Pulsation and Vibration Control in Positive Displacement ......API Standards Department, telephone...

This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee

having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved.

F

n
Pulsation and Vibration Control in Positive Displacement Machinery Systems for Petroleum, Petrochemical, and Natural Gas Industry Services llo
t 548

1

ibutio

API RECOMMENDED PRACTICE 688 FIRST EDITION, APRIL 2012

ittee B

a

ral D

istr

or Com

m

Not For

Gene



For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on



F

n
Pulsation and Vibration Control in Positive Displacement Machinery Systems for Petroleum, Petrochemical, and Natural Gas Industry Services llo
t 548

1

butio

Downstream Segment a tri
API RECOMMENDED PRACTICE 688 FIRST EDITION, APRIL 2012
ittee B

eral D

is

or Com

m

Not For

Gen

Special Notes

API publications necessarily address problems of a general nature. With respect to particular circumstances, local, state, and federal laws and regulations should be reviewed.

Neither API nor any of API's employees, subcontractors, consultants, committees, or other assignees make any warranty or representation, either express or implied, with respect to the accuracy, completeness, or usefulness of the information contained herein, or assume any liability or responsibility for any use, or the results of such use, of any information or process disclosed in this publication. Neither API nor any of API's employees, subcontractors, consultants, or other assignees represent that use of this publication would not infringe upon privately owned rights.

API publications may be used by anyone desiring to do so. Every effort has been made by the Institute to assure the accuracy and reliability of the data contained in them; however, the Institute makes no representation, warranty, or guarantee in connection with this publication and hereby expressly disclaims any liability or responsibility for loss or damage resulting from its use or for the violation of any authorities having jurisdiction with which this publication may conflict.

API publications are published to facilitate the broad availability of proven, sound engineering and operating practices. These publications are not intended to obviate the need for applying sound engineering judgment regarding when and where these publications should be utilized. The formulation and publication of API publications is not intended in any way to inhibit anyone from using any other practices.

Any manufacturer marking equipment or materials in conformance with the marking requirements of an API standard is solely responsible for complying with all the applicable requirements of that standard. API does not represent, warrant, or guarantee that such products do in fact conform to the applicable API standard.

Classified areas may vary depending on the location, conditions, equipment, and substances involved in any given situation. Users of this Recommended Practice should consult with the appropriate authorities having jurisdiction.

Users of this Recommended Practice should not rely exclusively on the information contained in this document. Sound business, scientific, engineering, and safety judgment should be used in employing the information contained herein.

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

Publisher, API Publishing Services, 1220 L Street, NW, Washington, DC 20005.

Copyright © 2012 American Petroleum Institute



For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

Foreword

This document is intended to describe, discuss and clarify the design of pulsation and vibration control for positive displacement machinery systems used for services in the petroleum, petrochemical and natural gas industries. The original focus of this document was to provide insight on the many changes to the pulsation and vibration material in the Clause 7.9 of the 5th Edition of API 618 for reciprocating compressors only. Due to industry interest, the scope of this document has been expanded to include other types of positive displacement equipment (such as pumps and screw compressors). However, due to publication schedules, these other types of positive displacement equipment will be addressed in future editions.

This document is not intended to be an all-inclusive source of information for this complex subject. Rather, it is offered as an introduction to the major aspects of pulsation and vibration control for positive displacement machinery addressed during a typical system design. A significant amount of the material has been extracted from documents previously published by the contributors. The different design philosophies of the various contributors are consolidated in this document to help users understand the choices available and make informed decisions about what is appropriate for their application. While the theory is generally applicable to all types of positive displacement machinery, the text in this edition will frequently refer specifically to reciprocating compressors.

Nothing contained in any API publication is to be construed as granting any right, by implication or otherwise, for the manufacture, sale, or use of any method, apparatus, or product covered by letters patent. Neither should anything contained in the publication be construed as insuring anyone against liability for infringement of letters patent.

Shall: As used in a standard, “shall” denotes a minimum requirement in order to conform to the specification.

Should: As used in a standard, “should” denotes a recommendation or that which is advised but not required in order to conform to the specification.

This document was produced under API standardization procedures that ensure appropriate notification and participation in the developmental process and is designated as an API standard. Questions concerning the interpretation of the content of this publication or comments and questions concerning the procedures under which this publication was developed should be directed in writing to the Director of Standards, American Petroleum Institute, 1220 L Street, NW, Washington, DC 20005. Requests for permission to reproduce or translate all or any part of the material published herein should also be addressed to the director.

Generally, API standards are reviewed and revised, reaffirmed, or withdrawn at least every five years. A one-time extension of up to two years may be added to this review cycle. Status of the publication can be ascertained from the API Standards Department, telephone (202) 682-8000. A catalog of API publications and materials is published annually by API, 1220 L Street, NW, Washington, DC 20005.

Suggested revisions are invited and should be submitted to the Standards Department, API, 1220 L Street, NW, Washington, DC 20005, [email protected].

iii



For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on



For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

Contents

Page



Part 1: Pulsation and Vibration Control Fundamentals for Positive Displacement Machinery

1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

3 Fundamentals of Pulsation and Mechanical Vibration Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33.1 Overview of Pulsation Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.2 Overview of Mechanical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4 Fundamentals of Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.1 Overview of Acoustic Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.2 Overview of Mechanical Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3 Concurrent Acoustical and Mechanical Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.4 Design Philosophies For Varying Degrees Of Acoustic And Mechanical Control . . . . . . . . . . . . . . . . . . 744.5 Design Approach and Philosophy Selection Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5 Flow Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.2 Flow Measurement by Measuring Differential Pressure (DP) - Orifice Plate, Nozzle, and Venturi . . . . . 805.3 Flow Measurement by Turbine Flowmeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.4 Flow Measurement by Vortex Flowmeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.5 Flow measurement by ultrasonic flowmeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.6 Flow Measurement by Coriolis Flowmeters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6 Results Reporting Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

7 Field testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.1 Confirmation that Design Requirements Have Been Met . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.2 Vibration Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.3 Excessive Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.4 Premature Valve Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.5 Driver Overload . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.6 Failure to Deliver Expected Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

8 Valve Dynamic Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 908.1 The VDPA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 908.2 Valve Reliability and Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918.3 Application Of Analysis Results To Valve Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918.4 Valve Dynamics Analysis Report. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Figures1 Piston Motion and Velocity for a Slider Crank Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Single Acting Compressor Cylinder with Rod Length/Stroke = ∞ and No Valve Losses . . . . . . . . . . . . . . 53 Symmetrical, Double Acting Compressor Cylinder with Rod Length/Stroke = ∞ and

No Valve Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

v

Contents

Page



4 Unsymmetrical, Double Acting Compressor Cylinder with Rod Length/Stroke = 5 and No Valve Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5 Traveling Wave in Infinite Length Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Mode Shapes of Half Wave Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Mode Shapes of Quarter Wave Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Reducer with Dynamic Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Elbow with Dynamic Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1010 Tee with Dynamic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1112 Pulsation Suppression Device with Dynamic Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1211 Elbow with Dynamic Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1213 Shaking Force for Sample Pulsation Damper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1314 Shaking Force for Sample Pipe Lateral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1415 Head End (HE) Pressure-Volume Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1516 Ideal (Adiabatic) PV Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1617 Valve Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2118 Losses Due to Pulsation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2119 Losses Due to Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2220 Effect of Clearance Volume, Condition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2321 Effect of Clearance Volume, Condition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2422 Effect of Clearance Volume, Condition 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2523 Effect of Suction Temperature, Condition 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2624 Effect of Suction Temperature, Condition 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2725 Effect of Suction Pressure, Condition 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2826 Effect of Suction Pressure, Condition 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2927 Pump Cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3128 Pump Cavitation Field Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3229 Components of Pump Section Head. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3330 Amplification Factor for Various Damping Ratios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3831 Effect of Separation Margin from Mechanical Natural Frequency on Amplification Factor. . . . . . . . . . . 3932 Common Piping Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4033 Non-dimensional Piping Shaking Force Guideline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4234 API 618 Design Vibration Guideline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4535 Non-dimensional Pulsation Suppression Device Shaking Force Guideline . . . . . . . . . . . . . . . . . . . . . . . 4736 Example of Internal Cylinder Pressure Force versus Crank Angle and Frequency Spectrum . . . . . . . . 4837 Example of Rod Loads Due to Gas Force, Inertial Force and Combined Rod Load . . . . . . . . . . . . . . . . 4938 Conceptual Guidelines for Vent and Drain Piping Valve Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4939 Conceptual Guidelines for Vent and Drain Piping Valve Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5040 Conceptual Guidelines for Vent and Drain Piping Valve Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5041 Frequency Factors for Idealized Pipe Spans and Bends (1st and 2nd Natural Frequencies) . . . . . . . . . 5342 Frequency Factor (l) versus Ratio (L/h) for Uniform U-Bend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5443 Concentrated Weight-Correction Factors for Ideal Piping Spans

(P = Concentrated Load, W = Weight per Unit Length) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5544 Typical Compressor Flange Deflections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5645 Plot of a Pipe System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5747 Typical Branch Connection Finite Element Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

Contents

Page



46 Lowest Mode Shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5848 Example of a Partial Finite Element Model of a Compressor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5949 Typical Dynamically Fixed Clamps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6150 Example of a Hold Down Type Support with no Allowance for Thermal Displacement

in the Vertical Direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6251 Example of a Spring Hold Down Type Support which Allows Thermal Motion in the

Vertical Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6352 Allowable Shaking Forces per API 618, 5th Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6553 Example of Pipe and Support Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6754 Lumped Acoustic Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7055 Analogous Electrical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7156 Electronic Analog for One Pipe Section (Simplified Version without Flow Resistance) . . . . . . . . . . . . . 7157 Measuring Flow Expressed a Change of the Vortex Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8158 Compressor Configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8559 Cylinder Nozzle Pulsation (Predicted vs. Guideline). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8560 Pulsation Suppression Device Line-Side Pulsation (Predicted vs. Guideline) . . . . . . . . . . . . . . . . . . . . . 8661 Pulsation Suppression Device Shaking Force (Predicted vs. Guideline). . . . . . . . . . . . . . . . . . . . . . . . . . 8662 Compressor System Finite Element Model with Test Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8763 Typical Display of Valve Motion versus Crank Angle, Cylinder Pressure versus Volume

and Analysis Results Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Tables1 Frequency Factors for Various Pipe and Support Arrangements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 Example of a Maximum Span Table for 25 Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553 Effect of Pipe Support Structures on Mechanical Natural Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 Generic Piping Shaking Force Criterion from Clause 7.9 of the 5th Edition of API 618 . . . . . . . . . . . . . . 645 Generic Piping Shaking Force Criterion from Clause 7.9 of the 5th Edition of API —

Based on Pipe Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Overview of Pulsation Impact on Various Flowmeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797 Compressor Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 848 Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 849 Gas Composition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8510 Lowest Mode Shape and Mechanical Natural Frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8811 Recommended Design Results for Cylinder Stretch Load Case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8812 Expected Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88For

Committe

e Ball

ot 54

81

Not For

Genera

l Dist

ributi

on

Contents

Page



Part 2: Reciprocating Compressors

1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

2 Comments On API 618, 5th Edition, Clause 7.9 – Pulsation and Vibration Control . . . . . . . . . . . . . . . . . 94

API 618 Annex M (informative) Design Approach Work Process Flowcharts . . . . . . . . . . . . . . . . . . . . . . . . . . 113

API 618 Annex N (informative) Guideline for Compressor Gas Piping Design and Preperation for an Acoustic Simulation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

API 618 Annex O (informative) Guidelines for Sizing Low Pass Acoustic Filters . . . . . . . . . . . . . . . . . . . . . . . 119

API 618 Annex P (informative) Piping and Pulsation Supression Device Shaking Force Guidelines . . . . . . . 122

Figures618-4Piping Design Vibration at Discrete Frequencies108M-1 Design Approach 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113M-2 Design Approach 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114M-3 Design Approach 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115O-1 Nonsymetrical Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119P-1 Non-dimensional Piping Shaking Force Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123P-2 Non-dimensional Pulsation Supression Device Shaking Force Guidelines . . . . . . . . . . . . . . . . . . . . . . 123P-3 Shaking Forces along the Piping Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124P-4 Shaking Forces along the Pulsation Supression Device Axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124P-5 Examples of Shaking Force Restraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Tables618-6Design Approach Selection97N-1 Compressor Data Required for Acoustic Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118P-1 Cylinder Assembly Weights Possibly Requiring Strengthening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on



Pulsation and Vibration Control in Positive Displacement Machinery Systems for Petroleum, Petrochemical, and Natural Gas Industry Services

Part 1: Pulsation and Vibration Control Fundamentals for Positive Displacement Machinery

1 Scope

The purpose of this document is to provide guidance on the application of pulsation and vibration control requirements found in the API purchasing specifications for positive displacement machinery. The fundamentals of pulsation and piping system analysis are presented in this Part.

