Pd Ps

2

 + C3

Pd Ps

3 2 . (5.40)

There are numerous tools for solving the problem. A handy approach is using the “Trendline” feature in Excel’s scatter plot, as shown in Fig. 5.12. The results are as follows, with two to four coefficients:   ⎧ Pd 2 ⎪ ⎪ F = −1594.44 + 1292.11 ⎪ e ⎪ ⎪ ⎪  2   Ps ⎨ Pd Pd 2 + 476.89 Fe = 920.78 − 936.44 ⎪ Ps   Ps   ⎪  3 ⎪ ⎪ ⎪ Pd 2 Pd Pd ⎪ 2 ⎩ Fe = −3004.11 + 4299.22 − 1803.44 + 324.44 . Ps Ps Ps (5.41) We can verify that the ASP values at the surge points are all close to 30%. In actual implementation, the surge reference line should be chosen so that all the surge points fall on or to the left of the line. The unconstrained curve-fitting solution shown in Fig. 5.41 has half the surge points on the right-hand side of the surge reference line, which is usually unacceptable. The proper solution is by solving a curve-fitting problem as follows: 

  2  3 2 Pd Pd Pd + C2 − C0 + C1 + C3 (5.42) J = min C0 ,C1 ,... Ps Ps Ps     2  3  Pd Pd Pd 2 + C2 s.t. Fe − C0 + C1 + C3 ≤ 0. Ps Ps Ps 



Fe2



146

5 Invariant Coordinates and Surge Indicators

Fig. 5.12 Surge reference lines calculated with Excel

Dedicated tools are needed to solve this constrained curve-fitting problem. Optimization algorithms such as Excel Solver11 can be used to find the constrained solution. A non-negative least-squares (NNLS) method (Lawson and Hanson 1974) is used in the companion software CPACS, which is a fast and reliable analytic solution for solving this curve-fitting problem. See Appendix A for more information on the software tool. The surge reference lines calculated with CPACS are shown in Fig. 5.13. Note that all the surge points are now on or to the left of the surge reference line. The corresponding ASP formulas are given by   ⎧ Pd 2 ⎪ ⎪ F = −1616.28 + 1377.04 ⎪ e ⎪ ⎪ ⎪  2  Ps ⎨ Pd Pd 2 Fe = 840.81 − 862.54 + 473.66 ⎪ Ps  Ps   ⎪  3 ⎪ ⎪ ⎪ Pd 2 Pd Pd ⎪ 2 ⎩ Fe = −3204.93 + 4562.07 − 1900.58 + 338.55 . Ps Ps Ps (5.43)

11

Microsoft Excel® is a trademark of Microsoft Corporation. Solver is part of Excel.

5.4 Calculation of Anti-surge Parameters

147

Fig. 5.13 Surge reference lines calculated with CPACS tool

The ASP values for all the surge points are listed in Table 5.8. All ASPs have a value of 30% or smaller, indicating that they are all on (ASP = 30%) or to the left (ASP < 30%) of the SRL. The surge reference line with three coefficients is selected as the best tradeoff between complexity and accuracy for this example, as shown in Fig. 5.43. The corresponding ASP formula is thus given by Fe  2 .   Pd Pd + 473.66 840.81 − 862.64 Ps Ps

ASP = 

(5.44)

The final performance map with the surge reference line (SRL), surge control line (SCL), capacity control line (CCL), and surge trip line (STL) is given in Fig. 5.14 (comparing with Fig. 4.17). Validating the performance curve and surge reference line via incipient surge test is a critical step in commissioning, which is discussed in detail in Chap. 8. The three surge points from the incipient surge tests are shown in Fig. 5.14. Their values are close to the surge reference line, as shown in Table 5.8, which confirms that the manufacturer-provided performance curves match well enough with the actual compressor in the field.

148

5 Invariant Coordinates and Surge Indicators

Table 5.8 Example: compressor performance data, with anti-surge parameters

Fig. 5.14 Example of performance map

5.5 Summary Theoretical analysis of pump and compressor behavior is customarily based on polytropic head and volumetric flow since a fixed relationship exists between the two. The performance map under this head and flow coordinate is not affected by inlet condition changes, allowing the surge lines to be visually and mathematically described. The head versus flow coordinate is thus called an invariant coordinate. In practical applications, however, the head and flow are neither directly measurable nor can they be readily calculated in real time. The relationship based on alternative variables is thus needed as the basis for real-time applications. Reduced head and reduced flow are popular among commercial applications because the coordinate system based on the “reduced” variables preserves the invariant relationship

References

149

between the head and flow. These coordinate systems are called equivalent coordinates. Anti-surge control requires a timely and reliable indicator of the location of the operating point relative to the surge point. The SRL defines the minimum stable flow for all inlet conditions. A surge indicator based on this SRL offers a simple and convenient real-time indication of the surge condition to support real-time decisions for operation and control. One of the surge indicators, the anti-surge parameter (ASP), is based on equivalent flow, which offers a good compromise between flexibility and simplicity and is demonstrated with real-world examples.

References API (2014) API standard 670 – machinery protection systems. Technical report, American Petroleum Institute Batson BW (1996) Invariant coordinate systems for compressor control. In: Proceedings of the international gas turbine and aeroengine congress and exhibition. The American Society of Mechanical Engineers, Birmingham Bloch HP (2006) A practical guide to compressor technology, 2nd edn. Wiley Interscience Elliott H, Bloch H (2021) Compressor technology advances — beyond 2020. Walter De Gruyter Giampaob T (2010) Compressor handbook: principles and practice. The Fairmont Press Hafaifa A, Rachid B, Mouloud G (2014) Modeling of surge phenomena in a centrifugal compressor: experimental analysis for control. Syst Sci Control Eng 2:632–641 Honeywell (2023) Honeywell to acquire compressor controls corporation, driving the energy transition through leading automation and controls portfolio. https://www.honeywell. com/us/en/press/2023/04/honeywellto-acquirecompressor-controls-corporationdrivingtheenergytransitionthrough-leading-automation-and-controls-portfolio Lawson CL, Hanson RJ (1974) Solving least squares problem. Prentice Hall Mirsky S, Jacobson W, Tiscornia D, McWhirter J, Zaghloul M (2012) Development and design of anti-surge and performance control systems for centrifugal compressors. In: Proceedings of the forty-second turbomachinery symposium, Houston, Texas Niu S, Xiao D (2022) Process control – engineering analyses and best practices. Advances in industrial control. Springer

Chapter 6

Basic Control Schemes

The overall control strategy presented in Chap. 4 explains the basic principle of controlling the process and equipment. However, the process flow configuration varies drastically across different applications, making it impossible to have a universally applicable control design. Instead, the more practical and effective approach is to fully understand the process dynamics and equipment characteristics, as discussed in Chap. 2, apply the overall control strategy discussed in Chap. 4, and create fitfor-purpose solutions for each specific application. The surge indicators discussed in Chap. 5 provide the quantitative indications of the operating point in relation to the operating envelope and facilitate the detailed control design. This chapter presents several basic control designs that help understand the objectives and requirements. These basic control schemes can serve as the basis for scaling up to more complex process control solutions discussed in Chap. 7.

6.1 Centrifugal Pumps Figure 6.1 shows a simple pumping process in a complex process setting. The centrifugal pump P-101 transfers heavy crude oil from a processing tank T-101 to the downstream operation for further processing. The operating objective is to maintain the material balance by pumping out as much fluid as it enters the processing tank T-101 while maintaining the processing tank (static equipment) and the pump (rotating equipment) in safe and efficient operation. The overall control strategy is laid out in Chap. 4 as follows: 1. Capacity control. Capacity control is the normal regulatory control that keeps the supply and demand balanced to maintain the desired level in the tank and head and flow in the pump.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. S. Niu, Process Control for Pumps and Compressors, Advances in Industrial Control, https://doi.org/10.1007/978-3-031-43122-7_6

151

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6 Basic Control Schemes

Fig. 6.1 A typical process control solution with a centrifugal pump (reproduced, with permission, from Niu and Xiao 2022)

Fig. 6.2 Performance curve for a centrifugal pump

2. Protective control. The minimum recycle flow control is a protective overriding control against the pump surge. The pump flow must be maintained above the minimum flow limit for stable operation. The available control targets and control handles are illustrated in Fig. 6.1. Figure 6.2 shows the manufacturer-provided performance curves.

6.1.1 Capacity Control Capacity control aims to balance the supply and demand through the manipulation of the pump flow, regulated by either throttling the control valve or adjusting the pump speed.

6.1 Centrifugal Pumps

153

Fig. 6.3 A typical process control solution for a centrifugal pump with a fixed flow setpoint

Capacity Control with Fixed-Speed Pumps Most centrifugal pumps operate at a fixed speed, with a typical capacity control design as illustrated in Fig. 6.3. The level controller LC-102 serves as the capacity controller. A decrease in inlet flow FI-101 will cause the tank level LC102.PV to go down. The level controller LC-102 “senses” the level change and adjusts the valve opening LCV-102 to reduce the outlet flow FI-102. The reduced outlet flow causes the pump discharge pressure PI-102 to increase, resulting in less pump flow FI-103. As a result, the tank level LC-102.PV is brought back to its setpoint LC-102.SP and the supply-anddemand balance is restored. Conversely, when the inlet flow FI-101 increases, the tank level LC102.PV will go up. The level controller LC-102 opens the control valve LCV-102 to let out more flow, resulting in a lower discharge pressure PI-102 at the pump. The lower pressure results in a higher pump flow FI-103 to bring the tank level back on target. The pump curves can intuitively explain this change in the pump pressure PI-102 and flow FI-103. For fixed-speed pump operation, the performance map in Fig. 6.2 is reduced to a single fixed-speed line at 100% pump speed (2,897 rpm), as shown in Fig. 6.4. The increase in pump pressure PI-102 (thus the pump head) causes the operating point to move to the left along the constant-speed pump curve, resulting in less flow FI-103 from F1 to F2. The pump performance curve in Fig. 6.4 is rather flat, especially near the minimum flow (MIN FLOW) point. A flat line indicates a large process gain between head and flow, making the flow excessively sensitive to pressure changes, which can be challenging for operation and control. An improved control design is with a cascade control scheme shown in Fig. 6.5. A flow controller FC-102 is added at the discharge line. The level controller LC-102 and flow controller FC-102 work together to form a standard cascade

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6 Basic Control Schemes

Fig. 6.4 Performance curve for a centrifugal fixed-speed pump

Fig. 6.5 A cascade control scheme for a centrifugal pump

control loop, resulting in better control performance from more reliable control of the outlet flow FC-102.PV with the pump. See Niu and Xiao (2022), Smith (2010) for the benefits of cascade control. The control schemes in Figs. 6.3 and 6.5 are for supply-driven operations, where the fluctuations in the inlet flow FI-101 are propagated through the tank level LC-102 to the downstream operation FI-102. The operation becomes demand driven if the process flow is dictated by downstream demand, i.e., FC-102. The capacity control design for the demand-driven operation would change to Fig. 6.6. Higher demand from downstream operation (FC-102) results in more flow (FI-103) from the pump, lowering the discharge pressure PI-102. A lower discharge pressure (and lower head) results in a higher pump flow FI-103 that causes the tank level LC-102 to decrease. The level controller LC-101 detects the level change and opens the inlet valve to draw more inlet flow FI-101 into the tank.

6.1 Centrifugal Pumps

155

Fig. 6.6 Demand-driven capacity control for a fixed-speed pump

Fig. 6.7 Supply-driven capacity control with demand override

In practice, the supply-and-demand model can change unpredictably. For instance, a supply-driven operation can turn into a demand-driven operation due to reduced demand from downstream caused by a partial shutdown. A supply-driven control typically requires a demand override to protect the supply-and-demand balance fully. Similarly, a demand-driven control scheme should include a supply override. Figure 6.7 shows a complete supply-driven control scheme with demand override, where the overriding flow controller LC-101 is spawned off the same level transmitter LT-101. As an overriding controller, LC-101 remains dormant (output at 100%) during normal supply-driven operation when the normal tank level is below the controller setpoint LC101.SP. It becomes active if the tank level becomes excessively high (higher than the controller setpoint) due to reduced demand flow. The reverse-acting configuration will allow the controller to reduce the inlet flow to bring the tank level back on target.

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6 Basic Control Schemes

Fig. 6.8 A typical process control solution with a centrifugal pump

Fig. 6.9 Performance curve for a centrifugal variable-speed pump

Capacity Control with Variable-Speed Pumps Although most pumps operate at a fixed speed, some large-capacity pumps operate at variable speeds for energy efficiency. Figure 6.8 shows a typical capacity control design for a variable-speed pump, which is identical to the design in Fig. 6.5, except that the control handle is the pump speed instead of the control valve. On the performance map, the change in pump flow rate is achieved via speed variation, causing the operating point to move roughly along the constant-resistance curve, as shown in Fig. 6.9. Changes in system resistance (e.g., back pressure) can cause the operating point to move along the constant-speed curves. The combined effect allows the operating point to move within a wide area of the performance map.

6.1 Centrifugal Pumps

157

Fig. 6.10 A typical process control solution with a centrifugal pump

The complete capacity control scheme for a supply-driven variable-speed centrifugal pump with demand override is given in Fig. 6.10. The demand override with controller LC-101 propagates the supply-and-demand imbalance upstream, where adequate swing control must exist to accommodate the change in demand. As explained in Sect. 4.2, adequate swing streams and swing-control mechanisms must exist in all the above scenarios to ensure uninterrupted supply-and-demand propagation along the entire process flow path.

6.1.2 Minimum and Maximum Flow Control The process operation requires that the process throughput (capacity) be able to vary between zero and the desired maximum flow range. However, centrifugal pumps all have a stable flow range that must not be exceeded. For instance, the pump in Fig. 6.4 can only operate stably between a minimum flow limit of 114 m3 /h and a maximum flow limit of 315 m3 /h at 100% speed (2,897 rpm). This mismatch in the flow range required and the flow range available must be addressed by protective controllers. A minimum flow controller is required to ensure the pump flow is always above the minimum flow limit. As shown in Fig. 6.11, the minimum flow controller FC-103 is designed and configured as a reverse-acting PID controller with its setpoint FC103.SP equal to the minimum flow limit. During normal operation, the pump flow FC103.PV is higher than the setpoint FC103.SP; the reverse-acting PID controller FC-103 would drive the recycle control valve FCV-103 to the fully closed position. That is, the minimum flow controller FC-103 remains dormant with zero recycle flow. If the pump flow FC103.PV falls below the minimum flow limit, e.g., due to insufficient process flow from the tank inlet FI-101, the minimum recycle flow controller FC-103 opens the recycle valve to allow a portion of the pump flow to

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6 Basic Control Schemes

Fig. 6.11 Minimum recycle flow control for centrifugal pump

be recirculated back to the tank to make up the difference.1 The amount of recycle flow is given by  0, If FC103.PV ≥ FC103.SP Recycle Flow = FC103.PV − FC103.SP, If FC103.PV < FC103.SP.