The text begins with an overview of the fundamentals of pulsation and mechanical theory in Section 3. The intent of Section 3 is to introduce terminology and define the elements of the analysis process. Section 4 begins with a discussion of the acoustic and mechanical modeling techniques associated with the different design philosophies, which emphasize either pulsation or mechanical control, and concludes with a discussion on the appropriate selection of a Design Approach and Philosophy. Section 5 discusses the effects of pulsation on the accuracy of various types of flow measurement devices. Section 6 summarizes the requirements for documenting study results. Section 7 offers guidance on the performance of field testing to validate the results of the design process and to troubleshoot pulsation or vibration problems. Finally, methodologies for conducting a dynamic analysis of the compressor or pump valve performance are described in Section 8. The material in this Part is generally applicable to all types of positive displacement machinery.

Part 2 deals specifically with reciprocating compressors and provides commentary regarding each paragraph of Clause 7.9 of API 618, 5th Edition. It is the intent of the API Subcommittee on Mechanical Equipment that similar material be provided on reciprocating pumps and screw compressors in future editions.

2 Terms and Definitions

For the purposes of this document, the following definitions apply.

2.1acoustic simulationProcess whereby the one-dimensional acoustic characteristics of fluids, and the reciprocating compressor dynamic flow influence on these characteristics, are modeled taking into account the fluid properties, the compressor model and the connected vessels and piping, and other equipment. The model is based upon the governing mathematical equations (motion, continuity, etc.). The simulation should allow for determination of pressure/flow modulations at any point in the piping model resulting from any generalized compressor excitation. (Refer also to 2.2, 2.4, 2.9, 2.13, 2.16, and 2.18.)

2.2active analysisPortion of the acoustic simulation in which the pressure pulsation amplitudes due to imposed compressor(s) operation for the anticipated loading, speed range and state conditions are predicted. (Refer to 2.1.)

2.3amplification factorMeasure of acoustic or vibration sensitivity to excitation when the frequency of the excitation source is coincident with or near an acoustic or mechanical natural frequency. A high amplification factor (AF > 10) indicates that vibration during operation near a natural frequency could be excessive. A low amplification factor (e.g. AF < 5) indicates that the system is not as sensitive to excitation when operating in the vicinity of the associated acoustic or mechanical

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

1

2 API RECOMMENDED PRACTICE 688



natural frequency. The effect of the amplification factor on the system response near the associated natural frequency is presented in Figure 30. The method of calculating the amplification factor is explained in 3.2.3.

NOTE Low amplification factor does not guarantee low pulsation or vibration levels.

2.4analog simulationMethod using electrical components (inductances, capacitances, resistances and current supply devices) to achieve acoustic simulation. (Refer to 2.1.)

2.5coefficient of restitutionRatio of the relative velocity of two particles after impact to their relative velocity before impact. This term is used to help describe the dynamic motion of the moving components of valves in positive displacement compressors and pumps.

2.6combined rod loadAlgebraic sum of gas load and inertia force on the crosshead pin. Gas load is the force resulting from differential gas pressure acting on the piston differential area. Inertia force is the force resulting from the acceleration of the total reciprocating mass. The inertia force acting on the crosshead pin is the summation of the products of all reciprocating masses (piston and rod assembly and crosshead assembly including pin) and their acceleration.

2.7dampingInherent property of a dynamic system by which mechanical energy is removed. Examples of energy dissipation in machinery and piping systems are internal material damping and friction forces due to relative motion of the piping and supports.

2.8designTerm that may be used by the equipment manufacturer to describe various parameters such as power, pressure, temperature, or speed.

NOTE This terminology is typically used only by the equipment manufacturer and not in the purchaser’s specifications.

2.9digital acoustic simulationMethod using various mathematical techniques on digital computers to achieve the acoustic simulation. (Refer to 2.1.)

2.10frequencyNumber of cycles of a repetitive motion within a unit of time. Frequency is calculated as the reciprocal of the period of the repeating motion. Frequency is generally expressed as cycles per second (cps or Hertz) or cycles per minute (cpm). The latter units (cpm) afford ready comparison of the measured vibration with shaft rotating frequency.

2.11infinite length line (boundary condition)Term used for an acoustically non-reflective boundary condition. In this case the waves move away from the source and are not reflected at any point in the line. This is a method used to create an acoustically non-resonant piping system for the purpose of evaluating preliminary designs of pulsation suppression devices, or in the case that the piping for the model is not available.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

PULSATION AND VIBRATION CONTROL IN POSITIVE DISPLACEMENT MACHINERY SYSTEMS FOR PETROLEUM, PETROCHEMICAL, AND NATURAL GAS INDUSTRY SERVICES 3



2.12maximum continuous speedHighest rotational speed at which the machine, as built, is capable of continuous operation with the specified fluid at any of the specified operating conditions.

2.13mode shape of an acoustic resonanceDescription of the pulsation amplitudes and phase angle relationship at various points in the piping system. Knowledge of the mode shape allows the analyst to understand the pulsation patterns in the piping system. (Refer to 2.1.)

2.14natural frequencySynonymous with resonant frequency (see 2.17).

2.15oil stictionCondition where the moving sealing element of a compressor valve “sticks” to the stationary sealing element because of the adhesive effect of oil that is present. When stiction occurs, it increases the force required to open the sealing element.

2.16passive analysisPortion of the acoustic simulation in which a constant flow amplitude modulation over an arbitrary frequency range is imposed on the system, normally at the cylinder valve locations. The resulting transfer function defines the acoustic natural frequencies and the mode shapes over the frequency range of interest. (Refer to 2.1.)

2.17resonanceTerm applied to either acoustic or vibration forced response. Resonance occurs when a forcing function frequency coincides with, or is near, an acoustic or mechanical natural frequency, resulting in an amplified response limited only by the amount of dampening in the system.

2.18pulsation spectral frequency distributionDescription of the pressure pulsation harmonic amplitude versus frequency at a selected test point location for an active or passive acoustic analysis. (Refer to 2.1.)

2.19stiffnessEquivalent spring rate in Newtons/millimeter (N/mm) or pounds/inch (lbs/in.) of mechanical system elements. Examples of components for which stiffness is important are piping supports and cylinder supports.

3 Fundamentals of Pulsation and Mechanical Vibration Theory

In order to understand how to control pulsation and vibration in positive displacement machinery systems, it is imperative that one understands the differences between acoustical and mechanical concepts. In 3.1, the acoustic issues, along with acoustic control techniques, will be addressed. In 3.2, the elements of the mechanical system will be explained along with the concept of acoustic-mechanical coupling and the mechanical techniques for controlling vibration.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.1 Overview of Pulsation Concepts

Pressure variations that result from oscillatory flow of positive displacement machinery are the subject of this section. These variations in pressure are referred to as pulsation. Pulsation occurs in systems handling both gases and liquids. High vibration, support degradation and fatigue failures caused by dynamic forces induced by the pulsation are the most common problems resulting from pulsation. In order to reduce the possibility of detrimental pulsation and vibration at the design stage, it is necessary to understand several technical concepts.

Excitation mechanisms are first addressed in 3.1.1. Acoustic response is then explained in 3.1.2. In 3.1.3, the most common results of excessive pulsation are reviewed and the concept of acoustic-mechanical coupling is explained. Closing the discussion about pulsation concepts is a review of the techniques used for pulsation control in 3.1.4.

3.1.1 Excitation Sources

In systems utilizing positive displacement machinery, the flow of gas or liquid is not steady. Instead, the fluid moves through the piping in a series of flow pulses (dynamic or time varying), which are superimposed upon the steady (average) flow.

As an example, the magnitude and shape of the flow pulses through the compressor valves in a reciprocating compressor cylinder are determined by physical, geometrical and mechanical characteristics of the compressor (rotational speed, bore, stroke, loading, compression ratio, etc.). These flow pulses act as excitations which create pressure and flow modulations (acoustic waves) that move through the process fluid as it moves through the piping system. Generally, the predominant pressure and flow modulations generated by a reciprocating compressor are at frequencies which can be modeled as one-dimensional waves.

An important part of the acoustic analysis is the development of a compressor model that accurately predicts the dynamic flow excitation (flow versus time) delivered by the compressor. Some simplified examples are shown in Figure 1, Figure 2, Figure 3, and Figure 4.

3.1.2 Acoustic Response and Resonance

The flow pulses caused by the reciprocating action of the compressor or pump create pressure pulses or waves that move through the piping system as shown in Figure 5.

While the flow pulse frequencies generated by the compressor are a function of the mechanical properties of the compressor, the acoustical response in the piping is a function of the mechanical properties of the compressor, the thermophysical properties of the gas, and the acoustical network defined by the attached piping.

When a particular harmonic of running speed is near or coincident with an acoustical natural frequency, the acoustic response (dynamic pressure amplitude) is amplified. These resonances that occur when an excitation frequency coincides with a natural frequency can be simple organ-pipe type resonances or complex modes involving all of the piping.

For simple constant diameter lines with open and/or closed boundary conditions, specific pipe lengths determine acoustical natural frequencies. If a line length coincides with integer multiples of one half or one quarter of the wavelength, depending on the combination of open or closed end conditions, an acoustical resonance can be excited. End conditions are defined as either open or closed. For half wave resonances, both end conditions must be the same, i.e. open-open or closed-closed. For quarter wave resonances, the end conditions must be opposite, i.e. one open end and one closed end. Examples of these configurations are shown in Figure 6 and Figure 7, and are defined by Equation (1) and Equation (2).

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 1—Piston Motion and Velocity for a Slider Crank Mechanism

Figure 2—Single Acting Compressor Cylinder with Rod Length/Stroke = ∞ and No Valve Losses

0

0

100

Pis

ton

velo

city

200Crank angle (degrees)

300 360

1

5

6

23

4

Key1 Crank end2 Head end3 Q4 Q5 Actual piston motion6 Sine wave

s

d

0

125

100

75

50

25

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Flow

am

plitu

de

Harmonic

Flow frequency spectrum

0

200

0

-200

-400100

Flow

am

plitu

de

Degrees of rotation

Flow vs. time

200 300 400For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 3—Symmetrical, Double Acting Compressor Cylinder with Rod Length/Stroke = ∞ and No Valve Losses

Figure 4—Unsymmetrical, Double Acting Compressor Cylinder with Rod Length/Stroke = 5 and No Valve Losses

0

125

100

75

50

25

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Flow

am

plitu

de

Harmonic


0

200

0

-200

-400100

Flow

am

plitu

de

Degrees of rotation

Flow vs. time

H.E. = C.E.

200 300 400

0

125

100

75

50

25

01 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Flow

am

plitu

de

Harmonic


0

200

0

-200

-400100

Flow

am

plitu

de

Degrees of rotation

��

200 300 400

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 5—Traveling Wave in Infinite Length Pipe

Figure 6—Mode Shapes of Half Wave Responses

where� is the wavelength = a/f;a is the acoustic velocity;f is the frequency = 1/t;T is the time period of one cycle;t is the time.

t = 1/2( � /a)

t = 0

t = ( � /a)

t

+P

- P

T

) sin( t X x �

=

1 � f2

11/2 � f3

1/2 � f1

Pipe closed at both ends Pipe open at both ends

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Formula for half wave (closed-closed and open-open acoustic response frequency):

(1)

where

f is the acoustical natural frequency (subscript indicates order);

n is 1, 2, 3,…;

a is the speed of sound;

L is the length of pipe.

Formula for quarter wave (open-closed acoustic response frequency):

(2)

where

f is the acoustical natural frequency (subscript indicates order);

n is 1, 3, 5,…(odd integers);

a is the speed of sound;

L is the length of pipe.