(6.1)

There are many variations in process configuration corresponding to the choices in fixed- versus variable-speed operation, supply-driven versus demand-driven control, and fixed versus variable setpoint for minimum flow control.

Minimum Flow Control with Fixed-Speed Pump and Volumetric Flow The minimum flow controller FC-103 in Fig. 6.11 is a standard PID controller that takes the actual flow measurement as the process value (FC103.PV). The desired flow rate is the controller setpoint (FC103.SP), and the controller output (FC103.OP) determines the valve opening FCV-103, thus the outlet flow rate. A characteristic of centrifugal machines is that the relationship between the fluid head and volumetric flow does not change with the fluid property (e.g., density) and the operating condition (pressure and temperature). Therefore, for this pump operating at a 100% fixed speed, the minimum flow limit of 114 m3 /h remains the same for all liquids and under all operating conditions. This minimum flow limit can thus be directly taken as the flow setpoint (FC103.SP) for the minimum flow controller FC-103. In other words, the process value (FC103.PV) for the flow controller FC-103 is the actual pump flow measurement in m3 /h, and the controller

1

Note that the recycle line takes off between the pump flow measurement and process flow measurement locations, which implies that pump flow PI-103 is not always the same as the process outlet flow FI-102.

6.1 Centrifugal Pumps

159

setpoint (FC103.SP) has a constant value of 114 × (1 + 10%) = 125 m3 /h, which includes a 10% control margin. If the measured pump flow rate FC103.PV falls below 125 m3 /h, the recycle valve would be opened to maintain the flow at 125 m3 /h.

Minimum Flow Control with Fixed-Speed Pump and Mass Flow Although the pump curve is provided as head versus volumetric flow, as shown in Fig. 6.2, the actual online measurement may be the mass flow rate instead of the volumetric flow rate.2 If the fluid density is assumed to be constant, the mass flow limit can be calculated from the minimum volumetric flow and treated as a constant value. In this example, assume that the oil density is 960 kg/m3 . With a 10% safety margin, the minimum mass flow limit is calculated as3 : Fm = ρ Fv = (960 ÷ 3600) × 114 × (1 + 10%) = 33.4 kg/s. (kg/m3 )

(s/h)

(m3 /h)

(6.2)

The control design in Fig. 6.11 remains unchanged, except that the engineering units of FC103.PV and FC103.SP are now all in mass flow (kg/s), and the flow setpoint value is set to 33.4 kg/s instead of 125 m3 /h.

Minimum Flow Control with Variable-Speed Pump and Variable Setpoint Now, let us extend the minimum flow control to variable-speed operation where the control handle is the pump speed instead of the discharge control valve. With the fixed-speed operation, the operating point can only move along a single fixed-speed performance curve (Fig. 6.4). In contrast, with the variable-speed operation, the operating point can move across multiple speed lines, as shown in Fig. 6.9. The minimum flow limit has a different value at different pump speeds, approximately proportional to the machine speed (according to the affinity laws). For example, as the pump speed varies from 100% speed (2897 rpm) to 50% speed (1450 rpm), the minimum flow limit decreases from 114 m3 /h to 57 m3 /h. The maximum flow limit changes from 315 m3 /h to 158 m3 /h. If fixed flow setpoints

2

It is also possible that the pump performance curve is provided in mass flow, but the actual flow measurement is in volumetric flow rate. 3 The flow conversion from m3 /h to kg/s also needs to multiply by 3600 s/h to be correct in engineering units.

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6 Basic Control Schemes

Fig. 6.12 Minimum and maximum flow limits for a centrifugal pump

are used for the minimum and maximum flow control, the feasible operating region would be limited to the shaded area in Fig. 6.12, between the two vertical lines ➀ and ➁, while the feasible operating region by design is between lines ➂ and ➃. This reduced feasible area does not even include the best operating point (BEP) and is thus clearly unacceptable. The flow controller FC-103 can use a variable setpoint to accommodate the variable minimum flow limits. The minimum flow limits at different pump speeds are given from the pump performance curves in Fig. 6.12. As the pump speed changes, the setpoint of the minimum flow controller FC-103 is re-calculated and automatically adjusted. For example, if the flow measurement is provided as mass flow Fm in kg/s, and assuming that the actual fluid density ρ is the same as that in the datasheet, the flow can be calculated from the pressure rise as4 Fm = C



Pd − Ps .

(6.3)

The coefficient C can be calculated from the head and flow data with a selected minimum flow point on the performance curve, e.g., h = 1, 220 m and Fv = 114 m3 /h, after appropriate unit conversion, as follows:

4

If the flow measurement is in volumetric flow (m3 /h), the setpoint calculation must be changed to volumetric flow, which is straightforward. Obviously, from the pump curve, the flow setpoint can be calculated from the pump speed. Based on Affinity Laws, the pump is a linear function of the machine speed, and the calculation is trivial. However, speed measurement is not as fast and reliable as pressure and is not preferred.

6.1 Centrifugal Pumps

161

Table 6.1 Minimum flow calculation for pump

Pd − Ps = ρ g h = 960 × 9.8 × 1, 220 (kg/m3 )

(m/s2 )

(m)

= 11, 477, 760 = 11, 478 (kPa) (Pascal)

(6.4)

Fm = ρ Fv = (114 ÷ 3600) × 960 (m3 /h)

(s/h)

(kg/m3 )

= 30.4 (kg/s) Fm C=√ Pd − Ps 30.4 =√ = 0.284. 11478

(6.5)

(6.6)

The flow setpoint can then be calculated from the pressure rise as  Fm = 0.284 Pd − Ps .

(6.7)

In practical applications, the minimum flow values on the performance map do not fall precisely on the same line due to errors and approximations. The most conservative calculation among all scenarios should be used. For this purpose, we start with digitizing the performance curve and collect all the minimum flow values for all speeds. The results are listed in Table 6.1. The pressure rise Pd − Ps and the mass flow Fm are calculated with Eqs. 6.4 and 6.5 for every pump speed at the surge and choke points. The coefficient C is then calculated for each minimum flow point, and the results are listed at the bottom of the table. The most conservative value is the largest at all given speeds, C = 0.286 at 2,610 or 1,450 rpm. The calculation formula of the surge reference line for this pump is thus given as  Fm = 0.286 Pd − Ps .

(6.8)

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6 Basic Control Schemes

Fig. 6.13 A typical process control solution with a centrifugal pump with variable flow setpoint

It is customary to have a safety margin for control, typically 10% extra flow, added to the minimum flow limit:  Minimum Flow Limit: Fm = 0.286 Pd − Ps × (1 + 10%)  = 0.315 Pd − Ps . (6.9) The modified control design will include pressure measurements on the suction and discharge side, as shown in Fig. 6.13. An online calculation block FY-103 is added to compute the minimum flow limit from the suction Ps and discharge pressures Pd . The result is sent down to the flow controller FC-103 as its remote setpoint (FC103.RSP).5 The process value (FC103.PV) for the minimum flow controller FC-103 is the actual flow measurement in kg/s.

Minimum Flow Control with Variable-Speed Pump and Fixed Setpoint In practice, operations often prefer a fixed setpoint for the minimum flow controller FC-103 instead of a variable setpoint at different speeds. For this purpose, a surge indicator, the anti-surge parameter (ASP) in Eq. 5.33, can be used as the new process variable (FC103.PV) to indicate the distance between the current operating point and the minimum flow limit. The anti-surge parameter is defined from Eq. 6.8 based on Eq. 5.33:

5

The PID controller FC-103 needs to be in RCAS mode to receive remote setpoint (FC103.RSP) from external calculation block FY-103; see Niu and Xiao (2022) for PID controller modes.

6.1 Centrifugal Pumps

163

Table 6.2 Minimum flow calculation for pump, with anti-surge parameters

Fig. 6.14 Minimum flow controller with a fixed ASP setpoint

Fm × 30% Pd − Ps Fm = × 30% √ 0.286 Pd − Ps Fm = 1.049 √ . Pd − Ps

ASP = C √

(6.10)

The ASP values for all the minimum flow limit points are calculated with Eq. 6.10 using the minimum flow data in Table 6.1 and appended to the end of the table. The minimum flow line has a reference value of 30% by definition. All the ASP values for the minimum flow points are 30% or smaller, indicating that the ASP calculation is based on the worst-case scenario, as shown in Table 6.2. In other words, any operating point with an ASP value greater than 30% is operating above the minimum flow limit. Therefore, a PID controller XC-103 with the calculated ASP value as the XC103.PV and a fixed setpoint (XC103.SP) of 30 × (1 + 10%) = 33% will achieve the same control result as with a variable setpoint in Eq. 6.9. The control design is illustrated in Fig. 6.14.

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6 Basic Control Schemes

The ASP value is calculated with XY-103 from the suction pressure PI-101, discharge pressure PI-102, and pump flow FI-103. As a protective overriding controller, if the process value XC103.PV is higher than the setpoint XC103.SP, the reverse-acting controller will continue closing the valve until it is fully closed. Therefore, the recycle valve remains fully closed during normal operation when the process flow exceeds the minimum flow limit. Only when XC103.PV is below XC103.SP will the controller open the recycle valve.

End-of-the-Curve Control with Fixed Setpoint If the system resistance at the downstream operation becomes very low, the operating point may move to the far right of the performance curve. Operating over the curve leads to choked flow and reduced efficiency. An anti-choke controller XC-102 can be added to prevent the operating point from going too far to the right. Anti-choke control is also called the end-of-curve control or maximum flow control. The same ASP value calculated by XY-103 is fed to the anti-choke controller XC-102 as its process value XC102.PV. From Table 6.2, the ASP setpoint (XC102.SP) for the anti-choke controller can be set to 92.7% × (1 − 10%) = 83.4%, based on the smallest (thus most conservative) values of all the maximum flow points. The protective control design with both anti-surge and anti-choke controls is shown in Fig. 6.15, with an operating range between ASP=33% and 83%. End-of-curve control can be readily added with fixed-speed pump control since a discharge valve is installed. However, it is rarely implemented for variable-speed pump control because of the need for discharge throttling valve. √ An orifice-based flowmeter has a turndown ratio of 10:1 in DP, or 3.16:1 ( 10 = 3.16) in terms of flow. From Table 6.2, the ratio between maximum flow and minimum flow is about 3.1, which is no surprise since the diffuser of a centrifugal machine behaves like a flow restriction component similar to an orifice plate. In summary, the minimum flow control design can be based on a fixed flow setpoint for a fixed-speed pump or a variable flow setpoint for a variable-speed pump. However, the design with an anti-surge parameter is more generic. It operates with a fixed setpoint and is thus preferred. It is also consistent with anti-surge control for centrifugal compressors, as we move on to compressor control in the next section.

6.1.3 A Complete Control Design A complete control design, including capacity control and minimum flow control, is depicted in Fig. 6.16. The capacity control is through variable pump speed, and the minimum flow control is through the recycle valve.

6.2 Centrifugal Compressors

165

Fig. 6.15 Minimum flow control and end-of-curve control for a centrifugal pump

Fig. 6.16 Capacity control and end-of-curve control

If end-of-curve control is also desired, the design in Fig. 6.16 becomes Fig. 6.17 and becomes fairly complex. However, with the basic designs discussed above, and the incremental increase in complexity, the design is still relatively straightforward to understand.

6.2 Centrifugal Compressors Centrifugal compressors work by the same principle as centrifugal pumps. However, the control design is considerably more complex due to the variable density of the compressible gases that a compressor handles. Figure 6.18 shows a generic process configuration with a single-stage centrifugal compressor and the potential process measurements and control handles. This section discusses this simple compression

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6 Basic Control Schemes

Fig. 6.17 A complete pump control solution

Fig. 6.18 A simple compression process with a single-stage compressor

process’s basic capacity control and anti-surge control design. The discussion of complex compression processes involving multiple compressors is deferred to Chap. 7.

6.2.1 Capacity Control Capacity control follows the overall control strategy discussed in Chap. 4. It is typically achieved by throttling the control valves if the machine is configured as fixed speed or manipulating the machine speed if a variable-speed gearbox or variablefrequency drive (VFD) motor is installed. A critical decision is between supply-driven and demand-driven control. The suction header pressure is typically controlled for supply-driven operation, with the supply/demand imbalance propagated from suction to discharge and from upstream to downstream. On the other hand, in demand-driven operations, the discharge

6.2 Centrifugal Compressors

167

Fig. 6.19 Supply-driven capacity control with throttling valve

Fig. 6.20 Supply-driven capacity control with speed

pressure is used for capacity control, and the material imbalance is propagated backward from downstream to upstream. A supply-driven capacity control with fixed-speed operation is illustrated in Fig. 6.19. The dashed (blue) line indicates the direction of propagation of the supply/demand imbalance, with the suction header pressure P1 and discharge pressure P2 being the relay points. The suction pressure controller PC-101 serves as the capacity controller and manipulates the suction flow control valve PCV-101 to adjust the process flow, which forces the compressor flow to change. The change in compressor flow leads to changes in discharge pressure. The discharge header pressure controller PC-102 detects the discharge pressure change and adjusts the flow to the downstream operation. If the compressor operates at variable speed, the supply-driven capacity control will be through the same suction pressure controller PC-101 but via adjustment of the compressor speed, as shown in Fig. 6.20. If the capacity, or process flow, is dictated by downstream demand, the operation becomes demand driven, as shown in Fig. 6.21. Demand change is propagated backward, from downstream to upstream, via the discharge pressure controller PC-102 and the machine speed to the suction pressure controller PC-101.

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6 Basic Control Schemes

Fig. 6.21 Demand-driven capacity control with speed

Fig. 6.22 Supply-driven capacity control with recycle

Capacity control can also be achieved with recycling, as illustrated in Fig. 6.22. Recycling is the easiest but also the most inefficient way of capacity control. It is rarely used as the primary capacity control for centrifugal compressors. Similar to the pump controls discussed in Sect. 6.1, the supply-and-demand model may reverse due to operational needs or plant upsets. For example, the supply-driven operation in Fig. 6.20 changes to demand driven if the downstream consumption is suddenly limited due to, e.g., a partial shutdown. Protective overriding control may become necessary for reliable operation to handle the reversal of the supply-anddemand model. A supply-driven operation with demand override is achieved through suction pressure control with discharge pressure override, as shown in Fig. 6.23. The dashed (blue) line designates the propagation path of the supply-driven control. In contrast, the dotted (red) line indicates the propagation path if the supply-driven operation becomes demand driven.6

6

The capacity control becomes compressor driven if the throughput is limited due to the compressor hitting the maximum speed or motor power limit. In this case, the operation upstream of the compressor becomes demand driven, while the operation downstream turns supply driven. Consequently, the critical requirement is that both upstream and downstream operations must have the means to adjust the supply and demand to align with compressor capacity (swing control).

6.2 Centrifugal Compressors

169

Fig. 6.23 Supply-driven capacity control with demand override

Since capacity control is concerned with the supply-and-demand relationship along the entire process flow path, including the compressor, the design must be based on a holistic view of the supply-and-demand model. The basic control design discussed here provides the foundation for addressing more complex control needs. For more in-depth discussions on capacity control, see Niu and Xiao (2022).

6.2.2 Anti-surge Control An anti-surge controller is a standard protective controller that monitors and regulates the compressor flow in real time to prevent the compressor from going into a surge, similar to a minimum flow controller for a centrifugal pump. The control scheme is typically a standard PID control loop, and is straightforward. The challenge is calculating the anti-surge parameters (ASP), which is the process value (PV) of the anti-surge controller that indicates the location of the operating point in relation to the minimum flow limit. Figure 6.24 shows a typical anti-surge control scheme for a single-stage centrifugal compressor. The anti-surge controller UC-111 is a standard PID controller, with the process variable (UC111.PV) being the anti-surge parameter (ASP), calculated with the function block UY-111 from suction pressure PI-111, discharge pressure PI-112, and the suction flow FI-111. The measurement range of the ASP is from 0 to 100%, with the surge reference line (SRL) at 30% and the stonewall at approximately 100% (see Sect. 5.3). The anti-surge control setpoint UC111.SP has a fixed value of 33%, which is 10% to the right of the surge reference line (30%×(1+10%)=33%). The controller output (UC111.OP) is sent to the anti-surge control valve UCV-111. When the ASP stays above the setpoint value of 33%, which indicates that the compressor flow is above the minimum flow limit, the reverse-acting anti-surge controller UC-111 will keep the recycle valve fully closed. If the ASP valve falls below 33%, e.g., due to

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6 Basic Control Schemes

Fig. 6.24 Anti-surge control scheme, with flow measurement on suction

low process flow, the anti-surge controller UC-111 will open the recycle valve by a calculated amount to keep the compressor flow above the minimum flow limit. The orifice-based flowmeter FI-111 is typically located on the suction side, as highlighted in Fig. 6.24, which is the preferred design for energy efficiency and calculation simplicity. However, the orifice plate inevitably causes permanent pressure losses. This pressure loss at the suction side may be unacceptable for certain lowpressure operations. The alternative design is to place the flowmeter at the discharge side where the pressure has been elevated, as highlighted in Fig. 6.25. The control design is identical to that with the flowmeter on the suction, except that the ASP calculation is slightly different, involving further approximations. For compressors where simplicity outweighs efficiency, the control design can be simplified to using two differential pressure measurements, one across the orifice for flow measurement and another across the compressor as pressure rise, as shown by Eq. 5.31. This primitive control scheme is shown in Fig. 6.26, which is almost identical to Fig. 6.24, except that the ASP calculation in UY-111 is based on two differential pressures PDI-111 and PDI-112 with a different calculation formula (see Eq. 5.31). It was used in many early compressor control design (Boyce et al. 1983).

6.2 Centrifugal Compressors

Fig. 6.25 Anti-surge control scheme, with flowmeter at discharge

Fig. 6.26 Anti-surge control scheme, with differential pressure DP for flow

171

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6 Basic Control Schemes

6.2.3 Anti-surge Parameter Calculation The primary challenge for anti-surge control is to know how far the current operating point is from the surge limit. Like pump control, the surge indicator is the anti-surge parameter (ASP), calculated from online pressure and flow measurements. The recommended anti-surge parameter (ASP) is given by Eq. 5.28 and is reproduced here: ASP =  C0 + C1



Pd Ps



Fe ,  2  3 Pd Pd + C2 + C3 + ··· Ps Ps

(6.11)

where Fe is the equivalent flow through the flow-measuring orifice (FT-111). Ps and Pd are the absolute suction pressure (PI-111) and discharge pressure (PI-112), respectively. The number of terms inside the square root in the denominator (C0 , C1 , C2 , · · · ) depends on the complexity of the surge line. It will be determined based on compressor performance data and the flow transmitter data. The equivalent flow Fe of the compressor is derived from the DP-based flow measurement and is given as  Fe = Fm,r

Ps Pr

 Ps,r . Ps

(6.12)

As an equivalent flow, Fe has the same measurement range and engineering unit as the reference mass flow Fm,r that it is derived from. The primary challenge to anti-surge control is the availability of the performance data required by Eqs. 6.11 and 6.12 for anti-surge parameter calculation. A greenfield project starts from scratch. Therefore, the data’s availability and integrity are usually not a concern since the data suppliers, such as manufacturers and contractors, are all readily accessible. For a brown-field project, however, it is usually the contrary. The availability and integrity of the data are the biggest challenge. For a green-field project, before the plant is built and operational, the data for design are primarily based on best engineering knowledge and offline calculations dictated by the basis of design. They may include the predicted gas property, desired operating pressure and temperature, and required capacity (mass flow rate). The different operating scenarios the machine is expected to operate, such as winter, summer, heavier gas, lighter gas, and turndown conditions, are typically provided. Table 6.3 lists the typical data types and their engineering units for describing the characteristics. These variables are illustrated on the control schematic in Fig. 6.27. It is critical to have a coherent view of the different types of data and their roles in control design.

6.2 Centrifugal Compressors

173

Table 6.3 Typical process data for compressor control Measurements Pressure Temperature Compressibility Adiabatic Index Volumetric Flow Differential Pressure Density Mass Flow Rate Speed Molecular Weight Polytropic Head Polytropic Efficiency

Suction Side Discharge Side Base Units Other Units Imperial Ps Ts Zs κs Fv,s P s ρs

Pd Td Zd κd Fv,d P d ρd Fm N M Hp η

kPa(a) K m3 /hr kPa kg/m3 kg/s % kg/kmol kJ/kg %

bar(a) ◦C m3 /s mbar

psi(a) ◦F gpm psi lb/ft3 lb/s

rpm lb/kmol %

Fig. 6.27 Control target and handles for centrifugal compressor control

The data requirements can be classified into five categories, as listed in Table 6.4, corresponding to the five essential components in a standard feedback control loop in Fig. 6.28. For example, the compressor API datasheet specifies the desired operating points, serving as the basis of design or control objectives. The flowmeter datasheet defines the requirements for flow measurement, and the valve datasheet provides the characteristics of the control valve. The amount of data required can be overwhelming to the unprepared. There is no standard or even consensus on what data must be provided and in what format. Therefore, the end user must define their data requirements at the earliest opportunity. Of the various data suppliers, the compressor manufacturer is the crucial one. The process control engineer may need to insist on the preferred data type and format the equipment manufacturers must provide for control design. For example:

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6 Basic Control Schemes

Table 6.4 Data requirements for anti-surge control design ➀ ➁ ➂ ➃ ➄

Role in Control

Data Type

Preferred Format

Primary Supplier

Control Objective Equipment Dynamics Flow/Pressure Meters Recycle Valves Control Scheme

API Design Datasheet Performance Curves Flow Meter Datasheet Valve Datasheet ASP formula + Setpoints

Spreadsheet+Table Spreadsheet+Chart Tabular Tabular Equation

Process Engineer Manufacturer Manufacturer Manufacturer Process Control

Fig. 6.28 Essential components of a control loop

1. Curves versus spreadsheet. Traditionally, the performance data are provided as “curves.” These curves must be “read out” as sampled values before use, which is tedious and error prone. For modern applications, the equipment manufacturers should provide all relevant data in digital format (e.g., spreadsheet) to avoid this digitization process. 2. Head versus pressure. The equipment manufacturer typically supplies the performance data as head/efficiency versus flow or pressure/temperature versus flow. Since the invariant coordinates for control design (see Chap. 5) are based on pressure ratio, the latter is always preferred. However, having the head and efficiency data in addition to pressure and temperature is very beneficial for cross-validation purposes. Example 6.1 ASP calculation with software tools. The ASP calculation is usually facilitated by dedicated software tools, except for simple ones involving limited performance data. However, software tools are not a replacement for technical know-how. A solid understanding of process control technologies and compressor characteristics is required to use the tools correctly.

6.2 Centrifugal Compressors

175

Here we demonstrate the concept and procedure of ASP calculation with a reduced set of actual data. The companion CPACS software tool7 can be used to enter and organize the compressor data, visualize the performance map, and assist the control design. An example of the compressor data is shown in Fig. 6.29. The first row of the spreadsheet shows the type of data that can be entered, along with the engineering units in the second row. Some data may be redundant, but having as much data as possible is always beneficial for cross validation. The compressor data may be provided with different engineering units. The unit conversion is usually tedious and error prone. Most software tools should have the unit conversion automatically taken care of internally. The ASP coefficients for the desired ASP formula are calculated with the chosen coordinate system and the selected operating scenarios. The ASP formula using pressure ratio versus equivalent flow and with three coefficients is shown in Fig. 6.30, along with the surge reference line (SRL) and surge control line (SCL): Fe  2 .   Pd Pd + 473.66 840.81 − 862.64 Ps Ps

ASP = 

(6.13)

The measurement range of the ASP is 0 ∼ 100%, with the SRL at 30% and the stonewall roughly at 100%. Appendix A provides more details on using software tools to facilitate data management, surge analysis, and control design.

6.2.4 † Flowmeter Design Capacity control and anti-surge control rely on fast and reliable flow measurements. However, measuring the actual flow inside the machine is not practical. Instead, the flow is usually measured at the suction or discharge line using a DP-based flowmeter such as an orifice or Venturi tube. The flowmeter design must align with control requirements, including the flow measurement range, maximum pressure drop, and proper compensation for pressure and temperature. The flowmeter datasheet provides the connection between the differential pressure P (measured) and the inferred flow. The process control engineers should be capable of validating flowmeter designs for process control needs.

7 CPACS stands for Compressor Performance Analysis and Control Support. The CPACS tool is an Excel add-in and is freely available at http://github.com/niucontrol/CPACS. Download the user manual for a full description of the functionalities.

176

6 Basic Control Schemes

Fig. 6.29 The compressor API design data

Fig. 6.30 Performance map for a compressor

With a DP-based flowmeter, such as a restrictive orifice in Fig. 3.13a, the actual measurement is the pressure drop P across the orifice. The flow through the orifice (Fv or Fm ) is then inferred from the pressure drop P with Bernoulli’s equation.8 Between any two points ➀ and ➁ on the flow line, we have 1 1 P1 + ρ1 v12 = P2 + ρ2 v22 , 2 2

8

(6.14)

Head, flow, and ASP are all inferred from other online measurements and, thus, they are all called inferential properties.

6.2 Centrifugal Compressors

177

where P1 and P2 are the pressure measurements at the two points, respectively. ρ1 and ρ2 are the densities. v1 and v2 are the flow velocities. Assume the change in fluid density across the orifice is negligible (ρ1 = ρ2 ). By continuity of mass, A1 v1 = Av2 = Fv , where A1 and A2 are the cross-sectional areas of the orifice and the vena contracta, and Fv is the volumetric flow. We then have:  1  2 ρ v2 − v12 2   2 Fv Fv2 1 − 2 = ρ 2 A22 A1   1 1 1 2 − 2 . = ρ Fv 2 A22 A1

P1 − P2 =

(6.15)

Define P = P1 − P2 , we have 

P Fv =  2 2 ρ 1 − (A2 /A1 )  π 2 P d2 =  4 1 − β4 ρ  P =C , ρ A2

(6.16)

where d is the diameter of the orifice and D is the diameter of pipe, and with: A1 =

1 π D2, 4

A2 =

1 π d 2, 4

A2 = A1



d D

2 = β2, β =

d D

C is the flow coefficient. The more generic equation for mass flow measurement is given by ISO5167 (ISO-5167 2003) standard9 as π ε d2 Fv =  4 4 1−β Cd



P =C 2 ρ



P ρ

 Cd π  Fm =  ε d 2 2 P ρ = C ρ P, 1 − β4 4

(6.17) (6.18)

where Cd is the discharge coefficient and ε is the expansion factor. They are experimentally determined coefficients that account for friction losses and other discrepancies between theory and practice. 9

Note that ISO 5167 (all parts) applies only to flow that remains subsonic throughout the measuring section and where the fluid can be considered single phase. It does not apply to the measurement of pulsating flow.

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6 Basic Control Schemes

The critical information is the flow coefficient C, a relative measure of the efficiency in allowing fluid to pass through. The flow coefficient connects the pressure drop P across an orifice valve with the corresponding flow rate Fm or Fv . One of the crucial design parameters of the flowmeter for compressor control is the measurement range. The design requirement is to ensure that the flowmeter’s effective measurement covers compressor’s flow range, required by both capacity control and anti-surge control. A DP-based flowmeter has an inherent turndown limit, below which the measurement is no more trustworthy. The turndown ratio is typically 10:1 by DP or 3:1 by flow,10 see Fig. 3.13b. In other words, the effective flow measurement range is approximately 30% to 100% of the maximum range. As shown in Sect. 3.3.2, compressor flow has an approximate turndown ratio of about 3:1 as well. If the stonewall is defined as 100%, the surge line is approximately 30%. The effective range of the flowmeter roughly matches the compressor range. However, if the two ranges do not match, engineering knowledge is required to strike a trade-off. Example 6.2 Flowmeter data and flowmeter sizing. The flowmeter datasheet describes the relationship between the flow rate and pressure drop under the design or calibration condition. An example of the orifice flowmeter datasheet is given in Fig. 6.31. The flowmeter’s maximum and turndown flow rate can be visualized on the same performance map as shown in Fig. 6.32. The measurement range provided by the flowmeter and the measurement range required by the process control design can be visually compared and intuitively verified from the map. For validation purposes, the maximum flow is achieved at the maximum pressure drop of P = 25, 000 Pa (250 mbar), with the given orifice size of 0.240 m (240 mm): Fm = 

Cd 1 − β4

=√

ε

π 2 d 2 P ρ 4

0.59789

1− = 47.65 kg/s.

0.713174

× 0.99744 ×

√ 3.14159 × 0.2402 × 2 × 25000 × 46.26 4 (6.19)

The sizing of the equipment and devices is primarily the responsibility of the process, equipment, and instrumentation personnel. However, it is crucial for process control to cross validate the sizing calculation and ensure it is acceptable for both capacity control and anti-surge control. The pressure drop is expected to be sufficiently large to achieve the required measurement accuracy for process control, which demands a smaller orifice opening. However, operations also have other requirements, such as a limit on the maximum pressure loss at the flowmeter. Therefore, the design must consider many constraints, 10

Flow is proportional to the square root of P; thus, the flow turndown is

√

10:1=3.16:1.