Figure 7—Mode Shapes of Quarter Wave Responses

3/4 � f2

11/4 � f3

1/4 � f1

Pipe open at one end and closed at the other end

fna2L------=

fna4L------=For

Committe

e Ball

ot 54

81

Not For

Genera

l Dist

ributi

on




3.1.3 Effects of Pulsation

Pulsation, which is produced by a moving element such as the piston of a positive displacement pump or compressor, propagates through the suction and discharge valves, the internal gas passages, the pulsation suppression devices and the attached suction and discharge piping systems. The types of problems that can result depend upon the magnitude and frequency of the pulsation. Vibration, fatigue failures, performance degradation, driver overload and flow metering inaccuracy are some of the problems that result from excessive pulsation. Each of these will be discussed in more detail in the following sections.

3.1.3.1 Shaking Force

Pulsation itself will not produce vibration of the piping system; points of acoustical-mechanical coupling are necessary to develop a dynamic force, which in turn produces the vibration. Geometric discontinuities such as elbows, reducers, tees and capped ends are common force-coupling points in compressor piping systems.

Elbows or bends have differential areas due to outside and inside radii differences, which result in dynamic forces in the plane of the elbow when pulsation is present. Therefore, when possible, the number of elbows in a piping system should be minimized to reduce the number of force coupling points. Location of dynamic restraints (clamps) near elbows is desirable since dynamic forces will occur at these locations.

Force coupling points occur at reducers, tees and other points in the piping having unbalance areas. Probably the most easily understood case of a force coupling unbalanced area is that of a capped end. This condition occurs at the ends of all vessels, the compressor pulsation supression device being one such vessel. The forces acting on the closed ends of the volume bottles can produce high vibration of the bottles themselves.

Equipment, vessels and pipe runs can typically be considered rigid along their axis, thus the effective shaking force is the sum of pulsation multiplied by unbalanced area at each geometric discontinuity. The pulsation magnitude and phase angle and the force direction at each unbalanced area must be considered as shown in Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, and Figure 14. The figures illustrate examples of dynamic shaking forces at points of acoustic-mechanical coupling.

Equations used in Figure 8:

(3)

(4)

where

F is the shaking force;

Pdyn is the dynamic pressure;

D is the internal diameter;

FResult is the resultant shaking force;

φ is the elbow angle.

F Pdynπ4---D2=

FResult 2Pdynπ4---D2 ϕ

2--- cos=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Equation used in Figure 9:

(5)

where

F is shaking force;

Pdyn is dynamic pressure;

D1 is internal diameter of larger pipe;

D2 is internal diameter of smaller pipe.

Figure 8—Elbow with Dynamic Forces

Figure 9—Reducer with Dynamic Forces

Key1 F2 = Pdyn2 FResult3 F1 = Pdyn4 �

5 D

�4 D2( )

�4 D2( )

1 2

3

4

5

5

F Pdynπ4---× D1

2 D22–( )=

Key1 D1 2 D2 3 Pdynamic

1 23For

Committe

e Ball

ot 54

81

Not For

Genera

l Dist

ributi

on





(6)

where



D is the internal diameter of pipe.


(7)

(8)

(9)

where

FA is the shaking force in direction A;

FB is the shaking force in direction B;

PA is the dynamic pressure at elbow A;

PB is the dynamic pressure at elbow B;

FTotal is the resultant shaking force;

id is the internal diameter of the projected area.

Figure 10—Tee with Dynamic Forces

F Pdynπ4---D2=

Key1 D 2 Pdynamic

1

2

FA PAπ4--- id( )2=

FB PBπ4--- id( )2=

FTotal FB FA–=For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on





(10)

where

Fmax is the maximum shaking force;


D is the internal diameter.


(11)

(12)

where


Ahead is the projected internal area of head;

Abaffle is the projected area of baffle with choke tube;

Figure 11—Elbow with Dynamic Forces

Figure 12—Pulsation Suppression Device with Dynamic Forces

A A

A

FTotal = FB – FA

A = Projected area

FA = PA x

FA

� id 2

4

FB

FB = PB x � id 2

4

Fmax Pdynπ2---D2=

Key1 D 2 Pdynamic

12 2

F P1 Ahead×( )– P2 Abaffle×( ) P3 Abaffle×( )– P4 Ahead×( )+ +=

Abaffle Ahead Achoke–=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Achoke is the area of choke tube bore;

P1 is the dynamic pressure at first head;

P2 is the dynamic pressure at first head-side of baffle;

P3 is the dynamic pressure at second head-side of baffle;

P4 is the dynamic pressure at second head.


(13)

(14)

where


P1 is the dynamic pressure at pipe tee;

P2 is the dynamic pressure at pipe reducer;

P3 is the dynamic pressure at elbow;

Atee is the area of pipe tee bore;

Areducer is the differential area of pipe reducer;

Aell is the bore area at elbow.

Figure 13—Shaking Force for Sample Pulsation Damper

Force direction–

–P1

+P2

–P3

+P4

+

AheadAbaffle

Achoke

F P1 Atee×( )– P2 Areducer×( ) P3 Aell×( )–+=

Areducer Atee Aell–=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.1.3.2 Vibration

Pulsation that results in high shaking forces can cause excessive vibration in a piping system. However, excessive vibration can occur even in cases where the dynamic forces are low if an excitation frequency is close to, or coincides, with a mechanical natural frequency. In this case, vibration will be amplified, typically a factor of 5 through 10 compared to the off-resonance condition. The amplitude at resonance is limited by the damping of the system. The concepts of resonance and the magnification of vibration at resonance will be covered in more detail in 3.2.

3.1.3.3 Fatigue Failure, Piping, and Support Degradation

Fatigue failures of main piping small bore attachments and piping support degradation are common problems associated with vibration caused by pulsation induced forces.

3.1.3.4 Compressor Performance and Overload

To discuss compressor performance and overload, it is helpful to understand how required compression power is determined.

The power required for compression is calculated with the line integral of a pressure-volume (PV) card. That is, the required power is proportional to the area within the PV card. A typical pressure-volume card is shown in Figure 15.

Suction: Points A to B

The suction valve is open at Point A and the piston is moving away from the cylinder head. Gas enters the cylinder through the valves until the piston reaches inner dead center (IDC), at which point the valve closes.

Compression: Points B to C

The piston moves towards the head with both suction and discharge valves closed. As the pressure within the cylinder increases to discharge pressure (slightly above), the discharge valve opens.

Discharge: Points C to D

The piston continues to move toward the head with the discharge valve open and gas leaving the cylinder into the discharge system. When the piston reaches outer dead center (ODC) at point D, the discharge valve closes.

Figure 14—Shaking Force for Sample Pipe Lateral

Force direction–

–P1

+P2

+P3

+

Atee AellAreducer = Atee – Aell

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Expansion: Points D to A

With the compressor piston at ODC at point D, both suction and discharge valves are closed and the piston is moving away from the cylinder head. This expands the trapped gas to suction pressure (slightly below) at point A at which point the suction valve opens and the cycle begins again.

The suction and discharge volumetric efficiencies (VEs and VEd) are labeled in the plot as well. The volumetric efficiencies are defined as the ratio of the volume of gas drawn in (suction) or expelled (discharge) to the cylinder swept volume.

NOTE Inner dead center (IDC) is also referred to as bottom dead center (BDC) and outer dead center (ODC) is also referred to as top dead center (TDC).

The power required to compress gas in a reciprocating compressor is proportional to the entire area within the PV card. Some of this power is used to increase the pressure of the gas from suction to discharge pressure. Power is also required to open the compressor valves, flow gas through the valves and cylinder passages, and overcome any losses due to pulsation at the compressor valves. The total power to compress the gas can be defined as follows.

Total Power = Isentropic (Adiabatic) Power of Compression

+ Valve and Passage Losses

+ Losses from Pulsation Levels

+ Losses from Pressure Drop through Pulsation Suppression Devices

Each of the terms in this equation is explained in 3.1.3.4.1.

Figure 15—Head End (HE) Pressure-Volume Card

%

PressureDischarge

Suction volumetric efficiency (VE )

0 100% Stroke

BA Suction

Expansion

Compression

DC

Discharge volumetric

efficiency (VE )d

s

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.1.3.4.1 Adiabatic Power of Compression and Theoretical Capacity

Adiabatic power of compression is a theoretical minimum power required to increase a gas from suction to discharge pressure. It can be derived with the line integral of the PV card without any losses. Figure 16 shows theoretical (adiabatic) PV cards for head end and crank end of a double acting cylinder. By integrating the ideal PV card, the theoretical adiabatic (isentropic) power of compression (English units) is determined from Equation (15).

(15)

where

TGHP is the theoretical adiabatic gas horsepower (hp);

n is the isentropic exponent of compression and expansion;

P1 is the suction pressure (psia);

VE1 is the suction volumetric efficiency (%) [see Equation (17)];

B is the cylinder bore (in.);

r is the piston rod diameter (in.);

S is the stroke (in.);

N is the unit speed (rpm);

P2 is the discharge pressure (psia).

Constant:

(16)

Assumptions: PVn = constant, n is the same for compression and expansion.

Figure 16—Ideal (Adiabatic) PV Diagrams

TGHPn

n 1–-----------P1 VE1 B2 r2–( )× S× N×

P2

P1

-----

n 1–n

-----------

1–× 1.983× 10 8–×=

1.983 10 8–× 1100--------- π

4---× 1 min

60 sec---------------× 1 ft

12 in.--------------× 1

550ft lbs–sec hp–-------------------

----------------------------×=

Constant Discharge

Crank

Constant Suction

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The mass flow rate depends on the gas properties, compressor geometry and the speed of the compressor. The most common way to calculate the mass flow rate is from Equation (18). The volumetric efficiency (VE1) is calculated first from Equation (17).

(17)

where

VE1 is the suction volumetric efficiency in %;

Loss is the slippage loss (in %), which is a function of suction pressure, compression ratio, gas component and lubrication method [Engineering Book, 1987, NGPSA];

CL is the cylinder end volumetric clearance (% of end swept volume);

Nv is the isentropic volume component, Log average of suction and discharge values of n.

The theoretical compression capacity, Q, in million standard cubic feet per day (mmscfd) can be calculated with Equation (18).

(18)

where

Q is the capacity (mmscfd);

Zstd is the compressibility of the gas at 14.7 psia and 60°F;

Z1 is the compressibility of the gas at suction conditions;

T1 is the suction temperature (°R).

An example problem 1 follows:

Calculate the theoretical adiabatic horsepower and capacity for each end of the following compressor cylinder. This is tabulated in Table 1 as Condition 1.

Bore = 14.76 in.

Rod Diameter = 4.5 in.

Stroke = 12.6 in.

Speed = 360 rpm

Head End Volumetric Clearance = 40.0 %

Crank End Volumetric Clearance = 9.3 %

1 This is merely an example for illustration purposes only. Each company should develop its own approach. They are not to be considered exclusive or exhaustive in nature. API makes no warranties, express or implied for reliance on or any omissions from the information contained in this document.

VE1 100 Loss– CL–P2

P1

-----

1Nv------

1–×=

Q0.2314 10 6–× B2 r2–( )× S× N× VE1× P1× Zstd×

T1 Z1×-----------------------------------------------------------------------------------------------------------------------=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Gas Properties:

Specific Gravity = 0.1636

Suction Temperature = 80°F = 539.67°R

Suction Pressure = 200.0 psia

Discharge Pressure = 400.0 psia

Suction Compressibility = 1.004

Standard compressibility = 1.0 (assumed for this example)

Isentropic (adiabatic) exponent Suction = 1.364

Isentropic (adiabatic) exponent Discharge = 1.353

Answer:

Calculate the volumetric efficiency for the head end from Equation (17).

In this case, the slippage loss was determined to be 6.2 % and the value for Nv was determined to be 1.369. Therefore:

Then calculate horsepower for the head end as follows:

Repeating the calculations for the crank end:

VEHE 100 6.2– 40–400200---------

11.369-------------

1–× 67.4%= =

TGHPHE1.364

1.364 1–---------------------- 200× 67.4× 14.762 02–( )× 12.6× 360× 400

200---------

1.364 1–1.364

----------------------

1–× 1.983× 10 8–×=

TGHPHE 3.75 200× 67.4× 217.86× 12.6× 360× 2( )0.27 1–[ ]× 1.983× 10 8–×=

TGHPHE 3.75 200× 67.4× 217.86× 12.6× 360× 0.20× 1.983× 10 8–× 198.1 hp= =

VECE 100 6.2– 9.3–400200---------

11.369-------------

1–× 87.7%= =

TGHPCE1.364

1.364 1–---------------------- 200× 87.7× 14.762 4.52–( )× 12.6× 360× 400

200---------

1.364 1–1.364

----------------------

1–× 1.983× 10 8–×=

TGHPCE 3.75 200× 87.7× 197.6× 12.6× 360× 2( )0.27 1–[ ]× 1.983× 10 8–×=

TGHPCE 3.75 200× 87.7× 197.6× 12.6× 360× 0.20× 1.983× 10 8–× 233.8 hp= =

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




From Equation (18), the capacity calculation will then be:

Comparing the calculated capacity to the capacity in Table 1, we get the same number of 12.40 mmscfd. However, comparing the calculated horsepower to that shown in Table 1 (or by integrating the PV curve shown in Figure 20), the adiabatic horsepower is 431.9 hp versus 478 hp. The difference between the integrated and calculated horsepower is a function of what number is used as slippage loss. A slippage loss factor is used to account for normal wear of parts and inefficiencies in compressor operation. Experience shows that using the slippage loss will reasonably reflect the capacity of a compressor; however, the work required to move that amount of gas is more reasonably reflected by performing the horsepower calculations with no slippage loss. In other words, there is energy consumed due to the wear and inefficiencies.

Repeat the calculations with zero slippage loss:

Calculate the volumetric efficiency for the head end from Equation (17):

Then, calculate horsepower for the head end as follows:

TGHPTOTAL TGHPHE TGHPCE+ 198.1 hp 233.8 hp+ 431.9 hp= = =

QHE0.2314 10 6–× 14.762 02–( )× 12.6× 360× 67.4× 200× 1.0×

539.67 1.004×-------------------------------------------------------------------------------------------------------------------------------------------------=

QHE0.2314 10 6–× 217.86× 12.6× 360× 67.4× 200× 1.0×

539.67 1.004×-----------------------------------------------------------------------------------------------------------------------------------=

QHE 5.69 mmscfd=

QCE0.2314 10 6–× 14.762 4.52–( )× 12.6× 360× 87.7× 200× 1.0×

539.67 1.004×------------------------------------------------------------------------------------------------------------------------------------------------------=

QCE0.2314 10 6–× 197.6× 12.6× 360× 87.7× 200× 1.0×

539.67 1.004×--------------------------------------------------------------------------------------------------------------------------------=

QCE 6.71 mmscfd=

QTOTAL QHE QCE+ 5.69 mmscfd 6.71 mmscfd+ 12.40 mmscfd= = =

VEHE 100 0– 40–400200---------

11.369-------------

1–× 73.6%= =

TGHPHE1.364

1.364 1–---------------------- 200× 73.6× 14.762 02–( )× 12.6× 360× 400

200---------

1.364 1–1.364

----------------------

1–× 1.983× 10 8–×=

TGHPHE 3.75 200× 73.6× 217.86× 12.6× 360× 0.20× 1.983× 10 8–× 220.1 hp= =

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Repeat the calculations for the crank end:

The total theoretical gas horsepower is 474.6 hp, which compares closely to 478 hp.

3.1.3.4.2 Valve Losses

Valve losses will be imposed upon the adiabatic power curve. These will usually range from 5 % to 10 % of the mean pressure and will generally be higher as compressor speed increases.

These losses can also be estimated using simple orifice equations and knowledge of the cross-sectional flow area through the valve; but for driver purposes, they should be determined with more precision. The compressor manufacturer, the valve manufacturer, or other designated designer should provide this data as part of the valve performance analysis.

When these values are added to the adiabatic power curve, they result in modifications to the curve as shown in Figure 17.

3.1.3.4.3 Pulsation Losses

Clause 7.9 of the 5th Edition of API 618 allows peak-to-peak pulsation levels at the cylinder flange to be as high as 7 % or 3 × R % (R is the stage pressure ratio) of average absolute line pressure flange, whichever is less. The greatest impact upon power required is when this pulsation occurs at 1× or 2× running speed, as shown in PV diagrams in Figure 18.

Adding pulsation losses to the example problem increases power requirements, as shown in Figure 18.

3.1.3.4.4 Losses for Allowable Pressure Drop

Clause 7.9 of the 5th Edition of API 618 allows pressure drop across the pulsation suppression devices to be as high as 1.67 × (R – 1)/R % (R is the stage pressure ratio) of line pressure for the average static flow. If dynamic flow is considered, then the actual pressure drop can be twice this value as long as the value for the static is not exceeded.

This results in the additional cylinder discharge pressure increase, suction pressure decrease, and power increase shown on the PV curve in Figure 19.

Pressure drop through the pulsation control components in reciprocating compressor systems, and the resulting power loss, is due to resistance to flow. From a conceptual standpoint, there are two types of flow.

— Steady (static) flow

— Dynamic flow with or without flow reversal

VECE 100 0– 9.3–400200---------

11.369-------------

1–× 93.9%= =

TGHPCE1.364

1.364 1–---------------------- 200× 93.9× 14.762 4.52–( )× 12.6× 360× 400

200---------

1.364 1–1.364

----------------------

1–× 1.983× 10 8–×=

TGHPCE 3.75 200× 93.9× 197.6× 12.6× 360× 0.20× 1.983× 10 8–× 254.5 hp= =

TGHPTOTAL TGHPHE TGHPCE+ 220.1 hp 254.5 hp+ 474.6 hp= = =

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 17—Valve Losses

Figure 18—Losses Due to Pulsation

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




All of these flows generate frictional and localized component pressure drops. For all types, the power loss can be calculated using Equation (19). Equation (19) shows that the power loss is proportional to the flow rate cubed. Power requirements can exceed driver capacity if the pressure drop is excessive.

More specifically,

hp = DP × Q (19)

where

hp is the horsepower loss;

DP is the pressure drop (lb/ft2) and DP is proportional to Q2;

Q is the actual flow rate (ft3/s) at flowing conditions.

The instantaneous pressure drop through an element (such as an orifice) is calculated based on the instantaneous flow due to both types of flow described above.

Generally, the power losses due to dynamic flow are significant only for an orifice installed in a compressor nozzle. Since the dynamic flow through the orifice remains relatively constant for the range of pressure drop needed to attenuate the compressor “nozzle resonance”, the lower (non-resonant) flow harmonics constitute the majority of the dynamic flow.

There is much disagreement in the industry concerning the significance of dynamic power losses due to dynamic flow. Most agree that these mechanisms exist, but disagree on its relative importance.

The techniques used to determine these power losses are generally the same in the case of simulations. Dynamic losses are minimized when pulsation is minimized.

Figure 19—Losses Due to Pressure Drop

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




In summary, the total (static + dynamic) power losses attributable to pressure drop through the pulsation control components are not easily determined without complex computer modeling. For the user, it is important to identify who is accountable for determining these losses prior to the sizing of the driver. Alternatively, give guidelines to meet during the design stage.

3.1.3.4.5 Effect of Clearance Volume

These examples 2 show the effect of varying VE on the power required, the mass flow, and the rod loads. The first case, Condition 1 shows the results of high clearance, and therefore, low volumetric efficiency. P-V diagram for Condition 1 is shown in Figure 20.

2 These are merely examples for illustration purposes only. Each company should develop its own approach. They are not to be considered exclusive or exhaustive in nature. API makes no warranties, express or implied for reliance on or any omissions from the information contained in this document.

Example Condition 1

Calculated: Condition 1, Speed 360 rpm

High Clearance - High Ps - Mid Ts

Stg Cyl(psia) (°F) Comp Clearance VE Q (mmscfd)

P1 P2 T1 T2 Ratio HE% CE% HE% CE% Cyl Stage

1 4 200.0 400.0 80 188 2.0 40.0 9.3 67.4 87.67 12.4 12.4

Stg Cyl(kips)

AHP IHPAHP/IHP

BHPBHP BHP(%) AXHP(%)

RL(+) RL(-) (%) per mmscfd Rated Rated

1 4 28 37 474 526 90 553 44.5 22 0

Figure 20—Effect of Clearance Volume, Condition 1

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




In Condition 2, the clearance has decreased, thus improving the volumetric efficiency. P-V diagram for Condition 2 is shown in Figure 21.

Example Condition 2


Mid Clearance - High Ps - Mid Ts



1 4 200.0 400.0 80 188 2.0 32.0 9.3 72.7 87.7 12.8 12.8

Stg Cyl(kips)

AHP IHPAHP/IHP



1 4 28 37 490 526 93 573 44.4 23 0


For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Note that for Condition 2, the brake horsepower has increased by 20 hp to 573 hp, the capacity has increased by 0.4 mmscfd to 12.8 mmscfd, and the rod loads have not changed significantly. In Condition 3, the clearance is further reduced. P-V diagram for Condition 3 is shown in Figure 22.

Note that the horsepower has now increased to 592 hp. Also, the mass flow has increased from 12.4 mmscfd in Condition 1 and 12.8 mmscfd in Condition 2 to 13.3 mmscfd in Condition 3. In summary, tighter clearances, with all other conditions constant, result in greater mass flow and greater horsepower required.

Example Condition 3


Low Clearance



1 4 200.0 400.0 80 188 2.0 24.0 9.3 78.0 93.9 13.3 13.3

Stg CylRL(+) RL(-)

AHP IHPAHP/IHP


(kips) (%) per mmscfd Rated Rated

1 4 28 37 505 562 90 592 44.2

All Cylinders… 505 562 90 592 24 0


For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.1.3.4.6 Effect of Suction Temperature

Returning to the clearances of Condition 1, let us now see the effect of changes to suction temperature. First, in Condition 4, the suction temperature drops from 80 °F to 40 °F. P-V diagram for Condition 4 is shown in Figure 23.

Example Condition 4


High Clearance – Low Suction Temperature



1 4 200.0 400.0 40 142 2.0 40.0 9.3 67.4 87.7 13.4 13.4

Stg CylRL(+) RL(-)

AHP IHPAHP/IHP


(kips) (%) per mmscfd Rated Rated

1 4 28 37 474 527 90 554 41.3

All Cylinders… 474 527 90 554 22 0

Figure 23—Effect of Suction Temperature, Condition 4

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Note that the mass flow rate and the horsepower increased above the base case. In Condition 5, the suction temperature has been increased from 80 °F to 160 °F. P-V diagram for Condition 5 is shown in Figure 24.

Note that the mass flow rate has decreased to 10.8 mmscfd and the brake horsepower has decreased to 551 hp.

Example Condition 5


High Clearance – High Suction Temperature



1 4 200.0 400.0 160 281 2.0 40.0 9.3 67.4 87.7 10.8 10.8

Stg Cyl(kips)

AHP IHPAHP/IHP



1 4 28 37 474 523 91 551 51.5

All Cylinders… 474 523 91 551 22 0

Figure 24—Effect of Suction Temperature, Condition 5

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.1.3.4.7 Effect of Suction Pressure

Now, returning to the base case for clearance and suction temperature, observe the effect of variations to suction pressure. For Condition 6, the suction pressure has been decreased from the base condition of 200 psia to 120 psia, while holding the discharge pressure constant at 400 psia. P-V diagram for Condition 6 is shown in Figure 25.

Observe that the mass flow rate has decreased to 5.6 mmscfd, the overall brake horsepower has decreased to 452 hp, the temperatures have risen to 279 °F (from 188 °F), and the rod loads have increased from 28 kips and 37 kips tension and compression to 42 kips and 50 kips, respectively.

Example Condition 6


High Clearance – Low Suction Pressure



1 4 120.0 400.0 80 279 3.33 40.0 9.3 37.4 80.7 5.6 5.6

Stg CylRL(+) RL(-)

AHP IHPAHP/IHP


(kips) (%) /mmscfd /Rated /Rated

1 4 42 50 409 430 95 452 82.2

All Cylinders… 409 430 95 452 18 0

Figure 25—Effect of Suction Pressure, Condition 6

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




For Condition 7, the suction pressure has been increased to 160 psia. P-V diagram for Condition 7 is shown in Figure 26.