6.2 Centrifugal Compressors

179

3

Fig. 6.31 Orifice-based flowmeter datasheet

Fig. 6.32 Compressor curves with maximum and minimum flow lines

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6 Basic Control Schemes

sometimes conflicting, to finalize. Many rounds of interactions between multiple stakeholders are usually necessary. The flowmeter design is to determine the orifice size based on the maximum flow rate required by process design within the limit of maximum allowable pressure loss. For the orifice meter in Fig. 6.31, with the requirement of maximum flow Fm = 47.75537 kg/s at DP P = 25, 000 Pa (250 mbar), the orifice diameter can be calculated from Eq. 6.18 as

Fm2

(6.20) d =

4  Fm2 1 2 ρP (π ε C + ) d D4 8

47.755372

=

4 2  47.75537 1 + (3.14159 × 0.59789 × 0.99744)2 × 46.26 × 25, 000 4 0.3366 8 = 0.2399 m = 239.9 mm

(6.21)

which agrees with the 240 mm specification in the datasheet. If we want to achieve a 60.0 kg/s flow at P = 25 kPa, the orifice size would need to increase to

60.02

d =

4  60.02 1 + (3.14159 × 0.59789 × 0.99744)2 × 46.26 × 25, 000 0.33664 8 = 260.0 mm. (6.22)

6.2.5 Instrumented Safeguarding If the anti-surge control fails to stop the pump or compressor from entering a surge, then the anti-surge trip logic must detect the surge condition and proactively trip the compressor to avoid damage. This machine safeguarding function provides the third line of defense against surge, as shown in Fig. 4.1. Tripping a compressor introduces its own risks to the machine (Botros et al. 2015). The compressor should trip only when deemed absolutely necessary. For instance, a single short surge is not a significant risk, but multiple surges within a short period are. It is critical to strike a reasonable balance between keeping the operation online and protecting the machine from damage. The trip logic is typically based on either a long surge cycle (e.g., longer than 3 s) or repeated short surge cycles within a short period. See Elliott and Bloch

6.2 Centrifugal Compressors

181

Fig. 6.33 Anti-surge trip conditions

(2021). For example, API 670 recommends the criterion of 3 surges within 10 s (API 2014). • Deep surge: A surge cycle lasting longer than, e.g., 3 s. • Repeated surge: Three repeated surge cycles within, e.g., 10 s.11 The trip conditions are summarized and illustrated in Fig. 6.33. The anti-surge trip of the compressor is in addition to other normal SIS trip protections, such as those on pressure, temperature, flow, or vibration.12 Anti-surge trip logic is based on the same anti-surge formula (ASP) value calculated in Eq. 6.11, with the same range from 0 to 100%, corresponding to zero and the choked flow. With the surge reference line at 30%, the anti-surge trip line is typically set to half the surge reference value, i.e., 15%. If the ASP value falls below this limit, the anti-surge trip logic generates a trip request to the existing safety instrument system (SIS), which processes the request following the standard protocols. One of the actions is to de-energize the anti-surge control valve, which is always fail-open, to cause it to open at full speed. In a typical implementation, all control functions are implemented in control systems such as standard DCS. The anti-surge trip logic is implemented in the safety instrument system (SIS), independent of the anti-surge control in DCS, to avoid common mode failures. One generic implementation of the anti-surge trip logic based on three surges is shown in Fig. 6.34. Tripping the compressor upon detecting the first or second surge is also common, which is a straightforward simplification of the trip logic. 11

If two surges occur within 3 s, they are counted as one surge cycle. A surge may produce noisy transmitter signals and the possibility of multiple surge counts from a single surge cycle. 12 The surge trip signal can be discerned from the first-out event in the sequence of event recording.

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6 Basic Control Schemes

Fig. 6.34 Segregated safeguarding and control in implementation

The convention used in the SIS logic is that a signal of ONE (=1) indicates a healthy condition, while a signal of ZERO (=0) indicates a trip condition. The different function blocks are explained as follows: 1. Surge cycle. The anti-surge parameter (ASP) is calculated in the SIS independent of the ASP calculated in DCS. The ASP value is compared with the surge trip limit (SP, typically set to 15%). If the ASP value is higher than SP, a ONE signal, indicating healthy condition, is produced by the “>” gate as the input to the first OR gate. This ONE input locks the OR gate output to ONE (healthy). If the ASP drops below SP, a ZERO signal, indicating surge condition, is produced by the “>” gate and propagates to the first OR gate. The OR gate output depends on another input from the startup delay block. If both inputs are ZERO, the OR gate will produce a ZERO value, indicating a surge condition to trigger the surge counting. 2. Block (D): Startup override. When the motor is started, the compressor needs some time to reach the minimum stable condition. Since the ASP value may start from zero during startup, the trip signal must be masked until the ASP value reaches its normal stable value to avoid nuisance alarms and trips. Block (D) is a DELAY ON block and provides a T0-second delay on the propagation from its input to its output. That is, when the input of Block (D) (i.e., the motor running status) changes from ZERO to ONE (ON LOAD), its output will remain at ZERO for T0 seconds before changing to ONE. The ONE signal passes through the negation gate and produces a ZERO signal as input to the first OR gate. 3. Block (A): Start of surge counting. A surge longer than T1 seconds is counted as one surge cycle. Block (A) is a DELAY OFF block. When its input changes from ONE to ZERO, it starts a T1-second countdown. During the T1 seconds, the

6.2 Centrifugal Compressors

183

DELAY OFF block blocks the input signal, and the output signal remains ONE. When a surge occurs, the output of the first OR gate changes from ONE to ZERO, and the DELAY OFF block (A) blocks the signal for T1 seconds. At the end of the T1 seconds, if the OR gate output is still ZERO (i.e., surge condition still on), the ZERO signal will pass through the final AND gate and generates an SIS trip signal. 4. Block (B) and Block (C): Surge counting toward the three-surge cycles. Block (B) is a DELAY ON block. When its input changes from ONE to ZERO, and its output will immediately flip from ONE to ZERO and hold the ZERO output for T2 seconds. Block (C) is a DELAY OFF block, identical in functionality to Block (A), but a different delay time can be assigned if required. Upon receiving the first surge signal (a dip in ASP value), block (B) output changes to ZERO and holds the ZERO for T2 seconds. The output of Block (C) changes to ZERO after T1 seconds and thus opens the second OR gate to receive the second surge dip. The T1-second delay imposed by Block (C) ensures that if two surges occur in less than T1 seconds, it will be treated only as one. If the second ASP dip comes in within T2 seconds of the first surge dip, the second Block (B)/Block(C) will start counting. The Block (B) output will remain at ZERO for T2 seconds, while the Block (C) output will change to ZERO after T1 seconds, and the last OR gate is ready to take the third surge dip. If a third surge comes in before the first T2 seconds countdown expires, the surge dip (ZERO) will pass through the first, third, and fourth OR gate and produces a trip signal. If there are no more surges within the T2 seconds count, the Block (B) countdown expires, and its output changes from ZERO to ONE and blocks the corresponding OR gate. If any surge dips are longer than T1 seconds, a trip signal will be produced immediately since the first trip condition is met.

6.2.6 A Complete Control Design A complete control scheme, including both capacity control and anti-surge control, is shown in Fig. 6.35 for fixed-speed supply-driven operation and Fig. 6.36 for variablespeed supply-driven operation. The capacity is controlled with the suction pressure controller PC-101 by manipulating either the suction valve PCV-101 or machine speed SC-101. At the discharge side, pressure controller PC-102 is the relay point to propagate the supply-and-demand fluctuations to downstream operation. Adequate swing capacity and control mechanism must exist to absorb the fluctuations in the gas flow from the compressor. The discharge pressure controller PC-103 is an overriding controller to prevent the discharge pressure from going excessively high. Similarly, pressure controller PC-101B is provided to protect the suction header if the capacity controller PC-101 fails to maintain the suction pressure. The controller UC-111 provides the anti-surge control function through the anti-surge control valves UCV-111.

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6 Basic Control Schemes

Fig. 6.35 Basic capacity and anti-surge control with fixed-speed drive

Fig. 6.36 Basic capacity and anti-surge control with variable-speed drive

The control designs shown in Figs. 6.35 and 6.36 are acceptable but with inherent flaws. One of the flaws is that the interaction between the two manipulated variables (suction value and recycle valve in Fig. 6.35; machine speed and recycle valve in Fig. 6.36) and the two controlled variables (capacity and surge margin) is not adequately addressed, which may result in inefficient operation or sub-optimal performance. Proper decoupling with a multivariable control scheme is preferred, which is the topic of advanced control design in Chap. 7.

6.3 Reciprocating Pumps and Compressors

185

6.3 Reciprocating Pumps and Compressors Reciprocating pumps and compressors work on different principles than centrifugal machines. One significant difference is that reciprocating machines do not suffer from the surge and choke phenomena. As a result, the control solution for processes with reciprocating machines is much more straightforward.

6.3.1 Capacity Control for Reciprocating Machines The capacity control of reciprocating machines is similar to that of centrifugal machines in concept. The system resistance does not impact the pump flow; therefore, the typical control handles are the recycle flow and machine speed. The basis for capacity control is the supply-and-demand relationship of the overall process configuration, with the pump or compressor as an integral part. For example, the capacity control of a supply-driven process is achieved with a pressure controller PC-101 at the suction header, as shown in Fig. 6.37a. The pressure controller PC-102 propagates the supply-and-demand imbalance forward to downstream. The protective controller PC-103 provides overriding control if the supply-driven control reverses to demand driven and resulting in excessively high discharge pressure. A demand-driven control has the capacity controller PC-102 on the discharge side, as shown in Fig. 6.37b. The supply-and-demand relationship is propagated backward via the two normal regulatory controllers, PC-102 and PC-101, with the overriding controller PC-103 to protect the pump against changes in the supply-anddemand relationship that can potentially cause an excessively low suction pressure. Other means for reciprocating compressor capacity control include inlet valve uploaders and clearance pockets. Valve uploaders are mechanisms that open or close one or more of a cylinders’ inlet valves to provide unloading. For instance, valve uploaders with three-step uploading can provide 0, 50%, and 100% of the nominal cylinder capacity. On the other hand, the clearance pocket is a volume chamber separated from the normal cylinder-end clearance volume by a valve or

Fig. 6.37 Reciprocating machine with capacity and protective control

186

6 Basic Control Schemes

plug. Opening the clearance pocket reduces the cylinder inlet volumetric flow by trapping the additional gas in the enlarged clearance volume at the end of the piston stroke.

6.3.2 Protective Control for Reciprocating Machines Since surge and choke are not concerns in reciprocating machines, protective control is mainly about protection against extreme pressures. The compression ratio of a reciprocating machine is limited only by the driver’s power rating. The overriding controller PC-103 provides the protective control function against excessively high discharge pressure (Fig. 6.37a) for supply-driven control or low pressure on the suction side (Fig. 6.37b) for demand-driven control.

6.4 Practical Considerations A successful control scheme must properly address many practical details and potential abnormal operating scenarios. Some important considerations are listed here.

6.4.1 Speed of Response Pumps and compressors operate at very high speeds with extremely fast responses in pressure and flow. The control loop has five essential components. The speed of response of the control loop depends on all the components in the loop and is dictated by the worst-performing component. Process measurements such as flows and pressures with hard-wired 4 ∼ 20 mA signals have a typical response time of tens of milliseconds. Fieldbus (FF) signals, which have a latent transmission delay, are usually not adequate for anti-surge control, although sufficient for capacity control. The final control element (FCE), with a typical response time in seconds, is the bottleneck for control. The typical requirement is that the recycle valve should be able to move from a fully closed to a fully open position in less than two seconds. On the process side, the speed of response is measured by the response time from the time the recycle valve is opened to the time the desired recycle flow is attained. The surge volume, measured by the amount of gas entrapped at the machine’s discharge, is a critical factor affecting the speed of response. In case of a surge, it is critical to allow the trapped gas between the compressor discharge and the recycle to quickly recirculate back to the suction, as shown in Fig. 6.38. The recycle line is preferably taken off before the discharge cooler to minimize the surge volume. However, the recycled gas requires a suction cooler after the recycle tie-in point to cool it down.

6.4 Practical Considerations

187

Fig. 6.38 Minimizing surge volume to increase speed of response

Fig. 6.39 Surge volume with hot recycle

For multi-stage compressors or multiple compressors operating in series, the recommended piping is illustrated in Fig. 6.38, where the take-off of the recycle lines is from upstream of the coolers and is sent back upstream of the suction coolers. With this arrangement, the surge volume for each stage is minimized. If for process reasons, e.g., in E&P operation where a suction cooler may not be installed, the recycle flow must be drawn from downstream the cooler (cold recycle), the surge volume will include the discharge cooler, which can significantly increase the response time. See Fig. 6.39. A bypass line (the red line) may need to be provided if the speed of response becomes a concern, which is determined by vigorous dynamic simulation. A cold bypass line is taken downstream of the discharge cooler. In extreme cases, such as startup and trip, a hot bypass line upstream of the discharge cooler may also be required to protect the compressor. The speed of control calculation, if implemented in standard DCS, is determined by the scan frequency of the DCS. With modern DCS systems, it is common to see

188

6 Basic Control Schemes

execution speed at 100 ms or faster. Some proprietary implementations may offer control systems that execute at 10 to 20 ms. However, considering that the bottleneck is the control valve at a speed of 2,000 ms (2 s) (Elliott and Bloch 2021), it is hard to justify raising the control calculation speed to 10 ms for most applications. Unlike most control solutions from commercial vendors where the regulatory control, protective control, and safeguarding function are all lumped in a single proprietary software and hardware system, the control strategy discussed in this book has a clear separation between the three levels of the functions as three lines of defenses against a surge. Capacity control does not require the same speed of execution as anti-surge control does. During turndown, the capacity control starts to open the recycle valve as soon as the operating point reaches the capacity control line (CCL), which is ahead of the surge control line (SCL). Most of the time, the capacity control is sufficient to stabilize the operating point at the CCL without triggering the anti-surge control. If capacity control fails to hold the line and anti-surge control must respond, the valve stem is already lifted up from its seat by the capacity control action, thus reducing the response time of the anti-surge control valve. Lifting the valve from its seat can take up to half a second if starting from a fully closed position.

6.4.2 † Sensitivity Analysis Compressor control, including capacity control, anti-surge control, and anti-choke control, all depend on knowing the location of the operating point in relation to the surge line. Although an accurate formula is desired to represent the SRL, many practical factors affect the accuracy of the SRL calculation, with the following being a few: 1. Surge points. The surge points on the performance curves provided by the pump and compressor manufacturers are estimated based on the mechanical construction of the machine and the equation of states (EOS) of the fluid property. Although the performance data are usually verified by surge tests at manufacturer’s facility and incipient surge tests at the site, the accuracy of these surge points can still vary noticeably. A 1% or 2% error is not uncommon. 2. Surge reference line. The surge reference line (SRL) is, at best, an approximation of the last known location of the most conservative surge points and surge lines. The SRL may shift unpredictably with time. The changes in the gas property (e.g., molecular weight) and operating condition (e.g., temperature and pressure) also impact the ASP calculation results. In addition, the assumption of Z s /Z d being constant does not exactly hold and can be a source of error. 3. Accuracy of curve-fitting. The surge reference line is derived from the surge points via curve fitting. The ASP formula for representing the SRL is not a perfect fit to the surge points. 4. Field instrumentation. Errors and uncertainties in measurements are inevitable. These errors will directly affect the accuracy of the ASP calculation.