With this change, the mass flow has increased to 9.0 mmscfd and the brake horsepower has increased to 534 hp. The discharge temperatures have decreased to 227 °F and the rod loads have increased to 35 kips and 44 kips tension and compression, respectively. As can be seen from this example, changes from the expected suction pressure can have a dramatic effect on the horsepower required, the discharge temperature, and rod loads. While the examples provided here were based on changing the base suction pressure for simplicity, variations caused by pulsation can cause similar effects.

Example Condition 7


High Clearance – Medium Suction Pressure



1 4 160.0 400.0 80 227 2.50 40.0 9.3 55.7 84.9 9.0 9.0

Stg Cyl(kips)

AHP IHPAHP/IHP



1 4 35 44 470 507 93 534 60.0

All Cylinders… 470 507 93 534 21 0

Figure 26—Effect of Suction Pressure, Condition 7

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.1.3.4.8 Summary

The performance of reciprocating compressors can be affected by piping acoustics and compressor interaction. The horsepower required to drive a compressor can be increased sufficiently by pulsation effects, such that the driver is incapable of supplying sufficient power to drive the compressor and achieve the rated conditions. Generally, however, valve losses and other pressure drop losses are the most important contributors to horsepower loss.

The PV diagram generated during an acoustical study can be used to evaluate these performance effects.

The evaluation should ensure that restrictive elements of the pulsation suppression hardware, such as orifices and choke tubes, do not impose an excessive horsepower penalty. It should also ensure that the influence of pulsation effects acting in the cylinder does not overload the cylinder. Finally, it should ensure that the total horsepower loss from compressor valves, pulsation suppression hardware, and pulsation effects does not exceed the selected driver’s capability to drive the compressor at rated speed and produce specified flow under specified conditions of suction and discharge pressure.

The pulsation simulation should produce data for time varying pressure drop through restrictive components near the compressor such as compressor valves, orifices, and choke tubes. The time varying pressure drop is then used to determine the effective time-averaged horsepower loss. The portion of the total load on the compressor resulting from compression work to meet design conditions can be compared to the losses in these restrictive elements.

The total power lost in restrictive elements added to the ideal compression power should be less than the available driver power by some margin to account for uncertainty in the calculations, and the contribution of small additional losses from piping friction. It is not uncommon for the power loss through the valves and pulsation suppression components to be as low as 10 % when minimizing power consumption is a primary focus. It is also not uncommon for the power losses to be as great as 50 % of the ideal compression power when prediction of power loss is not explicitly included in the pulsation suppression design. In the circumstances where efficiency of operation is not a critical issue, and the driver is adequately sized, the user may decide to accept these higher power losses in exchange for pulsation control by restrictive elements that add pressure drop as opposed to less restrictive methods such as reactive filtering.

3.1.3.5 Pump Cavitation

Cavitation occurs in pump systems when the negative peak of the dynamic pressure wave, added to the steady state pressure, approaches the vapor pressure of the liquid, Figure 27. Cavitation can occur even in those systems which have ample net positive suction head (NPSH) according to Hydraulic Institute Standards. These standards specify that, in addition to the net positive suction head required (NPSHR) by the manufacturer, an allowance should be made for the inlet piping pressure drop and acceleration head.

Acceleration head calculations, as set forth by the Hydraulic Institute Standards, are an attempt to account for the dynamic behavior of the system using quasi-static assumptions. In practice, these calculations can be inadequate since they ignore the dynamic acoustical response characteristics of the fluid. Accurate calculations of the pulsation levels in the pump systems must consider the dynamic flow by taking into account all the parameters which significantly influence the system, including the pump fluid end, the pump valves, and the associated suction piping.

3.1.3.5.1 Causes of Cavitation

Cavitation occurs in liquids when the local static (absolute) pressure falls below, or attempts to fall below, the liquid vapor pressure. The liquid locally flashes, creating a vapor bubble. The extent of cavitation depends upon many factors including nuclei concentration. The nuclei serve as seed for formation of the cavitation bubbles. Abundant nuclei are usually available in the form of dissolved gas, liquid impurities, and surface imperfections. The subsequent collapse of vapor pockets as the fluid is swept into the higher pressure regions of the pump may cause damage of pump parts, generate sound and vibration, and produce flow and pressure pulsation in the piping.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The occurrence of cavitation can be seen from field data obtained on a triplex pump (Figure 28). As the pulsation caused the negative peak of the pressure-time wave to drop below its vapor pressure, cavitation occurred and the waveform flattened off (since the fluid cannot support a negative pressure beyond the vapor pressure). As the pressure increased, the bubbles collapsed and high cavitation spikes occurred. These high frequency, high amplitude spikes can result in high dynamic forces in the system. In order to prevent cavitation, it is necessary to supply additional suction head, or to reduce the pulsations which may be causing the reduction of the available head.

Cavitation can also be caused by the dynamic effects of valves. Valve parameters such as lift, valve mass, spring rate, preload, valve lip area, flow areas, etc., can greatly influence local cavitation at the valve and plungers. The valve effects can be simulated with computer programs which include these variables and also consider the system acoustics.

3.1.3.5.2 Discussion of Hydraulic Institute Standards to Prevent Cavitation

The Hydraulic Institute standards have recommendations and guidelines for pump systems to help prevent cavitation. Several definitions are reviewed below, which are important to the understanding of pump design guidelines.

Net Positive Suction Head Required (NPSHR)—The net positive suction head required (NPSHR) for a pump is usually specified according to the Hydraulic Institute Standards. The NPSHR tests are typically conducted by throttling the suction while holding the discharge pressure and pump speed constant until either a 3 % loss in capacity occurs or cavitation noise is clearly audible.

Net Positive Suction Head Available (NPSHA)—The net positive suction head available (NPSHA) is the absolute pressure in the liquid (less vapor pressure at the pumping temperature) available at the pump inlet. The static pressure can be calculated by subtracting the pressure drop, elevation and acceleration head losses between the suction tank or source and the pump. Problems typically occur when the NPSHA is lower than the NPSHR at the pump. The component which most often causes the NPSHA term to be inaccurate is the acceleration head component.

Figure 27—Pump Cavitation

Inst

anta

neou

s pr

essu

re (P

SI)

Time

If Pd > Ps - Pvp : then cavitation will occur

Ps = static pressurePd = dynamic pulsations, 0-pkPvp = vapor pressure

Ps

Pd

Pvp

P = 0

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Acceleration Head—The acceleration head formula given in the Hydraulic Institute Standards is a commonly used design criterion. The use of the acceleration head in the NPSHR calculation is an attempt to consider the effects of pulsations using static concepts. The pulsation levels should be used instead of the acceleration head for the calculations. This component is difficult to calculate without a comprehensive simulation technique; therefore, investigators have attempted to take the dynamic pressure component into account by incorporating a conservative calculation of the acceleration head.

These components of suction head are described graphically in the Hydraulic Institute Standards, as shown in Figure 29.

Equation (20) from the Hydraulic Institute Standards can be used to calculate the acceleration head.

(20)

where

ha is the acceleration head, ft of liquid;

L is the actual length of suction line (not equivalent length), ft;

v is the velocity of liquid in suction line, ft/sec;

N is the rotational speed of crankshaft, RPM;

C is the constant, depending on the type of pump:

= 0.400 for a simplex single-acting;

= 0.200 for a simplex double-acting;

= 0.200 for a duplex single-acting;

Figure 28—Pump Cavitation Field Data

Time (seconds)

0.00

Pre

ssur

e (P

SI)

0.01 0.02 0.03 0.04 0.05

Cavitation spikes

Vapor pressure

haLνNC

Kg---------------=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




= 0.115 for a duplex double-acting;

= 0.066 for a triplex either single- or double-acting;

= 0.040 for a quintuplex either singe- or double-acting;

= 0.028 for a septuplex either single- or double-acting;

= 0.022 for a nonuplex either single- or double-acting;

K is the constant which compensates for compressibility of the liquid:

= 1.4 for deaerated water (relatively incompressible);

= 2.5 for hydrocarbons with high relative compressibility;

g is the gravitational constant (32.2 ft/sec2).

Figure 29—Components of Pump Section Head

Absolute pressureat source

Saturated vapor

Saturated liquid

Closedvessel

Absolutevapor pressure(at pumping temperature)plus 7 ft

Suctionfrictional losses(pipe and fittings)

Acceleration head

Velocity head

Pump valvelosses, etc.

PumpInletflange

NP

SH

R(s

peci

fied

bypu

mp

Mfr.

)

CL

Psource

PT

hs (min)

hf

ha

hv

1. When absolute pressure at source equals the absolute liquid vapor pressure:

Psource = Pv

Then minimum static suction head must equal (or exceed) the sum of all the losses and deductions:

Hs(min) = hf + ha + NPSHR

2. If actual static suction head exceeds the required minimum:

hs > Hs (min)

Then:

NPSHA = hs - (hf + ha )

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The acceleration head calculation does allow for the dynamic modulation of the fluid as it fills the plunger; however, it does not include the influence of resonant pulsations. It is necessary to consider both the pump excitation and the acoustical interaction of the piping resonances in order to determine the potential for cavitation.

The pump and its suction piping system form a complex acoustical system having numerous acoustical natural frequencies, which can be excited by the flow modulations generated by the pump. A reciprocating pump generates pulsations at integer multiples of the pump speed with the highest amplitude components normally at the plunger frequency and its harmonics. These harmonics can be amplified by the acoustical natural frequencies of the system. Amplification factors are typically 10 to 40 for pulsation resonances. Therefore, when there is a coincidence of an excitation frequency with an acoustical natural frequency of the system, amplification of the pulsation can occur which can result in severe cavitation in the pump manifold and suction piping.

3.1.3.6 Metering Errors

Since many flow measurement devices measure flow by means of a calibrated measurement of pressure drop across the meter, oscillating flow, which is inherent in positive displacement machinery piping systems, will result in a time-varying flow measurement. If the flow-measurement device is a non-linear device, such as the typical orifice based flow measurement system, the average pressure drop, and therefore the indicated average flow measurement, will not correspond to the actual average flow. This phenomenon can create a large flow measurement error, commonly referred to as metering error. Section 5 provides more detail about different types of flow-measurement devices. In general though, if highly accurate flow measurement is required, such as with custody transfer meters, careful consideration about the pulsation control and the location of the flow measurement device should be anticipated.

3.1.4 Pulsation Control Methods

Pulsation control in compressor piping systems can be accomplished by application of the basic acoustic elements of acoustical compliance (volume), acoustical inertance (choke tube), and resistance (pressure drop). These elements can be used individually or combined in various manners to achieve pulsation control. Pulsation suppression devices range from single surge volumes (empty bottles) to acoustic filters (bottles with internals or utilizing secondary volumes), often used in conjunction with orifice plates.

The user should understand that this discussion is not intended to enable one to design these elements themselves. The intent is to provide enough understanding of the input parameters to the design so that the user can recognize where variability or uncertainty of their process conditions could result in inaccuracies in the predicted performance, and to describe the types of modifications that are made in acoustical studies.

3.1.4.1 Surge Volumes

Surge volumes are often used to attenuate the pulsations produced by compressors. A surge volume is a relatively large (empty) bottle attached to the suction or the discharge of the compressor. The volume acts as an acoustic compliance (the equivalent of a mechanical flexibility), which can effectively isolate the piping fluid from the flow modulations induced by the compressor. The attenuation characteristics of the surge volume are a function of the volume enclosed by the bottle as well as the expansion ratio of the attached pipe and bottle diameters.

Economic and mechanical considerations limit the size of the surge bottles, and therefore, impose practical limits on the degree of overall acoustic attenuation that can be achieved. Resonance frequencies of the surge volume length can act as pass bands, and excessive shaking forces of the bottle itself can result if the surge volume is not designed properly.

3.1.4.2 Low-Pass Filters

The addition of a surge volume alone, within practical size limitations, can reduce pulsation amplitudes, but may not attenuate all pulsation frequencies sufficiently. Since there is a relatively high probability of having coincidences of

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




mechanical resonances of the piping with acoustically induced shaking forces, further reduction of amplitudes at higher frequencies is often required.