6.5 Summary

189

5. Recycle valve. Valve stiction or slip is common as the valve experiences wear and tear over time. As a result, even if the anti-surge control action is adequate, it may not achieve the desired response if the valve performance has deteriorated. An extra margin needs to be added to maintain the desired safety margin. 6. Control margin. The surge reference line serves as an indication of when the surge phenomenon may start. A safety margin must be included in practical operation and control, usually 10% of the flow. The choice of 10% is purely based on experience and may not be adequate for all applications. As most people tend to err on the safe side, this control margin may have a large built-in margin. For the above reasons, the SRL calculation is not rocket science requiring high precision. It is merely an approximation affected by many practical factors. It is critical to understand the key factors contributing to the impreciseness of the SRL and budget the effort accordingly when calculating the ASP coefficient. For instance, the SRL can be approximated with a straight line, a parabolic function, or as complex as a neural-network model. However, the incremental improvement gained by using a more complex formula is easily offset by other uncertainties or by adjusting other tuning parameters, e.g., the 10% safe margin. A balanced decision based on a holistic view of all the uncertainties is always recommended.

6.5 Summary The capacity control design of pumps and compressors is dictated by the overall process control needs, determined by the supply-and-demand relationship of the process flow configuration. The pump and compressors are controlled to respond to the overall process capacity control. The primary control handles can be one or more of the machine speed, control valve, and recycle valve. The control design thus varies with the control targets to meet, and the control handles available. However, the governing factor is the cause-and-effect relationship between the controlled and manipulated variables. The minimum recycle flow control of centrifugal pumps and anti-surge control of centrifugal compressors work on the same principle, except that a pump deals with an incompressible liquid, and a compressor handles compressible gases. The objective is to keep the machine flow above the minimum flow limit. However, the challenge is knowing the current flow rate in relation to the minimum flow limit. An incompressible liquid assumes a constant density, and calculating the minimum flow limit is relatively straightforward. It can be a fixed flow value for a fixed-speed pump or a variable flow value that can be inferred from the pressure or speed measurement. A more general approach that applies to all centrifugal machines is to use the antisurge parameter (ASP). The anti-surge control or minimum flow control becomes a standard PID control scheme, with the ASP value being the process value (PV), while the setpoint assumes a constant value at 33% with the SRL at 30%. With the

190

6 Basic Control Schemes

same ASP calculation, the choke reference line would have approximately a value of 100%. Therefore, anti-choke control can also be easily implemented if desired. Calculating the anti-surge parameters is the major effort in the control design involving centrifugal machines. The ASP calculation is based on several types of data from different sources and can thus seem overwhelming. Understanding the control objectives and data requirements can reduce the frustration. The control design for pumping processes is relatively straightforward compared to the control design for compression processes. However, many pumps in operation do not have adequate pump control, resulting in inefficient and unsafe operations and significant energy waste.

References API (2014) API standard 670 – machinery protection systems. Technical report, American Petroleum Institute Botros K, Hill S, Grose J (2015) A new approach to designing centrifugal compressor surge control systems. In: 44th turbomachinery and 31st pump symposia, Houston Boyce MP, Bohannan WR, Brown RN, Gaston JR, Meher-Homji C, Meier RH, Pobanz NE (1983) Tutorial session on practical approach to surge and surge control systems. In: Proceedings of the 12th turbomachinery symposium, College Station, Texas Elliott H, Bloch H (2021) Compressor technology advances — beyond 2020. Walter De Gruyter ISO-5167 (2003) Measurement of fluid flow by means of pressure differential devices inserted in circular cross-section conduits running full, 2nd edn. ISO Niu S, Xiao D (2022) Process control – engineering analyses and best practices. Advances in industrial control. Springer Smith CL (2010) Advanced process control – beyond single-loop control. Wiley Inc

Chapter 7

Advanced Control Solutions

Chapter 6 presents some basic control designs for simple pumping and compression processes. In practical applications, however, the process configuration can be significantly more complex in order to meet advanced operational requirements. Examples of this complexity include multi-stage compressors with a single driver; side streams joining or leaving the flow path; multiple machines operating in series or parallel; and wide variations in flow capacity, operating pressure, and fluid properties. The ever-increasing complexity requires a better understanding of the process flow, the machine characteristics, and the detrimental effects of a surge in order to reach the desired level of optimality in operation and control. Additionally, when multiple machines are operating together, they expose many optimization opportunities to improve reliability or efficiency. This chapter presents several design examples to show how the basic schemes presented in Chap. 6 can be used to achieve advanced control solutions for complex pumping or compression processes.

7.1 Integration Between Capacity and Anti-surge Control The different components of a complex compression system interact and even interfere with each other if not properly integrated. An integrated solution that may include capacity control, anti-surge control, load-balancing control, and other protective controls must be based on a coherent design to ensure overall optimality (Golden et al. 2002).

7.1.1 Capacity Control Revisited Capacity refers to the throughput flow. There are machine capacity and process capacity, corresponding to the machine flow and process flow. At the process level, the capacity refers to the process capacity, i.e., the process flow. Adjusting the machine capacity is an essential part of process capacity control. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. S. Niu, Process Control for Pumps and Compressors, Advances in Industrial Control, https://doi.org/10.1007/978-3-031-43122-7_7

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Fig. 7.1 Capacity turndown for centrifugal machines

Centrifugal machines have three primary control handles for capacity control: machine speed, system resistance, and recycling. While for reciprocating machines, the control handles are usually the machine speed and recycle since the flow is independent of the system resistance. The cause-and-effect relationship is illustrated in Fig. 7.1. • Machine speed. Reducing the machine speed causes the operating point to move along the constant-resistance curve until it reaches the minimum allowable speed at point C . Further reducing the process flow to C requires recycling. • System resistance. Increasing system resistance causes the pressure ratio to increase and flow to decrease. As the resistance increases, the operating point moves along the constant-speed curve from A to B until the surge line is reached. Turning down the capacity further from B to B will require recycling. • Recycle. The desired process flow can also be achieved by recycling from A to D without changing the machine speed or resistance. A fixed-speed reciprocating machine is typically based on direct recycling, which is simple and reliable but highly inefficient. It is typically the last resort for capacity control. The control handles affect the machine capacity in different ways. In most applications, capacity control is achieved with a combination of two or more control handles. For instance, a typical control design for a variable-speed machine uses the machine speed and throttling valves to maintain the desired flow and pressure. If the operating point drops below the surge limit, recycle flow must be introduced for further turndown. The trajectory of the operating points is illustrated in Fig. 7.2, where the capacity control is under a constant-pressure ratio. The operating point can reach any point within the operating envelope by using multiple control handles.

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Fig. 7.2 Capacity turndown for reciprocating machines

Fig. 7.3 A generic 2 × 2 compression process

We will demonstrate the control design with a supply-driven process consisting of two variable-speed compressors, each with two stages. See Fig. 7.3 for an illustration. This 2 × 2 process is generic enough to be scaled up to more trains or stages or scaled down to a single train or stage. The pressure ratio and throughput flow must be controlled, requiring all three control handles. The interaction among the multiple control handles and control targets constitutes a multivariable control problem, requiring an advanced control solution.

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Fig. 7.4 A minimal control design for capacity control

7.1.2 An Unintegrated Design A direct scale-up from the control design of a single compressor train in Fig. 6.36 to the 2 × 2 compression process in Fig. 7.3 is shown in Fig. 7.4. The capacity control is supply driven, with the suction pressure controller PC-001 manipulating the rotating speed of both compressor trains to control the process capacity. The discharge header pressure controller PC-002 propagates the supply variation further downstream. The pressure controllers at the suction and discharge headers (PC-001 and PC-002) maintain a constant compression ratio.1 With the pressure ratio under control, the trajectory of the operating points of all stages is approximately a horizontal line, as illustrated in Fig. 7.5. During severe capacity turndown, the operating point will move to the left along a horizontal line from point A to E , under the combined effect of speed reduction and pressure control (throttling). When the operating point reaches the SCL, about 10% of the flow to the right of the surge reference line (SRL), the anti-surge controller kicks in and quickly opens the recycle valve to increase the surge margin. The process flow continues turndown and reaches the desired point of E. The compressor flow, as the sum of process and recycle flow, remains at point E . The anti-surge controller (e.g., UC-111 for Stage 1) determines the required amount of recycle flow. 1

The two pressure controllers, PC-001 and PC-003, are installed at the suction and discharge headers, which differs from the pressure at the compressor suction and discharge. Strictly speaking, the pressure ratio P2 /P1 , not Pd /Ps , is kept constant by the two capacity controllers.

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Fig. 7.5 Trajectory of operating point for a primitive capacity control design

This minimal design works but is very primitive. The control result is not smooth or reliable because the anti-surge controller (UC-xxx) serves two conflicting roles: capacity control and anti-surge control during a severe turndown. The high priority of anti-surge control demands aggressive action, but capacity control requires smooth and accurate control actions. As a result, the turndown from point A to E (see Fig. 7.5) under pressure controller PC-001 is slow and smooth, but the further turndown from E to E under anti-surge controller UC-111 may be overly aggressive. The capacity control (PC-001, SC-101, SC-201) and anti-surge control (UC-111, UC-121, UC-211, and UC-221) functions are completely independent, although their control handles (speed and recycle valves) and control targets (capacity and surge margins) are heavily coupled. Without coordination, the machine can run into an inefficient operating scenario with a high recycle flow well before reaching the minimum flow limit. The capacity control must be decoupled from the anti-surge control to improve the control performance, requiring an integrated solution.

7.1.3 Integrated Design of Capacity and Anti-surge Control The control design in Fig. 7.4 relies on the anti-surge controllers (UC-xxx) to perform both capacity and anti-surge control duties with conflicting performance requirements. The result is thus not ideal when the operating point is near the surge line.

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Fig. 7.6 An improved control design for capacity control

An improved design is to enhance the capacity control with a split-range control so that the capacity controller and anti-surge controller are separated in function. The capacity control is responsible for maintaining the capacity, while the antisurge controller is dedicated to surge prevention only. This separation is achieved by introducing a capacity control line (CCL), typically set to 36%, which is 20% (of flow) away from the surge reference line (SRL). The capacity turndown is treated as a normal operating condition. The capacity controller uses the machine speed and the recycle in a split-range arrangement to adjust the capacity smoothly. The more aggressive anti-surge controller will be activated only when the capacity control fails to hold the capacity line, and the compressor flow falls below the surge control line (SCL). The schematic for this improved design is shown in Fig. 7.6. The capacity controller (e.g., UC-112) and the anti-surge controller (e.g., UC-111) are two separate controllers sharing the same recycle valve as the control handle. They can thus be independently tuned to suit the different dynamics. For example, the capacity controller can have a normal tuning for smooth control as the first line of defense against surge, while the anti-surge controller can be tuned much more aggressively to serve as the next line of defense. Under normal operating conditions, the operating point would remain at the right side of the CCL. If both

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Fig. 7.7 Trajectory of operating point with improved capacity control design Table 7.1 Capacity control with a split-range scheme Capacity Controller Output Process Flow Compressor Flow Recycle Valve 0% - 36% 0% - 36% 36% 100%-0% 36% - 100% 36% - 100% 36% - 100% 0%

UC-111 and UC-112 are active, the larger controller output will be sent down, via the high selector, to the recycle valve UCV-111. The trajectory of the operating point is illustrated in Fig. 7.7. Compared with Fig. 7.5, the recycle valve will be opened at the CCL instead of the SCL. The capacity turndown from Point A to E is via speed reduction under pressure control PC-001. Once the CCL is reached, the further turndown from E to E is via the recycle valve under the secondary capacity controller UC-112. The compressor flow will remain at E while the process flow can be reduced to zero by introducing sufficient recycle flow. The relationship can be illustrated in Fig. 7.8, where the process flow, compressor flow, and recycle flow constitute an interesting split-range control scenario: the turndown of process flow is firstly by reducing compressor flow. When the compressor flow reaches the CCL, the recycle flow is introduced to further reduce the process flow. The turndown of the process flow via the capacity controller is thus smooth and stable, as shown in Fig. 7.8a and illustrated by Table 7.1. Suppose the capacity controller UC-112 fails to hold the compressor flow at the capacity control limit, and the operating point reaches the SCL. In that case, the anti-surge controller UC-111 aggressively opens the recycle valve, which is by the

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Fig. 7.8 The split-range control in compressor capacity control

necessity of surge prevention, but is a significant disturbance to capacity control by itself. See Fig. 7.8b. Under normal operating conditions, the operating point would unlikely reach the surge control limit when the capacity control scheme performs well. In this sense, the improved capacity control helps the anti-surge control. This improved design scarifies a small margin of the operating capacity (between the CCL and SCL) but offers improved reliability and performance. This sacrifice is worthwhile for applications where the operation near the surge line is sporadic and temporary. A properly sized compressor would have the normal operating point near the best efficiency point (BEP), which is well away from the surge reference line and even the capacity control line. If the machine is constantly running at or near the surge line, it implies that the machine is oversized for the operation. The operation will be inefficient no matter how the control solution is designed.

7.1.4 † Integrated Design with Feedforward Compensation The design in Fig. 7.6 is an improvement over Fig. 7.4. However, the reactive nature of the capacity controller (e.g., UC-112) remains a drawback since it is based on the feedback principle and has to wait for the surge margin to drop below the capacity control limit before it reacts. A further improvement in control design is introducing feedforward actions to react to capacity turndown requests proactively, as illustrated in Fig. 7.9. The output (OP) of the capacity controller PC-001 represents the desired surge margin. This output can thus serve as the feedforward input to force the compressor to respond

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proactively via recycle valve instead of waiting for the compressor to respond passively through machine speed change. One modification to the design is to take the desired surge margin (i.e., the output of the capacity controller PC-001) as the process value (PV) for the capacity controllers UC-112, UC-122, UC-212, and UC-222. The controller compares the requested surge margin from capacity controller PC-001 with the capacity control limit (36% in this case) and reduces the recycle valve opening if the desired surge margin exceeds 36%. Conversely, if the surge margin requested by capacity control is below 36%, the controller UC-112 will open the recycle valve to allow more recycle flow. See Fig. 7.8. The second modification is introducing two load controllers XC-101 and XC-201, where the load is defined as the surge margin between 0% and 100%. The output of the capacity controller PC-001, the desired surge margin, is sent down to the load controllers. If the requested load is higher than the capacity control limit of 36%, the load controllers will adjust the machine speeds to achieve this surge margin. If the requested surge margin is less than 36%, the load controller would not further reduce the machine speed but instead relies on the recycle flow to achieve further capacity turndown. The trajectory of the operating point is the same as in Fig. 7.7, except that the controller UC-112 does not wait for the operating point to reach the capacity control line to introduce recycle flow. The capacity controller PC-001 triggers this action. Therefore, it is a feedforward signal to the capacity controller UC-112. Due to the feedforward nature, the control action is quick and proactive, leading to smooth capacity control performance and reducing the fluctuations that may drive the machine close to the SCL.