A more effective pulsation control device, compared to the simple surge volume, is the volume-choke-volume filter. This filter consists of two volumes connected by a relatively small diameter pipe (choke tube). The volumes of the two chambers serve as acoustic compliances, while the mass of fluid in the choke tube serves as an acoustic inertance. The combination of these acoustic elements in this manner produces a “low pass” filter which attenuates pulsation at frequencies above the resonant frequency (fH) referred to as the Helmholtz frequency of the two-chambered filter. This resonance will actually amplify pulsation at its frequency, but achieves filtering at frequencies well above its characteristic resonant frequency. Filters may also have pass bands which amplify certain frequencies. These pass bands are related to the lengths of certain elements such as choke tube length, bottle chamber length, etc.

The normal design procedure for low pass filters is to design the Helmholtz frequency below the lowest pulsation frequency to be attenuated. Effective pulsation reduction can be achieved for frequencies above the Helmholtz frequency.

3.1.4.3 Orifices

Orifice plates may also be used at various other locations in piping systems to reduce acoustical response at resonant frequencies. The pressure drop resulting from an orifice plate acts as acoustical damping and reduces pulsation amplitudes. The location of the orifice plate in relation to the acoustical mode shape is critical to the effectiveness of the added pressure drop.

3.1.4.4 Pressure Drop Considerations

Choke tubes and orifice plates, which are important elements used for pulsation control, result in increased pressure drop. Pressure drop and its effects on the compressor performance should be considered as important design criteria. Clause 7.9 of the 5th Edition of API 618 provides maximum allowable values as a percentage of line pressure.

Increased pressure drop translates into additional power requirement. Decreased pressure drop can result in larger pulsation bottles. The understanding of the interrelationship of pressure drop, performance, and pulsation bottle design is important to achieve proper pulsation control designs.

3.2 Overview of Mechanical Concepts

The mechanical natural frequency and forced vibration response characteristics of a compressor or pump system and the associated piping system are referred to as mechanical characteristics. When a mechanical analysis is performed, such as in Design Approach 3 of API 618, these characteristics are evaluated to ensure that the vibration and stress in any part of the system will not be excessive.

To understand how the evaluation of these characteristics is done requires an understanding of the concepts of basic beam theory and vibration, including resonance, amplification factor, separation margin and stress. In addition, it is important to understand the variability between ideal, theoretical conditions and non-ideal, actual conditions that will be found in most compressor, pump and piping systems.

3.2.1 Basic Beam Theory

The vibratory characteristics of piping spans can be described by the differential equations of motion for uniform beams combined with the appropriate boundary conditions, which then allow the natural frequencies of the piping spans to be calculated. The application of basic beam theory to the piping system design is explained in 3.2.7.2.1.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




From simple beam theory, the basic relation can be summarized as:

(21)

where

f is the natural frequency (Hz);

λ is the frequency factor;

L is the length of span (m);

E is the pipe material modulus of elasticity (N/m2);

w is the pipe mass per unit length (kg/m);

I is the moment of inertia (m4).

The frequency factors have been derived from either a theoretical end condition (for straight spans) or from finite element calculations (for spans with bends). The application of this expression for idealized pipe spans and bends is found in 3.2.7.2.1.

3.2.2 Resonance

Resonance is described as the amplification in vibration amplitude when the frequency of a harmonic (periodic) forcing function coincides with or is near to a natural frequency of the system. When a system operates in a state of resonance, the forced vibrations resulting from a given excitation mechanism (such as pulsation induced shaking forces) are amplified when compared to static deflection depending on the level of damping present in the system. A resonance is typically identified by a substantial vibration amplitude increase and a shift in phase angle between the exciting force and the vibrational response.

To avoid potential vibration problems in compressor, pump and piping systems, the most important step is to avoid resonance. Since compressor, pump and piping systems have numerous mechanical natural frequencies and generally very low damping, the avoidance of operating at resonance is best achieved by focusing on two factors of design. The first is to try to minimize the magnitude of the harmonic forcing functions as described in 3.1. The second is to make revisions to the piping support system or to revise the piping layout to change the piping mechanical natural frequencies.

3.2.3 Amplification Factor

As previously explained, resonance is typically identified by a substantial vibration amplitude increase and a shift in phase angle. The amplification factor indicates how substantial that vibration amplitude increase will be.

It is useful to examine single-degree-of-freedom response curves to understand the effects of resonance. The basic approach is to consider a simple spring-mass-damper system and compute the amplification factor as a function of frequency ratio.

fλ

2πL2------------ EI

w-----=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The amplification factor (AF) is the factor by which the static (zero frequency) deflection must be multiplied to determine the dynamic deflection (vibration amplitude). The equation for amplification factor for a single-degree-of-freedom system is included below:

(22)

where

x is the dynamic deflection (vibration);

xo is the static deflection, i.e. xo = F/k (F = applied force, k = effective stiffness);

ω/ωn is the ratio of forcing frequency to natural frequency;

ωn equals ;

m is the mass;

ζ is the damping ratio (percent of critical damping).

Note that at resonance (ω = ωn or ω/ωn = 1), the amplification factor is equal to 1/(2ζ). For example, a system with 1 % of critical damping has an amplification factor (AF) of 50, a system with 2 % of critical damping has an AF of 25, and a system with 5 % of critical damping has an AF of 10. Piping and compressor systems will typically have damping ratios from 1 % to 5 %; so, amplification factors of 10 to 50 are common. Figure 30 is a plot of amplification factor versus frequency ratio for damping ratios of 2.5 % to 50 %.

Some important concepts illustrated in Figure 30. The amplification factor begins at 1 and increases at a rate dependent on the damping ratio as resonance is approached. At resonance, the amplification factor is equal to 1/(2ζ). As the frequency increases beyond resonance, the amplification factor reduces below 1 and asymptotically approaches zero as the frequency approaches infinity. This is referred to as isolation. Since piping and compressors are multi-degree of freedom systems, the extent of isolation that can be applied to them is limited. Multi-degree of freedom systems are discussed later.

Another important concept is that significant amplification still occurs when the forcing frequency (i.e. the shaking force frequency) is 10 % above or below the mechanical natural frequency. As shown in Figures 30 and 31, the effective amplification factor at frequencies 10 % away from a particular mechanical natural frequency is 5:1 for all values of critical damping ratios less than 5 %. Therefore, the excitation frequency need not be exactly coincident with the mechanical natural frequency to significantly amplify vibration levels.

3.2.4 Separation Margins

Separation margin is defined as margin between the harmonic forcing function and the natural frequency of a compressor, pump or piping system element.

Figure 31 shows that the amplification factor for a response at resonance varies with damping, while the amplification factor for a response 10 % or more away from resonance depends only on the separation margin from resonance. Eliminating damping as a source of uncertainty requires a minimum 10 % separation margin.

The shift from resonance to 10 % off resonance reduces vibration by a factor of five to ten, depending on damping. The shift from 10 % to 20 % off resonance further reduces vibration by a factor of two. The shift from 20 % to 30 % off resonance only reduces vibration by a factor of 1.5. Clearly, the greatest reduction occurs close to resonance and most of the reduction occurs in the first 10 % shift away from resonance.

xx0

---- 1

1ωωn

------

2

–2

2ζ ωωn

------

2

+

------------------------------------------------------------=

km----

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Field experience generally shows that a 10 % shift of the natural frequency away from resonance results in acceptable vibration when the primary cause of the high vibration is resonance.

Considering the above theoretical and practical observations, a 10 % actual separation margin is recommended. Further, allowing for 10 % uncertainty in natural frequency predictions, a 20 % design separation margin is recommended.

The operation of double acting compressors results in significant pulsation-induced forces at one and two times rotational speed. Resonance shall be avoided at these frequencies, suggesting predicted mechanical naturalfrequencies should be at least 20 % above two times the compressor’s rotational speed.

In summary, the two design separation margin guidelines adopted by API 618 standard are:

— Minimum predicted mechanical natural frequencies should be greater than 2.4 times maximum compressor rotational speed.

— If possible, predicted mechanical and acoustical natural frequencies should be separated at least 20 % from frequencies with significant excitation forces.

Figure 30—Amplification Factor for Various Damping Ratios

20.00

15.00

10.00

Am

plifi

catio

n fa

ctor

(AF)

5.00

0.000.00 0.50 1.00 1.50 2.00

Frequency ratio - ��n

� = 0.025

� = 0.05

� = 0.10

� = 0.25

� = 0.50

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.2.5 Non-Resonant Shaking Force Limits for Piping Systems

3.2.5.1 Shaking Forces in Common Piping Configurations

Hooke’s Law (F = kx) and the previously developed definition for Amplification Factor can be combined for application to a dynamic system as follows:

F = kx becomes

where

F is the static force;

SF is the dynamic force;

x is the static deflection;

V is the dynamic deflection (vibration);

Figure 31—Effect of Separation Margin from Mechanical Natural Frequency on Amplification Factor

20.00

15.00

10.00

Am

plifi

catio

n fa

ctor

(AF)

5.00

0.000.00 0.50 1.00 1.50 2.00

Frequency ratio - ��n

� = 0.025, AF = 20

� = 0.05, AF = 10

5:1 Amplification for 10% margin

10% Above �n10% Below �n

AFVx--- or x

VAF-------= =

SFkVAF-------=For

Committe

e Ball

ot 54

81

Not For

Genera

l Dist

ributi

on




k is the spring constant (static stiffness);

AF is the amplification factor.

Rearranging the equation

(23)

Here, the ratio (k/AF) is effectively the dynamic stiffness and shows how the static stiffness is reduced by the amplification factor. The purpose of rearranging the equation is to illustrate that the dynamic force (SF) required to produce a given deflection (V) is dependent on the effective dynamic stiffness. That is, if the allowable dynamic deflection (V) is known, then the allowable dynamic force (SF) can be determined from the static stiffness and the amplification factor.

The highest vibration locations are typically midway between supports and at unsupported ends in the transverse direction. Acoustic shaking forces act in the axial direction of pipe runs causing vibration in the axial direction of that pipe run; but, maximum vibration actually occurs in the transverse direction of adjoining piping that runs perpendicular to the piping where the shaking force is acting. Figure 32 shows common adjoining piping configurations including spans with pinned to nearly fixed ends, L-bends and U-bends.

Direct application of the single degree of freedom amplification factor to the multiple degree of freedom piping configurations described above (and typical of actual piping systems) cannot be made. See 3.2.7 for calculation methods.

Figure 32—Common Piping Configurations

VibrationShaking force

Shaking force

Right turn in piping direction(pinned-pinned)

Upper elbow of cooler riser(L-bend, fixed-free)

Bypass piping from lateral(U-bend, fixed-free)

Vibration

VibrationVibration

Shaking force

Shaking force

Branch piping from header(fixed-pinned)

SFk

AF------- V×=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.2.5.2 Simplified Piping Shaking Force Limits to Non-Resonant Response

The piping shaking force guideline was simplified assuming non-resonant response. Simplification was made based on the following restrictions:

a) The shaking force guideline only applies when the separation margin criteria are met. Meeting the first separation margin criteria (minimum predicted mechanical natural frequencies are greater than 2.4 times maximum compressor rotational speed) requires a minimum axial support stiffness. Meeting the second separation margin criteria (predicted mechanical natural frequencies are separated at least 20 % from significant excitation forces) reduces allowable forces near resonant response to manageable levels.

b) An empirical upper limit was placed on the allowable shaking force.

The API 618 vibration criteria (discussed in 3.2.6.1) were used to develop the non-resonant shaking force guideline as follows:

(24)

where

SFP is the piping non-resonant shaking force guideline (lbF pk-pk);

n is the number of axial supports;

kS is the support axial static stiffness (lbF/in.);

VP is the piping design vibration guideline (in. pk-pk).

To ensure acceptable vibration for the first and second orders of compressor speed, the multipliers accounting for resonance (MA, MT) were replaced by the 0.66 factor and the following support stiffness requirement:

(25)

where

A is the pipe cross-section metal area (in.2);

= π / 4 × (OD2 – ID2);

I is the pipe cross-section area moment of inertia (in.4)

= π / 64 * (OD4 – ID4);

OD is the pipe outer diameter (in.);

ID is the pipe inner diameter (in.);

fnT is the minimum transverse natural frequency

(Hz, typically 2.4 times maximum compressor speed);

n is the number of axial supports.