7.2 Load-Balancing Control Multiple compressors are often used in parallel to increase the capacity or in series to achieve a higher head. Distributing the load among the different compressor stages or trains is an optimization problem of significant economic value.2 Surge and choke are two critical conditions limiting a compressor’s operating range. Avoiding surge has a higher priority than achieving the best efficiency. Thus, it makes more sense to use the surge margin as the basis for load balancing (Hafaifa et al. 2014). In other words, load-balancing control should keep all the compressors and all the stages at the same surge margin instead of the same flow or speed. In addition, load balancing based on surge margin (ASP value) also makes mixing and matching different designs and capacities simple and reliable in complex networks (Jacobson et al. 2016).

2

Pumping process with multiple pumps follows a similar concept but is more straightforward.

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Fig. 7.9 An integrated capacity control solution

7.2.1 † Load Balancing Among Compressor Trains For a complex compression process with multiple compressor trains operating in parallel, the flow distribution among the multiple trains can significantly impact the achievable capacity range and the operating efficiency. As discussed in Sect. 7.4, when multiple compressors of identical design operate in parallel, the best efficiency is obtained when all compressors have the same speed and flow (and thus head). However, when compressors of different designs and capacities are put together, running them all at the same flow rate or speed is no longer optimal. For example, Fig. 7.10 illustrates the flow and pressure range of two different compressors. Compressors operating in parallel share the same pressure ratio because of common suction and discharge pressure headers. It would be inefficient for the compressor with higher capacity to recycle simultaneously as the low-capacity compressor does. Instead, it is more efficient for the two parallel compressors to have different recycle flows.

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Fig. 7.10 Load of different compressors

A “lazy” approach designates one machine as the base load machine, operating at a fixed load (speed or flow), and the other as the swing machine to regulate the overall capacity. However, this “base loading” approach is inefficient (see Sect. 7.4). It also increases the surge risk because the swing machine is solely responsible for taking the capacity fluctuations. The control design in Figs. 7.4 and 7.6 balances the compressor load by forcing all the compressors to run at the same speed, which is acceptable if all the compressors have similar performance (capacity and head). In actual applications where compressors are of distinct sizes,3 the same speed and pressure ratio will cause the compressors to operate at different flow rates, with different efficiency and surge margin, as shown in Fig. 7.10. Instead of balancing the multiple compressor trains on speed or flow, it is safer and more efficient to balance the operation based on the surge margin. The integrated design introduces two load controllers, XC-101 and XC-201 in Fig. 7.9, which balance the two machines on the same surge margin. The two load controllers receive the same setpoint from the capacity controller PC-101 in the form of the desired ASP value and manipulate the respective compressor speed to drive the minimum ASP value for all stages on the same train (i.e., ASP1=min(ASP11,ASP12)) to the same setpoint value. Under the same compression ratio (head), the two compressors will operate with the same surge margin but at different speeds and flow rates (capacity). The per-

3

It is almost impossible to find two compressors with identical performance characteristics due to the difference in design, age, or wear. Even identically designed machines will exhibit different resistance to flow in a real-world setting, resulting in unbalanced loads if uncontrolled.

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Fig. 7.11 Load balancing for parallel compressors

formance curves are illustrated in Fig. 7.11, where the operating points for the two compressors are at A1 and B1, respectively. Note that the setpoint is set to the capacity control limit of 36%, which is the split point for the split-range control between machine speed and recycling. Above 36%, capacity control is achieved by machine speed. Below 36%, the recycle valve is opened to reduce the process flow further.

7.2.2 ‡ Load Balancing Among Stages For compressors with multiple stages on a common shaft, all stages will operate at the same speed. Since not all stages are built with perfect capacity balance, each stage will not approach the surge line simultaneously during severe turndown operations. The worst-performing stage will reach the surge line while others still remain safe from the surge limit. The conventional control design is a simple fan-out control that sends the same capacity control output to all the load controllers (e.g., XC-101) and capacity controllers (e.g., UC-112). The recycling at all stages is simultaneous, based on the worst-performing stage, as shown in Fig. 7.9, regardless of the actual surge margin of each stage. When the two compressors operate in series, they will be subject to the same mass flow rate, but the pressure ratio or speed is different. Recycling at the same time and

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Fig. 7.12 Load balancing among compressor stages

by the same amount by all stages based on the worst-case scenario is operationally inefficient, although simple in design. The more efficient design is to open the recycle line only when necessary. This just-in-time recycling is achieved with additional calculation blocks at each stage, e.g., XY-101 and UY-113, for the first stage of the first train. Other stages are configured similarly. See Fig. 7.12 for the complete design. The desired surge margin is calculated by the capacity controller PC-001 based on the suction pressure. An increase in pressure demands the machine to speed up and increase the throughput to bring the pressure back on target. The output of the capacity controller is the desired surge margin in ASP, which would be sent down to the capacity controllers at every stage. The calculation block XY-101 computes the difference between the desired ASP value for this train and the minimum ASP value of all the stages on this train. This value is the feedforward action each stage is expected to take. However, each stage does not have the same surge margin and does not need to recycle by the same

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Fig. 7.13 Load balancing among compressor stages (example)

amount. The difference between the ASP value of the current stage and the worstcase stage is calculated by UY-111 and extracted from the change request by the capacity controller. As a result, each stage will adjust the demanded value with its own surge margin and recycle only when the surge margin is exhausted. Figure 7.13 provides a sample scenario to illustrate the load-balancing concept among compressor stages. Assume that the compressor is in stable operation. Stage 1 of the first train has a surge margin of ASP = 42%, and Stage 2 with ASP = 34%. Suppose a sudden decrease in inlet gas flow causes the suction pressure to drop. The direct-acting capacity controller PC-001 responds with a decrease in its output to 30%, aiming to reduce the compressor throughput. This 30% is thus the new load target, in the form of surge margin ASP = 30%. The new load target ASP = 30% is sent down to the two load controllers, XC101 and XC-201, via the two high selectors, which clamp the value to 36%. In other words, the two load controllers are only required to bring the surge margin down

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to 36%. The new load target ASP = 30% is sent to the recycle valves of all four stages simultaneously. The four secondary capacity controllers UC112 to UC-222 are responsible for the flow turndown below 36%. An offset is added to the desired surge margin for each capacity controller UC-xx2 as calculated in Fig. 7.13. The result is that Stage 2 will start recycling since UC122.PV at 30% is below its setpoint of 33%. Stage 1 with ASP = 42% has a sufficient surge margin and does not need to recycle immediately. The calculation is repeated at each execution scan, and eventually, all stages will be running at approximately the same surge margin. For stability, the difference in valve opening among the stages should be limited, e.g., to LB5%) would degrade the control performance and is unacceptable. The test on the positioning performance can be conducted as follows: inject input signals in the order of 4 mA → 8 mA → 12 mA → 16 mA → 20 mA and observe whether the valve can be positioned quickly and to a reasonable accuracy (~2%) as indicated in Table 8.4. Then repeat the test in the opposite direction, i.e., 20 mA → 16 mA → 12 mA → 8 mA → 4 mA, and verify that the valve openings match the table from fully closed to fully open. • Deadband or dead angle. The anti-surge control valve is typically fully closed during normal operating conditions. It takes time to lift the valve stem from its seat before the valve starts to open. This delay is called the deadband, and excessive deadband slows down the valve opening. In case a surge condition is detected, the valve must open quickly, and the deadband is expected to be minimum. To test the deadband, put the valve in the fully closed position (input ≥20 mA), gradually reduce the signal, and record the signal value that causes the valve to start to open. Usually, this deadband should be less than 5%, i.e., the valve should start to open before the signal goes below 19 mA. In terms of time, the valve should not take more than 0.5 seconds to move from the full thrust on the seat with a step down of the signal from 20 mA. • Step resolution and hysteresis. For capacity control, a sticky valve degrades the control performance. The stiction is expected to be under 5%. The step resolution can be tested as follows: – Put the valve at 50% open (input = 12 mA). – Slowly increase the signal input, and observe how much signal change is needed before the valve move can be observed. – Do the same by slowly decreasing the signal.

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Similarly, to test the amount of hysteresis, start with the valve at 50% opening (input = 12 mA), slowly increase the signal input to 75% (input = 8 mA), and wait for the valve to settle. Then slowly decrease the signal input and observe how much signal change is needed to cause the valve to change direction. • Overshoot. Overshoot is detrimental to valve performance. Typically the overshoot in the valve position should be less than 3% of the steady-state change when responding to a step change in the input signal.

8.3 Plant Startup The initial plant startup is critical and has a high risk of equipment damage if improperly operated. The plant startup requires the participation of multiple parties, including the machine manufacturer, operations, rotating equipment engineer, process engineering, and process control.

8.3.1 Incipient Surge Test At the commissioning phase, the compressor has been shipped to the site, installed, and connected to the rest of the plant. The compressor performance data and the anti-surge control, which are based on simulated data from the manufacturer, must be validated with actual operating data from the field. The incipient surge test serves this purpose by pushing the operating point as close as possible to the surge limit to validate and improve the previously estimated surge points and the surge reference line. From a process control perspective, the objective of the surge test is to evaluate the accuracy of the anti-surge parameter (ASP), which by far has been exclusively based on predicted performance data. The incipient surge test is the first opportunity to validate the ASP with actual measurements and is thus very important. The surge test is almost always required as part of the commissioning activities for a new compressor installation. The surge test is typically performed with the machine in total recycle mode. The three performance lines: surge control line (SCL), surge reference line (SRL), and surge trip line (STL), in that order, are verified with the tests. Since the process gas may not be available, the surge tests are usually conducted with nitrogen or fuel gas. Although these gases differ from the actual gas, the test results are unaffected when viewed under invariant coordinates (see Chap. 5). 1. Sanity check of the SCL. The surge control line is typically 10% to the right of the SRL on the performance map. The SCL sanity check is to prove that when the compressor operates at SCL, no evidence of surge incipience is observed. The test can be performed as follows. With the anti-surge control in automatic

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mode, slowly reducing the process to cause the actual ASP value to decrease, approaching the surge control setpoint (typically at 33%). Once the ASP value goes below the surge control setpoint value, the output of the anti-surge controller should start to open the anti-surge control valve. The compressor must maintain the ASP value at 33% as the process flow decreases. A sanity check on the surge control line is necessary but not sufficient since the distance to surge cannot be verified based on this test alone. 2. Sanity check of the SRL. The test intends to validate and improve the accuracy of the actual SRL, which is instrumental to the success of both capacity control and anti-surge control. To verify the surge reference line, continue from Step 1. Keep the anti-surge control in automatic mode and maintain a sufficient level of recycle flow, e.g., 30% of valve opening. Slowly reduce the surge control setpoint to force the operating point to move further left to approach the SRL. During the surge test, closely monitor any sign of surge incipience. Stop the map exploration immediately to avoid entering an actual surge if an incipient surge is observed. Typical signs of surge incipience include vibrations in the machine and oscillation in the flow and pressure measurements. Once observed, the machine flow needs to be quickly increased to prevent the machine from experiencing an actual surge. If the ASP value at the point of an incipient surge is in the vicinity (e.g., 2% of SRL, or ASP between 30% × (1 ± 2%) = 30 ± 0.6%) of the SRL, it can be concluded that the ASP calculation is adequate. Suppose surge incipience is noticed much earlier or later than expected (relative to the SRL). In that case, it indicates that the ASP calculation deviates too much from the actual performance. The vendor-provided performance curves should be reviewed and validated. If necessary, the ASP calculation must also be reexamined and improved. This sanity check on the surge reference line is typically both necessary and sufficient. However, note that the field environment typically cannot be controlled as ideally as in the factory acceptance test environment due to difference in field installation and gas property; the test results have more uncertainties and should be interpreted with discretion. 3. Testing the STL. Testing the surge trip logic is part of the acceptance test. This test is intense since the compressor is intentionally moved beyond the manufacturerprovided limit to cause the machine to trip on an actual surge. The surge trip test is an excellent opportunity to further confirm the SRL via an actual trip event. Discuss with the commissioning engineers to agree on using the anti-surge controller to initiate the trip event. After the compressor is started successfully and running stably, gradually reduce compressor speed. The capacity control and the anti-surge control should be able to open the recycle lines to protect the compressor from a surge. The surge trip line is usually set at half the SRL, i.e., 15%. If not, lower the setpoint even more, and try again. The compressor flow can be reduced by slowly decreasing the anti-surge control setpoint of a selected stage to below 30% and testing whether the compressor would go to a surge trip. If the compressor load

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is high and the anti-surge valve remains closed, it may be necessary to reduce the process flow to force the compressor to surge.

8.3.2 Pre-startup The pump and compressor are usually started from the DCS console in the central control room via carefully designed logic and sequences. Testing on the startup sequence involves several parties’ joint efforts, including process control. Some required preparation for machine startup relevant to process control includes the following: • Verify that all solenoid valves on the anti-surge recycle line are de-energized, and cross check that all anti-surge control valves are fully open.4 • Check and ensure all controllers and calculation blocks are in the correct operating mode. For example, all anti-surge controllers, pressure protection controllers, and power constraint controllers are in AUTO mode, and the load controllers are in MAN mode. • Check and ensure that all control setpoints are set at the correct values. For first-time startups, set all anti-surge control setpoints to higher, more conservative values, e.g., 40% instead of 33%. This higher setpoint will cause the machine to recycle earlier, but it is safer for the initial test. • From the control overview screen on DCS, check and make sure that the process values of the suction/discharge pressures and flows are consistent and make sense. For example, before the compressor is started, all the suction and discharge pressures shall be approximately the same because of pressure equalization. When the motor is started, the suction and discharge pressures shall increase in ascending order from the first stage to the last. • Check and ensure that the values of the corresponding suction/discharge pressures and flows (PZ and FZ) for safeguarding match their corresponding readings (PI and FI) for control.

8.3.3 During Startup The automated startup procedure is typically initiated by pushing a button from the DCS screen. The compressor speed is ramped up quickly to reach the minimum stable speed, then slowly increases to reach the desired operating range. • During initial speed ramping, closely watch the pressures and flows of all stages as they increase. The ASP values calculated independently in DCS and SIS should 4

Because of de-energized solenoids, the fail-open recycle vales should be all in the fully open position.

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decrease in tandem, starting from 100% and slowly decreasing as the recycle valve is closed. • Watch and verify that all the anti-surge control valves (ASCV) close at the rate set by the rate of change limit (e.g., 5%/min). The ASCV will continue closing until the ASP values reach their setpoints. Depending on the load, the anti-surge control valves may go fully closed (when the load is high) or partially closed (when the load is low). • Manually and slowly increase the speed to the desired load (max 100%). Closely watch all the pressures, flows, and ASP values. Figure 8.3 shows the startup sequence of a variable-speed compressor in terms of the machine speed, recycle valve, and surge parameter. The speed change is divided into multiple steps as follows: 1. At a certain point of the startup sequence (T=0), a compressor LOAD signal is switched to active (=1). 2. Upon receiving the LOAD signal, compressor startup logic quickly ramps up the machine speed to above the minimum stable speed, e.g., from 0% to 75% within 45 seconds. 3. When the speed exceeds the minimum stable speed (e.g., 75%), the solenoid valves on the recycle lines for all stages are energized. The startup logic ensures that all anti-surge controllers are in AUTO mode. 4. Anti-surge controller automatically starts closing the anti-surge control valves because the ASP value is above the control setpoint. 5. The startup logic continues to ramp the machine speed to normal operating speed, e.g., 95%, but at a slower rate, e.g., 1%/min increase. 6. After the machine speed reaches 90% and anti-surge controllers reach the steady state, switch all load controllers to cascade modes for automatic capacity control. The typical startup sequence for a fixed-speed centrifugal compressor is more straightforward, as illustrated in Fig. 8.4.

8.3.4 Post-startup The control scheme, especially the PID configurations, should be fine-tuned to improve the performance after the compressor successfully starts and reaches a stable operational condition. These changes may include the following: • Controller response. For each anti-surge controller, increase the controller setpoint above its process value (PV) to force the controller to open the recycle valve. Monitor the transient response in the controller PV. • Controller fine tunings. Based on the transient behavior of the controllers, adjust the PID tuning parameters to improve the control performance. • Interaction between stages. When the anti-surge control valve opens in one stage, watch the surge parameters of other stages for inter-stage interactions. Watch

8.3 Plant Startup

Fig. 8.3 Startup sequence of a variable-speed compressor

Fig. 8.4 Startup sequence of a fixed-speed compressor

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how fast the anti-surge controller opens the recycle valves to maintain the surge parameter on the setpoint. Re-tune the controllers as necessary. • Discharge pressure constraint controllers. Temporarily lower the controller SP to below its PV and watch the response of the controller output and the control valve opening. Fine-tune the controller to achieve the desired speed of response. • Power constraint controller. Similarly, if the motor power constraint controller is implemented, temporarily decrease the setpoint to watch the decrease in machine speed. Step tests may be needed to introduce dynamic changes in the interested process variable to understand the process dynamics better. The process control engineer must update the process control narratives (PCN) document by incorporating any significant changes made during commissioning and startup. The status of the PCN document will change to “as-built” accordingly.

8.4 Performance Monitoring Health and performance monitoring is through various process variables and performance indicators. Many operating issues can be detected and avoided before they become costly. A thermodynamic analysis is the most straightforward and practical approach to determining performance issues based on key control variables and key performance indicators.5 The key performance indicator (KPI) is typically a derived variable that provides a reliable indication of the performance in the concerned area. The KPI must be intuitive, reliable, and comprehensive to help higher level decisions.

8.4.1 Performance Indicators There are many process measurements around the pumps and compressors for different purposes. Online control is based on fast and reliable measurements. Online monitoring may require additional measurements. For each process flow configuration, a group of critical variables for each compressor can provide a reasonably accurate description of the status and condition of the machine and should be continuously monitored. 1. Pressure, flow, temperature, and speed. The directly measurable process variables usually include pressure, flow, temperature, and speed. The changes in these measurements are governed by physical laws and are expected to be smooth under normal operating conditions. Any significant abrupt changes in the signal 5

Mechanical and electrical issues are primary concerns for online monitoring but are out of the scope of process control discussed in this book.

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Fig. 8.5 Control handles for centrifugal compressor control

profile may indicate an abnormal condition. For example, oscillation in flow and pressure may indicate an incipient surge. Persistently high discharge temperature may indicate decreased efficiency. The type and location of the measurements required by online monitoring are shown in Fig. 8.5. 2. Head. The polytropic head is one of the three basic variables describing pump and compressor performance (see Sect. 2.2.1). If the fluid head shows a significant decrease for the same machine speed and flow rate, it may indicate that the machine is experiencing increased energy losses. The machine’s efficiency should be evaluated for more insights. As discussed in Sect. 5.1, the head cannot be directly measured but can be indirectly calculated from the pressure ratio as follows:    n−1 Pd n n Z s R Ts −1 Hp = n−1 M Ps     Pd Ts Pd ln . · n = ln Ps Ps Td

(8.1) (8.2)

The gas molecular weight or density is needed to calculate the fluid head. They are available only offline; thus, monitoring the fluid head is typically based on both online measurements and offline gas property information. The machine should be inspected if the calculated head is significantly lower (e.g., by 10%) than expected from the manufacturer-provided performance curve. 3. Efficiency. The overall efficiency, including the mechanical and hydraulic efficiencies, is affected by many factors and is complicated to calculate accurately.

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Polytropic efficiency, on the other hand, concerns the thermodynamic behavior inside the machine and can be calculated from operating data as  Hp κ −1 n−1 = ηp = Hactual κ n     Pd Ts Pd ln , n = ln · Ps Ps Td

(8.3) (8.4)

where the ratio of specific heat κ is known from offline gas analysis, and other variables are from online measurements. A persistent drop of more than 2% in polytropic efficiency η p is usually an indicator of compressor performance issues, e.g., fouling. 4. Motor power and gearbox torque. The motor and gearbox’s condition must also be monitored as part of the process configuration. If available, motor power and gearbox torque are important variables to monitor online. Torque6 can be an essential variable for monitoring and protective control. For example, multiple incidents have been reported where the required torque exceeds the gearbox limit and causes severe damage to the gearbox. 5. Anti-surge parameter (ASP). Process measurements provide an isolated view into the status or health of a specific variable. However, most sophisticated performance indicators, such as surge indicators, are based on multiple variables and backed with physical insights. Surge is the most critical abnormal operating condition for a centrifugal machine that needs to be monitored. When a compressor approaches the surge condition, one or more symptoms will be observed, such as a sudden decrease in flow, excessive vibrations, and loud noises. However, relying on these symptoms or individual variables to monitor and detect surges is inaccurate and untimely. The ASP is derived from multiple field measurements based on engineering insight and is more effective for monitoring the surge phenomenon. 6. Power consumption. Another KPI of interest is power consumption. The actual power consumption (apparent power) can be directly measured with a watt-meter. The gas power, the useful power transferred to the fluid, can be calculated from the polytropic head and flow rate. ⎧ Rate]/[Polytropic Efficiency] ⎪ ⎨Power = [Polytropic Head] × [MassFlow    n−1 H p · Fm Pd n Fm n Ps ⎪ = −1 . = ⎩W ηp η P n − 1 ρs Ps The power consumption against throughput provides another overall performance indicator of operating efficiency.

6

A torque meter can provide additional information for verifying the compressor performance but is not widely installed for various reasons.

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8.4.2 Performance Visualization Visual presentation of the compressor status and health is an intuitive and powerful tool for performance monitoring, especially for the operators. Performance monitoring should include the actual measurement variables, the inferred performance indicators, and the control scheme. The focus can be on the real-time status, the machine’s health, or process unit’s operating efficiency. 1. Control overview diagram. An overview diagram on one screen provides an ata-glance summary of the critical variables and KPIs, offering the operators and engineers a holistic view of the status and performance for startup, operation, and troubleshooting. The overview page can be based on the control overview diagram (COD) from design, such as Fig. 7.15, with an appropriate color scheme to indicate the different status and condition, e.g., red color or flickering numbers to indicate an abnormal condition. 2. Live performance map. Modern DCS natively supports schematics, trending, and other HMI functionalities for general monitoring. For pumps and compressors, a live performance map is becoming a standard requirement for compressor performance monitoring. Live performance maps show the compressor’s operating point in relation to the surge line. Figure 8.6 is a real-life example of a compressor circuit with four parallel compressors, each with four stages. The four slanted lines are, from left to right, the surge trip line, the surge reference line, the surge control line, and the capacity control line (see Sect. 4.3.5 for definitions). The performance map is used as a backdrop image on the monitoring screen. The real-time pressure ratio and equivalent flow are mapped from the engineering units to screen pixels. The anti-surge parameter is calculated online and superimposed on the performance map. In this example, since all four compressors have identical designs, the four stages of each compressor share the same performance map. For instance, the first chart shows the performance map of the first stage of all four compressors, with the four real-time operating points superimposed on the performance map. The control solution is designed with load balancing among all the stages and compressor trains (see Chap. 7), all stages are balanced with the same surge margin. 3. Controller performance monitoring. Controller performance monitoring (CPM) is becoming indispensable in a modern operating plant. CPM continuously monitors and assesses the control loop’s status and performance and promptly alerts the concerned parties for abnormal conditions. The control scheme for pumps and compressors is part of the overall process control solution. All the controllers should be included in the CPM for continuous monitoring. The primary concerns include whether the controller operates in the intended modes (such as automatic and cascade) and whether the controlled variables track the desired setpoints satisfactorily. The status and performance of a control loop are calculated based on controller measurements or properties: controller mode (Mode), setpoint (SP), process value (PV), and controller output (OP).

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Fig. 8.6 Real-time monitoring of the operating point

Through CPM, the up-time and performance of the controllers, excess moves of the control valves, and frequency of operator interventions on control setpoints or outputs can be closely monitored to detect potential problems.

8.5 Troubleshooting and Problem-Solving Troubleshooting is always a challenging task and demands the most knowledge and experience. Since operation and control problems are highly unpredictable, there is no fixed recipe for troubleshooting. Nevertheless, there are some general methodologies and best practice procedures to follow (King 2016; Niu and Xiao 2022). A few particular aspects are given in this section.

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8.5.1 † Surge Detection Compressor surge control is one of the most critical and challenging tasks for troubleshooting. With a sound surge prevention scheme, the machine is not expected to enter surge conditions during normal operation. If a surge condition is detected or reported due to abnormal conditions, the critical first step is determining if it is genuinely a surge and what has caused it. Typical symptoms of surge may include the following: • Radial vibrations and axial thrust displacements. • “whooshing” noises or loud “bangs.” The noise can originate from the collapse of the gas voids within the compressor, the flexing of the suction filter walls, or the slamming shut of the non-return valves (McMillan 1983). • Flow fluctuations and oscillations. A deep surge starts with a sharp drop in the flow rate that is physically impossible for any other process reason. The flow can precipitously drop from the current operating point to zero (or even negative) in tens of milliseconds. Fluctuating pressures at suction and discharge can also be observed. • High gas temperatures. During a surge, the flow reversal can occur multiple times per second and not be cooled, the temperature increase can be rapid and thermal expansion can cause significant damage. The surge phenomenon is generally the result of one or more of the following deficiencies or events: • • • • • • • • • •

Inappropriate compressor design. Inadvertent loss of machine speed. Malfunction of the instrument, control valve, or guide vane. Poor matching of the compressor to the process requirements in capacity, type of gas, operating pressure, or temperature. Restrictions in the gas flow, such as blockage, internal plugging, and fouling, either at suction or discharge. Abnormal operating conditions, such as severe capacity turndown, startup, shutdown, and crippled operation. Inappropriate distribution of load among multiple compressors. Changes in the operating conditions such as pressure, temperature, and gas composition (see fluid density). Unfavorable arrangement of piping and process components of the system that potentially magnify surge. Inadequate anti-surge control system.

It is thus crucial to identify the cause of the surge and rule out non-control issues before investing time in troubleshooting the control scheme.

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8.5.2 † Troubleshooting of Surge Control Scheme Troubleshooting a control scheme requires the same knowledge as designing a control solution (Perez and Conkey 2016). As compressor control is based on feedback control, the general troubleshooting procedure is the same as with any other feedback control schemes, i.e., focusing on the five components of the control loop: process dynamics and machine characteristics, the process measurements, the final control elements, the control objectives, and the control algorithm. Process dynamics refers to both the machine characteristics and the process dynamics. The first question to ask is whether there have been any recent modifications to the process or machine that may change in the cause-and-effect relationship or the transient response behavior of the process variables. Process measurement problems are relatively easy to detect and fix. The most common instrumentation for machine control systems includes flow and pressure measurements. Common problems include blocked impulse lines, condensation, and processor failures in the instrument. For instance, the transmitters must be installed above the process piping for gas applications. The impulse tubing length must be short7 (shorter than the API RP 55 recommendation of 3 m) and with a rising slope of at least 30◦ to allow for free drainage of any condensate that may form within the tubing. Bends and elbows must be minimized to avoid leaks caused by tubing bending. Measurement provides a window of view into the process status and condition. Incorrect measurement can result in erroneous control action. For instance, one common problem with flowmeters is with calibration. An orifice-based flowmeter measures the pressure differential (P) across the orifice and deduces the flow rate. To infer the flow from the differential pressure requires an accurate representation of the relationship between them, which is ensured via regular inspection and calibration. Troubleshooting measurement problems can be based on spatial and causal information. For instance, the value difference in redundant measurements of the same variable should not exceed a certain threshold (spatial information). A flow through the compressor cannot change without a corresponding change in the pressure ratio, consumed power, or rotating speed (causal information) (Elliott and Bloch 2021; Niu and Xiao 2022). Control valves and machine speed are the final control elements (FCE) in compressor control, with the anti-surge control valve being the most critical. The performance of the anti-surge valve significantly impacts the control performance. Problems with the anti-surge control valve typically include the following: • Valve sizing. Too large or small a control valve is a problem for control performance. • Valve characteristics. The recycle valve serves the purpose of surge avoidance and is expected to be fast-open for anti-surge control and linear in characteristics 7

Long impulse lines contribute to signal noise, as the gas resonance phenomena in the impulse tubing can amplify pulsations in the pipe (Elliott and Bloch 2021).

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for capacity control. A good compromise is required to meet the two conflicting requirements. • Response speed. The valve is expected to open quickly if a surge condition is detected. Over time, the valve response may become slower or even stuck due to increased friction. Regular inspection and maintenance are essential. • Positioning accuracy. A valve is expected to move to a new position quickly and accurately without much delay or overshoot. Inaccurate positioning can degrade the control performance. A recycle valve can become “stuck” in one position due, most likely, to increased stiction or debris buildup in or around the valve seat. A “stuck” valve is a serious problem for control. The longer the valve remains in one position, the higher the risk of the valve becoming stuck. The risk can be mitigated by periodically sending a test command signal to the valve (Elliott and Bloch 2021). The test signal may be a single step, a series of steps, or a ramp. The perturbation should only be introduced when the system is in steady-state condition. The next component in the feedback control loop is the control setpoint. For instance, the surge control setpoint is determined during design and rarely changes during operation unless the control design is revamped. However, the controller setpoint may have been tampered with, driving the controller to a different operating condition. The last component is the control algorithm. The typical issue is with PID tunings. However, unless there are significant and permanent changes in other components in the control loop, the control algorithm and PID tuning typically do not need to change. Mechanical troubles are outside the process control scope. However, there are some occasions where process control can positively contribute to the troubleshooting effort from a unique perspective. Any changes to the control scheme must follow the proper management of change (MOC) procedure and be captured in the process control narrative (PCN) document.