SFp 0.66 n× ks× Vp×=

Minimum ks 25 A0.75× I0.25× fnT1.5× n 1–

n-----------×=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




To ensure acceptable vibration for the third and higher orders of compressor speed, both the non-resonant shaking force and the 20 % separation margin guidelines shall be simultaneously met.

In addition, an upper limit on the non-resonant shaking force guideline is specified as follows:

(26)

where

SFpmax is the maximum piping non-resonant shaking force guideline (lbf pk-pk);

NPS is the nominal pipe size.

The piping resonant and non-resonant shaking force guidelines are compared in Figure 33. In summary, the non-resonant piping shaking force guideline, with minimum support stiffness and maximum force limits, as shown above were adopted by API 618 standard.

3.2.5.3 Minimum ks Derivation

The guideline for the maximum allowable acoustic non-resonant shaking force in compressor piping systems is found in Clause 7.9 of the 5th edition of API 618. In Annex P of the 5th edition of API 618, the term ks (minimum active axial support stiffness) is introduced. In order to meet the minimum mechanical natural frequency guideline found in the 5th

edition of API 618, the active axial support stiffness will have to be greater than or equal to the value determined by Equation (27 [P-2]).

Equation (27 [P-2]) is as follows:

(27 [P-2])

Figure 33—Non-dimensional Piping Shaking Force Guideline

SFpmax 250 NPS×=

Non-resonantResonant

1

0.1SFP

n ks VP(2)

0.1 1Frequency/First Transverse Natrual Frequency

100.01

Minimum ks CKS A0.75× I0.25× fnT1.5× n 1–

n-----------×=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




where

CKS is the constant dependent on support stiffness units (SI Units: 1/130; US Customary Units: 25);

A is the pipe cross-section metal area (SI Units: mm2; US Customary Units; in.2)

= π / 4 × (OD2 - ID2);

I is the pipe cross-section area moment of inertia (SI Units: mm4; US Customary Units: in.4)

= π / 64 × (OD4 - ID4);

OD is the pipe outer diameter (SI Units: mm; US Customary Units: in.);

ID is the pipe inner diameter (SI Units: mm; US Customary Units: in.);

fnT is the minimum transverse natural frequency (Hz), (see P.3.2.5);

n is the number of active supports (or n = 2 as a minimum, see P.3.2.7).

The basis for Equation (27) follows.

From beam theory, the transverse natural frequency is given by

(28)

When rearranged to solve for the span length, Lsp, the equation becomes

(29)

The equation for axial natural frequency of the piping system along which the force is applied is

(30)

Rearranging to solve for stiffness, ka, gives

(31)

and mass, ma, gives

(32)

When La is the length of the pipe span between supports, then the value for the pipe mass becomes

(33)

ftλ2

2π------ g E× I×

ρ A× Lsp4×

-------------------------=

Lspλ2

2 π× ft×--------------------- g E× I×

ρ A×--------------------=

fa1

2π------ ka

ma

------=

ka ma 2πfa( )2×=

maρg---A La×=

maρg--- A

λ2

2πft

--------- g E× I×ρ A×

--------------------×=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




or simplified to

(34)

In the piping system, the force will be applied in the axial direction, so this is the direction that the minimum axial stiffness (ka) is required to resist the shaking force.

Equally important is the vibration of pipe that is perpendicular to the axial run; so the transverse mechanical natural frequency shall be also be considered. Both must be greater than or equal to 2.4 times maximum compressor speed. The minimum value of ka is calculated based on this but if it were desired to know the minimum ka required for a higher frequency, then the term x can be introduced where

or (35)

Where x = 1, or x > 1 for frequencies above API 618 minimum.

(36)

Now consider single pipe spans between two supports. Using the fundamental analytical methods approach described in 3.2.7.2.1, the values for frequency factors for various pipe arrangements and support types can be compared. These are shown in Table 1.

The formula can be simplified by multiplying all of the constants to give the correct value for the stiffness:

(37)

or

(38)

Table 1—Frequency Factors for Various Pipe and Support Arrangements

Span Type λ2 λ 5.19 × x2 × λ(x = 1) n Number of

Spans

Simply Supported 9.87 3.14 16.3 ≥ 2 ≥ 1

Fixed-Simply Supported 15.4 3.92 20.4 ≥ 2 ≥ 1

Fixed-Fixed 22.4 4.73 24.6 ≥ 2 ≥ 1

L-bend 16.5 4.06 21.1 2 1

U-bend 18.7 4.32 22.4 2 1

Z-bend 22.4 4.73 24.6 2 1

3D-bend 20.6 4.54 23.6 2 1

Fixed-Free 3.52 1.88 19.5(9.74 × 2) 1 1

maρg---

0.75 E0.25

2π( )0.5---------------- λ A0.75× I0.25×

ft0.5

---------------------------------×=

fa x× ft x× 2.4 maximum running speed×=

kaρg---

0.75

E0.25× 2π( )1.5× x2× λ× A0.75× I0.25× fn T,

1.5×=

0.283lbf

in.2--------

386in.

sec2---------

----------------------

0.75

30 106 lbf

in.2--------×

0.25

2π( )2 5.19=

ka 5.19 x2× λ× A0.75× I0.25× fn T,1.5×=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The greatest value of 5.19 × x2 for any span type is 24.6 as can be seen in Table 1. Rounding to 25, this becomes the constant CKS for US Customary Units found in Equation (P-2) in Annex P of API 618.

This expression now represents the minimum axial stiffness of the entire pipe and support structure in the direction in which the force is applied. The average support stiffness at an individual clamp location is given by:

(39)

where n = 2 for single spans, or extending to multiple spans:

(40)

Substituting into the expression for ka above gives Equation (27). An example of how to utilize this can be found in 3.2.7.2.

3.2.6 Design Vibration Limits

3.2.6.1 API 618 Guideline

The piping system design vibration criteria are shown in Figure 34, which is based on the following:

a) A constant allowable vibration amplitude of 0.5 mm peak-to-peak (20 mils peak-to-peak) for frequencies below 10 Hz.

b) A constant allowable vibration velocity of approximately 16 mm/s peak (0.63 in./s peak) for frequencies between 10 and 200 Hz.

Figure 34—API 618 Design Vibration Guideline

ks

ka

n----=

ks kan 1–

n-----------=

0.1 2.5

0.5

0.25

0.025

0.02

0.01

1

Frequency (Hz)

Vibr

atio

n G

uide

line

(inch

es, p

-p)

Vibr

atio

n G

uide

line

(mm

p-p

)

10 100 200 10000.001

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.2.6.2 Industry Standards and Charts

The design vibration guideline adopted by API 618 5th edition follows the form given in ISO 10816-6 with the deflection limits established by considering a number of industrial sources for allowable piping and compressor vibration. No single vibration guideline can completely account for the wide variation in geometry and supporting of actual compressor and piping systems. The adopted design vibration limit is a balance between typically acceptable vibration levels for large slow speed and smaller high speed compressor piping systems.

3.2.6.3 Discussion of Pulsation Supression Device Shaking Force Guidelines

Consistent with the approach taken for the piping shaking force guideline, the above-cylinder-mounted bottle (typically suction bottle) shaking force guideline was simplified to a non-resonant shaking force guideline as follows:

(41)

where

SFd is the pulsation suppression device non-resonant shaking force guideline (lbF pk-pk);

kt is the pulsation suppression device static support stiffness (lbF/in);

Vd is the pulsation suppression device design vibration guideline from Figure 34 (in pk-pk).

Minimum stiffness and maximum force guidelines are also specified as follows:

(42)

(43)

where

ncyl is the number of cylinders attached to pulsation suppression device;

SFd max is the maximum pulsation suppression device non-resonant shaking force guideline (lbF pk-pk).

The allowable force is much lower if a significant bottle shaking force frequency is near a mechanical natural frequency of the compressor manifold system.

The cylinder mounted bottle resonant and non-resonant shaking force guidelines for a hypothetical system are compared in Figure 35. In summary, the non-resonant cylinder mounted bottle shaking force guideline, with minimum stiffness and maximum force limits, are found in API 618, 5th Edition.

3.2.6.4 Cylinder Internal Pressure Forces

Cylinder internal pressure forces, or gas load, are caused by the gas pressure acting on the head end and crank end areas. The net cylinder internal pressure force is calculated from the head end internal cylinder pressure times the area of the head end head minus the crank end internal cylinder pressure times the area of the crank end head (less the piston rod area). The internal cylinder pressures vary with respect to the crank angle.

The cylinder internal pressure force causes the cylinder assembly to move back and forth along its axis, which is often referred to as “cylinder stretch” (even though the cylinder itself does not stretch significantly). The frequency domain plot of the internal cylinder pressure force shows that the force content at higher orders of run speed can be significant. As a result avoiding mechanical natural frequencies of the pulsation suppression devices at one and two times run speed may not be sufficient to ensure acceptable vibration levels. Depending on the amplitude of the

SFd 0.66 kt× Vd×=

Minimum kt 3 105× ncyl×=

SFd max 10,000=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




internal cylinder pressure forces at higher orders of run speed, mechanical natural frequencies might have to be avoided at higher orders as well. The forced mechanical response analysis of the compressor mechanical model, Step 3b1 of a Design Approach 3 in Clause 7.9 of the 5th edition of API 618 analysis, can be used to determine if the higher order components of the internal cylinder pressure force are significant.

Figure 36 is an example of internal cylinder pressure force versus crank angle and a frequency spectrum of the force.

3.2.6.5 Compressor Inertial Forces

Compressor inertial forces are caused by reciprocating weights in the compressor. The compressor inertial force versus crank angle (time) is nearly sinusoidal. As a result, depending on the connecting rod length to stroke ratio, the force amplitude at two times running speed is about 20 % of the fundamental. There are no significant harmonics above two times crank shaft speed. The gas force, or load, is equal and opposite to the cylinder internal pressure force (i.e. the cylinder internal pressure force acts on the heads of the cylinders, the opposing gas force acts on rod). The gas force plus the inertial force represents the total rod load.

NOTE Only the inertial forces contribute to the overall net forces and moments acting on the compressor, considering the compressor as a rigid body.

Figure 37 shows the rod loads due to gas force, due to inertial force and combined rod load.

3.2.6.6 Small Bore Piping

The pressure test connections and external drain piping specified in Clause 7.9 of the 5th Edition of API 618 have an insignificant effect on acoustical characteristics and are normally not included in the piping acoustic model. However, these small lines on the compressor suction and discharge nozzles and bottles can experience high vibration due to high frequency mechanical or acoustical excitation, including cylinder internal passage resonances, which cannot be controlled by bottle design. This can cause high vibration and failure of these appendages. Certain modifications, such as addition of orifices, that can reduce the level of excitation affecting these small piping are considered during the pulsation analysis. However, other non-acoustic excitations can occur. The following guidelines are recommended to minimize the possibility of vibration problems with these components:

Figure 35—Non-dimensional Pulsation Suppression Device Shaking Force Guideline

Non-resonantResonant

1

0.1SFd

kt Vd (2)

0.1 1Frequency/First Compressor Manifold System Natural Frequency

100.01

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




1) Avoid installation of these appendages when possible.

2) Minimize the unsupported cantilevered mass by installing vent and drain valves as close as possible to main piping.

3) Brace the cantilevered mass of the valves to the main pipe.

4) Use heavy wall piping and reinforced connections.

5) Where inspection openings are necessary, the use of studding outlets is recommended.

Figures 38 through 40 give conceptual guidelines for vent and drain piping valve supports, which could be used to solve or prevent vibration problems with small bore appendages.