8.6 Summary Commissioning, startup, operation, and maintenance are the critical steps to turn a sound control design on paper into a functioning application in the field. These steps require contributions from various disciplines to ensure the control implementation aligns with the design specification, performs as expected, and is accepted by operation personnel. Process control is essential throughout these steps to guarantee the control solution is satisfactory. During normal operation, constant monitoring and continuous improvement are essential for the control solution’s sustained performance, relying on a thorough comprehension of the process, equipment, and the process control solution.

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The most knowledge of the equipment and control solution is required to troubleshoot and correct operational problems, and practical experience is crucial; there is no substitute for it.

References Brun K, Nored MG (2006) Guideline for field testing of gas turbine and centrifugal compressor performance. Technical report, Gas Machinery Research Council, Southwest Research Institute Elliott H, Bloch H (2021) Compressor technology advances — beyond 2020. Walter De Gruyter King M (2016) Process control: a practical approach, 2nd edn. Wiley McMillan GK (1983) Centrifugal and axial compressor control. Instrument Society of America. http://compressorcontrolstudent.modelingandcontrol.com Niu S, Xiao D (2022) Process control – engineering analyses and best practices. Advances in industrial control. Springer Perez RX, Conkey AP (2016) Troubleshooting rotating machinery — including centrifugal pumps and compressors, reciprocating pumps and compressors, fans, steam turbines, electric motors, and more. Scrivener Publishing and Wiley

Appendix A

Performance Analysis and Control Design with Software Tool

Following the descriptions in this book, it is possible to analyze the compressor performance and design the control solution with the traditional pencil-and-paper approach, as shown in Sect. 5.4. However, the calculation becomes overwhelmingly complex for modern compressors with more stringent operating requirements and large amounts of data. Software tools are needed to facilitate all the activities, from data entry and visualization to performance analysis and anti-surge parameter calculation. This chapter provides an overview of the common activities related to performance analysis and control design, using the companion CPACS software tool.

A.1 Introduction Process control for pumps and compressors includes both capacity control and antisurge control (or minimum flow control for pumps). Anti-surge control is the most crucial component due to its criticality to equipment safety. It is also because the compressor characteristics is significantly different from that of static equipment that we are familiar with (King 2016; Niu and Xiao 2022). A software tool can help understand machines’ characteristics and behavior and facilitates the control solutions’ analysis and design.

A.1.1 Data Requirements A surge indicator like the anti-surge parameter (ASP) is developed with offline design data at design time and then used with real-time measurements during online operation. Collecting and analyzing these data is the first step of control design, requiring a good understanding of the compressor characteristics (Chap. 2). © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 S. S. Niu, Process Control for Pumps and Compressors, Advances in Industrial Control, https://doi.org/10.1007/978-3-031-43122-7

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The data required by anti-surge control design typically include the following, as shown in Table 6.4: 1. Compressor API design data. The compressor API datasheet defines the desired operating scenarios under which the compressor is expected to operate, such as design case, summer case, winter case, light gas, and heavy gas. Finalizing the design datasheet may require several interactions between the end user and the machine manufacturer. 2. Compressor performance data. The compressor vendor designs the compressor to meet the requirements specified in the API datasheet. The performance curves are the characteristic behavior predicted by the compressor manufacturer, confirmed by performance tests at the manufacturer’s facility and incipient surge tests at the site. A set of performance curves are provided for each design case. Figure 2.14 is an example of the performance curve in the traditional chart format. An example of the API datasheet can be found in Table 5.8. 3. Flowmeter data. The flowmeter datasheet defines the requirements of flow measurement. An example of the flowmeter datasheet is given in Fig. 6.31. 4. The valve data. The valve datasheet provides the characteristics of the control valve. Of importance to the anti-surge parameter calculation is the valve constant. 5. Real-time operating data. The ASP calculation aims to provide the surge indicator for online anti-surge control. Once online measurements are available, they can be collected and visualized on the performance map. It can be a painful experience to “excavate” the required data for an existing compressor that has been in operation for many years with incomplete or inaccurate documentation. Familiarity with the work process and data requirements is essential to identify and validate the data.

A.1.2 The Work Process The compressor control design is typically a part of a larger project, either green field or revamping. The anti-surge parameter calculation is the key effort of anti-surge control, lasting from the beginning to the end of the project. The work process is thus a progressive advancement of data collection, validation, processing, and continuous improvement. Consequently, one crucial interaction between process control and other parties in the project team is the data exchange, either as design input or deliverable. For a green-field project, the data availability is progressive as the project progresses. It is also very interactive between the design team and the data providers. The data requirement and inter-dependency are shown in Fig. A.1.

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Fig. A.1 Data requirements for anti-surge parameter calculation

Fig. A.2 CPACS main menu

A.1.3 The CPACS Software Tool CPACS, for compressor performance analysis and control support, is an Excel1 addin under the Windows operating system. The CPACS tool is freely downloadable from http://github.com/niucontrol/CPACS, along with the user manual. It aims to be a simple yet versatile engineering tool for process control engineers to enter, manage, and visualize compressor data; analyze the compressor control performance; and calculate the anti-surge parameters (ASP) for anti-surge control. Users are expected to have a basic understanding of thermodynamics, compressor characteristics, and control theory, as discussed in Chaps. 1 to 4 of this book, to effectively use this tool. To start CPACS, open the Excel file containing the CPACS file, and the CPACS menu should appear in the menu bar. The current version of CPACS has the following functions (see Fig. A.2): • Graph digitizer. For older compressors, performance data were typically provided by compressor vendors as performance curves. The performance data need to be “read out” from the curve. Graph digitizer facilitates this process. • Data analysis. This function provides all the functionality related to data visualization, validation, to anti-surge parameter calculation.

1

Microsoft Windows® and Microsoft Excel® are registered trademarks of Microsoft Corporation.

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A.2 Data Preparation and Management The first step in anti-surge control design is collecting the required data. Depending on the data source, this step is often the primary challenge and error source for ASP calculation with a significant impact on the online control performance.

A.2.1 Data Format Five types of compressor data can be entered into CPACS. Some are required, while some are optional. 1. Reference Condition (1REF). The reference condition is typically the same as the flowmeter calibration condition, which is recommended to match the certified condition (see Sect. 5.1) in the compressor API datasheet. If the flowmeter is installed on the discharge side, the reference inlet condition should use the certified condition from the compressor API datasheet as the suction condition. The reference condition is entered as one row. The first column shall be filled as 1REF (for reference condition). The second column is not used and can be left blank. The reference condition includes the following: • • • • • • • • • •

SPEED. Compressor speed. MW. Gas molecular weight. P1. Suction pressure. T1. Suction temperature. Z1. Gas compressibility at suction. P2, T2, Z2. Discharge condition if the flowmeter is on discharge. Leave them blank if the flowmeter is on the suction side. FM. Maximum mass flow in kg/s as the flow measurement range. DP. Maximum differential pressure (DP Measurement Range), corresponding to (i.e., matching) the measurement range of the mass flow. K1, K2. The ratio of specific heat (κ = Cp /Cv ) for suction and discharge (Optional). CV. Recycle valve flow coefficient in gpm. If the CV value is provided, the maximum flow line for the surge valve can be plotted on the compressor map.

2. Operating Limits (2LIMIT, optional). If applicable, the design constraints and operating limits can better define the operating envelope, allowing the anti-surge calculation to approximate the surge line better. Some common operating limits that may affect the operating envelope include the following: • Compression ratio (P2/P1). For a centrifugal compressor, the compression ratio is typically between 1.5 and 4.0. Although vendor data may cover a wider range, a compressor can rarely operate outside this range.

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• Discharge pressure (P2): In actual operation, there is almost always a highpressure trip setting on the discharge pressure to protect the equipment and piping. This trip limit implies that the operating point can never reach this area. That area can be excluded from the calculation to improve the design accuracy. • Motor power (POWER): For compressors driven by an electric motor, a certain region of the compressor operating envelope may never be reachable due to the power limit of the motor and should be excluded from the ASP calculation. The limits can also be specified on any other parameters. For example, to exclude the performance data above 100% speed, a value of 1.0 can be specified. 3. Design operating conditions (3DESIGN). The design condition derives from the compressor API Datasheet. They specify the different operating scenarios under which the compressor is expected to operate. In CPACS, each scenario is entered as a row. The first column in the row shall be filled as 3DESIGN (for Design Point). The second column is the name of the scenario or case (e.g., CASE A, SUMMER). Other required data for each scenario include the following: • • • • • • • •

MW, Molecular weight (kg/kmol). P1, Suction pressure (kPaa). T1, Suction temperature (Kelvin). Z1, Gas compressibility at suction (-). Typically gas compressibility has a value less than but close to 1.0. P2, Discharge pressure (kPaa). T2, Discharge temperature (Kelvin). Z2, Gas compressibility at discharge. Normally between 0.9 and 1.0. At very high pressure, the value can be higher than 1. FM, or FV1. Mass flow or volume flow at suction. Typically either mass flow or volume flow should be specified. If both are provided, cross validation is automatically performed.

The following data are optional. However, if available, they should be entered as they provide redundant information for CPACS to cross validate the data. • • • • • • •

SPEED, compressor speed. FV1, volumetric flow at suction. K1, ratio of specific Heat: optional for CPACS. K2, ratio of specific heat at discharge. HEAD, polytropic head. EFF, polytropic efficiency. POWER, gas power.

4. Performance data (4PERF). Performance data is available from the vendor as performance curves (charts) or spreadsheets. For ease of data entry, the spreadsheet format shall be requested. If the performance data are given as performance curves, the curves need to be digitized to extract the required performance data. The data are organized as follows:

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• Scenarios (Cases). The scenarios (or cases) are defined in the compressor API datasheets. • Speed lines. Each scenario can include multiple speed lines, typically 105%, 100%, 90%, 80%, and 70% of the normal speed. • Points. Each line includes multiple operating points, the first being the surge point and the last being the stonewall (choke) point. Between surge and choke points, there should be at least one point. Typically five points are recommended, and more points will give a more accurate representation of the performance curve. For each operating point, the following performance data are required: • • • • • • • • •

MW, molecular weight. SPEED, compressor speed. P1, suction pressure. T1, discharge pressure. Z1, compressibility at the suction. P2, discharge pressure. T2, discharge temperature. Z2, compressibility at discharge. FM, mass flow rate.

Optionally, the following can be included for cross-validation purposes. • • • •

POWER, gas power. HEAD, polytropic head. EFF, polytropic efficiency. K2, ratio of specific heat at the discharge side.

The discharge condition can be specified either as discharge pressure and temperature or as head and efficiency. The discharge pressure and temperature are automatically calculated if the polytropic head and efficiency are given (common for older/existing compressors). 5. 5RTOP: Real-time operating data. Real-time operating points, if supplied, are superimposed onto the operating envelope. The following data can be provided: • P1, suction pressure. • P2, discharge pressure. • FE or DP, equivalent flow, or differential pressure across the orifice.

A.2.2 Source of Design Data ASP calculation starts with data entry. In CPACS, click Calculate ASP to bring up the main interface, as shown in Fig. A.3.

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Fig. A.3 ASP calculation menu

For data entry from scratch, run NEW first to create a template. Data is entered by rows, with each row representing ONE operating point. The data are entered either via copy and paste from a vendor-provided electronic spreadsheet (preferred) or manually entered with digitized data from performance curves. 1. Manual data entry. Traditionally, the performance data are provided as “curves” on paper. The data values must be digitized first. The digitization process used to be based on pencils and rulers. The desired data values are extracted from the selected data points on the curve. The corresponding values are then “read out” and collected. For instance, Fig. A.4 shows the five points for one performance curve and the corresponding head and flow values. This manual digitization process is highly tedious and error prone, feasible only for simple cases with limited number of performance curves. CPACS has a digitization tool to facilitate this digitization process. The graphics digitizer menu opens the user interface, as shown in Fig. A.5. A scanned image (JPG or GIF) of the performance curve can be loaded into the digitization tool (Step 1). The tool is calibrated by selecting three points on the two coordinate axes (Step 2). After calibration, clicking on a selected point on the performance curve will produce the values (Step 3). The values are captured and saved to the spreadsheet for copy and paste to the CPACS main interface. 2. Batch and automated data entry. Data entry is a tedious and usually the most timeconsuming part of surge parameter calculation. For new projects/installations, it is strongly recommended that the vendor supply the compressor data (API datasheets + Performance curves) as electronic spreadsheets (e.g., Excel) to facilitate the data entry process. For instance, the largest compressor application the author worked on was a multi-billion dollar green-field project comprising 14 compressors with a total of 18 stages. The API datasheet specifies 19 operating scenarios. As a result, the performance curves include 19 cases for each compressor stage; each case has 8 speed lines (105%, 100%, 95%, 90%, 85%, 80%, 75%, and 70%), and each line has up to 20 operating points. Each operating point has more than 10 attributes (P1, T1, Z1, K1, P2, T2, K2, Z2, Mw, SPEED, FM, FV, POWER, HEAD,

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Fig. A.4 Manual digitization of compressor performance curve

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Fig. A.5 Digitization of compressor performance curve with CPACS

and EFF). The data entry can have over 4,000 operating points with over 40,000 individual values for each stage. It would require enormous effort to digitize and enter the performance data into CPACS (or any other control design tool) if only performance curves were provided. Fortunately, the compressor manufacturer agreed upfront to supply all the performance data in both curves and spreadsheets. The vendor data can be readily transferred to CPACS through copy and paste. Excel macros can be developed/utilized to further simplify this automated data entry process.

A.2.3 Engineering Units Compressor data can be provided in a wide range of engineering units. The mixed use of engineering units is another major challenge for most users. It is beneficial for the end user to understand the various engineering units commonly used. Most software tools can handle the unit conversion internally. CPACS uses a set of base engineering units for internal calculation. Table A.1 is a partial list of the acceptable engineering units by CPACS. User data can be supplied in units of their choice.

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Table A.1 Engineering units in CPACS Variable

Symbol Base unit Other units

Molecular weight Speed Flow, mass Flow, volume Flow, standard Flow, equivalent Pressure Pressure differential Temperature Polytropic head Efficiency Power Density

mw N FM FV FVS FME P DP T HEAD EFF W RHO

kg/kmol rpm kg/s m3 /h m3 /h kg/s kPaa kPa K kJ/kg % kw kg/m3

% kg/h, T/d m3 /s, m3 /d, gpm, cfm m3 /s, m3 /d kPag, bar(a), bar(g), psia, psig, atm mbar C, F, R, DegC, DegF J/Kg HP lbm/ft3

A.3 Data Visualization and Validation Due to the large amount of data, errors in data entry are very common. Although manual sanity check is essential and irreplaceable, software tools can help identify many common errors based on some simple validation rules.

A.3.1 Automatic Error Detection Clicking on LOAD will cause CPACS to read all the entered data into memory and simultaneously check for common anomalies, such as • Worksheet format error. A missing value in a specific cell, or a value with an incorrect data type, will be flagged as an error for correction. • Obvious data entry errors. For example, a zero or negative value for temperature (in Kelvin), an excessively large (>1.5) or small (