Figure 36—Example of Internal Cylinder Pressure Force versus Crank Angle and Frequency Spectrum

50,000

40,000

30,000

20,000

10,000

00 15 30

1X

2X 3X 4X

Inte

rnal

Cyl

inde

r For

ce O

rder

s (L

bf, 0

-pk)

Spe

ed R

ange

= [3

24 to

396

] (R

PM

)

45 60 75Frequency (Hz)

40,000

20,000

0

-20,000

-40,000

-60,0000 60 120 180 240 300 360

Forc

e (L

bf) a

t 360

(RP

M)

Crank Angle (deg) with Respect to TDC

Internal cylinder force

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 37— Example of Rod Loads Due to Gas Force, Inertial Force and Combined Rod Load

Figure 38—Conceptual Guidelines for Vent and Drain Piping Valve Supports

50,000

25,000

0

-25,000

-50,0000 60 120 180 240 300 360

Rod

Loa

ds (L

bf) a

t 360

(RP

M)

Crank Angle (deg) with Respect to TDC

Due to gas forceDue to inertia forceDue to gas plus inertia(Combined rod load)

For Retrofit:Use a split clamp.Do not weld the support directly to the pipe.

Split clamps

Minimize

Optional Strap 3/4 in. wide1/4 in. thick

with 1/16 in. thickFabreekaTM or

equivalent

Inside wall

Wedge

Split clamp

Drill and tapas required

FabreekaTM or equivalent

Outsidepipe wall

1 in.max

1 in.max

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.2.7 Guidelines for Mechanical Analysis

3.2.7.1 General

The main process piping extending from the pulsation suppression devices is generally evaluated independently from the compressor or pump system from the point of analysis. Pulsation transmitted to the piping induces forces at points of acoustic-mechanical coupling, which can cause excessive vibration of this piping.



Wrap around fullencirclement saddle

(1/2 in. min. thickness)

Minimize

MinimizeOutside shellor pipe wall

Optional

Wrap aroundpipe sleeve(1/2 in. min.thickness)

Channel beamor angle

Clamp assemblywith visco-elastic

materialDrill and tapas requiredChannel beamor angle

Optional

Supportrequired if

height is 4 in.or greater

Outsidevessel wall

Minimize

Strap 3/4 in. wide1/4 in. thick

with 1/16 in. thickFabreekaTM or

equivalent

Angle Strip 1/2 in. thick if required

1 in.max

1 in.max

Wedge

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Control of vibration of the piping is generally accomplished by limiting the pulsation transmission to the piping, and by maintaining the mechanical natural frequencies of the piping a sufficient margin above the significant pulsation frequency components.

Practical experience for determining the piping mechanical natural frequencies and then adjusting them (usually upward) are discussed in this section.

3.2.7.2 Piping Mechanical Natural Frequency Discussion

The purpose of calculating piping system mechanical natural frequencies is to determine whether or not the separation margin guidelines are met. These calculations are usually made using one of two methods. The first method involves the use of fundamental beam theory and exact closed form solutions. This method is referred to as the Fundamental Analytical Method (FAM). The second method involves the use of numerical solutions or Finite Element Methods (FEM). The accuracy of either method is greatly influenced by the assumed boundary conditions. When properly applied, the two methods should give similar results.

If basic design concepts for piping layout are followed (e.g. minimize the number of bends, place a clamp near each bend and near all concentrated masses, etc.), the natural frequencies of most piping systems can readily be evaluated using the FAM approach. The FEM approach for calculating natural frequencies is only required for unusual layouts (long flexible spans with complex three-dimensional bends between supports, etc.). However, if separation margin and shaking force guidelines are not met and the calculation of vibration amplitudes and dynamic stresses is required, the FEM approach is then employed.

3.2.7.2.1 Piping Mechanical Natural Frequency Analysis Using Fundamental Analytical Methods

Fundamental Analytical Methods are defined as the use of basic beam theory to calculate the mechanical natural frequencies of a piping system. This is necessary to determine the support layout in the basic design. It is important to include all significant factors and to realize that the calculated natural frequency is approximate at best. However, it is always important to keep in mind that a simple calculation method with the proper assumptions can be far superior to a rigorous finite element calculation with poor assumptions.

For example, designers are warned to be aware of piping natural frequency calculations where the weight of the fluid has not been properly included. It is not uncommon to be off by 30 % if the weight of the fluid is significant and is not considered. Also, boundary conditions in a piping system are difficult to estimate. Therefore the end conditions must be assumed and a possible range of the natural frequencies is the best that can be achieved. The basic relation used to calculate piping mechanical natural frequencies is:

(44)

where

f is the natural frequency (Hz);

λ is the frequency factor;

L is the length of span (m);

E is the pipe material modulus of elasticity (N/m2);

w is the pipe mass per unit length (kg/m);

I is the moment of inertia (m4).

fλ

2πL2------------ EI

w-----=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The basic expression has been derived from simple beam theory, and the frequency factors have been derived from either a theoretical end condition (for straight spans) or from finite element calculations (for spans with bends). Frequency factors for idealized pipe spans and bends are included in Figure 41. The frequency factors reflect the accuracy generally required for design considerations.

Unequal length piping bends raise another unique problem in the calculations of natural frequencies. To compensate for this, a plot of frequency factors versus bend aspect ratio has been included in Figure 42. The information given on the plot can be used to calculate the mechanical natural frequencies of L- and U-bends with variable dimensions.

The effect of concentrated masses in a system can be obtained through the use of Raleigh’s method, which will not be discussed here in detail. Applying this method, it can be shown that the first step is the determination of the natural frequency of a beam without the mass, and then the application of a correction factor to obtain the approximate solution. The equations and correction factors are provided in Figure 43.

With the above approach the maximum span for a given configuration can be calculated with a spreadsheet program. For example, Table 2 shows the maximum clamp spacing for a hypothetical design (straight pipe span) with a mechanical natural frequency greater than or equal to 25 Hz. The table is valid for simply supported end conditions (only translations are fixed) and is, therefore, conservative if clamps having rotational stiffness are used.

There are several other factors that influence the mechanical natural frequencies, which cannot be easily included in analytical calculation methods. When it is deemed necessary that these factors be considered, a finite element analysis is required. Again though, keep in mind that a simple calculation method with the proper assumptions can be far superior to a rigorous finite element calculation with poor assumptions.

3.2.7.2.2 Piping Mechanical Natural Frequency Analysis Using Finite Element Analysis Methods

As earlier indicated, there are several other factors that influence the accuracy of the mechanical natural frequency calculation and, consequently, the calculation of the vibration and cyclic stress levels. The accurate prediction of piping vibration and cyclic stress levels requires an accurate mechanical natural frequency calculation. This requires that all the factors which influence the accuracy of the mechanical natural frequency calculation be included. However, it is not possible to include all these factors using basic beam theory, and for this purpose, the finite element method is used. It should be noted that, due to the uncertainties of modeling assumptions, discrepancies between measured natural frequencies and those predicted by finite element modeling can easily be ±20 %.

Some of the component properties known to influence these predictions are:

— Flange flexibilities,

— Flexibility of structures on which pipe supports are mounted,

— Column/base flexibilities,

— Joint (branch connection) flexibilities,

— Dynamic pipe-soil interaction, and

— Compressor frame flexibility.

Accurate modeling of the above listed properties contributes strongly to integrity, safety, reliability, reducing need for maintenance and, capacity assurance.

Due to additional uncertainties involved in replicating the model during the fabrication and installation of piping systems, the variation from predicted values can be much greater than ±20 %. There are numerous publications that document this level of uncertainty.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 41—Frequency Factors for Idealized Pipe Spans and Bends (1st and 2nd Natural Frequencies)

Piping Configuration Frequency Factor

1st 2nd

Fixed -Free 3.52 22.4

Simply Supported 9.87 39.5

Fixed -Supported 15.4 50.0

Fixed -Fixed 22.4 61.7

A + B = L

A = B

L-Bend (Out of Plane) 16.5 67.6

L-Bend (In Plane) 59.4 75.5

A + B + C = L

A = B = C

U-Bend (Out of Plane) 18.7 35.6

U-Bend (In Plane) 23.7 95.8

A + B + C = L

A = B = C

Z-Bend (Out of Plane) 23.4 34.2

Z-Bend (In Plane) 22.4 96.8

L

L

L

L

A

B

B

C

A

BC

A

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.2.7.3 Flange Flexibilities

Flange joints connect the compressor nozzles mechanically to the cylinder with a gasket (or lens joint for high-pressure service). It has been shown that assuming a rigid flange joint can seriously overestimate those natural frequencies whose mode shape involves bending of the nozzle connected to the cylinder by the flange in question. The model should account for flange flexibility, as shown in Figure 44.

Figure 42—Frequency Factor (λ) versus Ratio (L/h) for Uniform U-Bend

20

10

8

65

4

3

2

1

Freq

uenc

y Fa

ctor

(�)

0.8

0.6

0.4

0.3

0.2

0.110 8 1

Ratio L/h0.8 0.6 0.5 0.4 0.3 0.2 0.16 5 4 3

Out-of-plane vibration

� = 0.500

� = 0.000

� = 0.083

� = 0.250

� = 0.750

� = 1.000

L

hd

A = L/h� = d/h

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 43—Concentrated Weight-Correction Factors for Ideal Piping Spans(P = Concentrated Load, W = Weight per Unit Length)

Table 2—Example of a Maximum Span Table for 25 Hz

Nominal Pipe Size Maximum Clamp Spacing

(NPS) (ft) (mm)

4 11.6 3538

6 14.1 4292

8 16.1 4898

10 17.9 5468

12 19.5 5955

14 20.5 6240

16 21.9 6670

18 23.2 7075

20 24.5 7458

22 25.7 7822

24 26.8 8170

26 27.9 8503

28 29.0 8824

30 30.0 9134

36 32.8 10006

42 35.5 10807

fp = f / 1 + C

Cantilever, load at end

Simply supported, load at center

Fixed supported, load at center

Fixed-fixed, load at center

L-bend, load at center of leg, equal legs (L)

U-bend, load at center, equal legs (L)

Z-bend, load at center, equal legs (L)

3.9

Beam Type

Correction Factor C forNatural Frequency Equation

2.0

2.3

2.7

0.63

2.31 Out of plane2.1 In plane

2.21 Out of plane2.09 In plane

PW

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 44—Typical Compressor Flange Deflections

AEL

Key1. moment distribution2. gasket3. bolt load4. gasket stiffness and reaction

5. bolt load6. bolt stiffness ~7. angular rotation due to moment

1

32

4

5

6

7

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.2.7.4 Flexibility of Pipe Support Structures

The pipe supports (preferably clamps) act to restrain the pipe from dynamic forces and should be included in the model. Sometimes these supports also restrict thermal growth and cause high static stresses. In the case of pipe supports designed to accommodate thermal growth by sliding under friction load and to restrain the pipe under expected dynamic loads, the analysis should ensure the friction forces are sufficient for this dynamic restraint.

Pipe support structures (e.g. I-beams, A-frames, and pipe racks) often run overhead, with relatively low flexibility in the horizontal direction as a result. In addition, they add mass to the system. Neglecting the mass and flexibility of such structures can again lead to an overestimate of the natural frequency, easily on the order of 20 % to 50 %. Ideally, although usually impractical, the model should include these structures directly. Where modeling the structures is impractical or otherwise impossible, conservative assumptions should be made to account for these effects. In Figure 45, a model of a pipe system including a pipe rack is shown and, in Figure 46, the lowest mode shape is shown. From Table 3, it can be seen that the system including the pipe rack is much more flexible than without the pipe rack.

Table 3—Effect of Pipe Support Structures on Mechanical Natural Frequencies

Mode Shape Number

Frequency (Hz)Without Racks

Frequency (Hz)Racks Included

1 19.9 12.8

2 25.1 18.6

3 26.3 19.1

4 28.2 20.5

5 28.7 24.2

Figure 45—Plot of a Pipe System

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.2.7.5 Joint (Branch Connection) Flexibility

The joint between a nozzle and a vessel has local flexibility, which depends on the diameter and thickness of the nozzle and pipe and the reinforcement type. A common representation is a flexibility factor, which relates the joint angular flexibility to the angular flexibility of a unit length of nozzle. Flexibility factors of 10 or higher are possible. This makes it essential to include this flexibility accurately in the analysis to avoid an overestimate of natural frequencies. The Welding Research Council (WRC) values for flexibility factor for thin walled pipe are not sufficient for natural frequency calculations, which can cause large errors in pipe natural frequency and dynamic stress predictions. The flexibility, for each such joint, should be based on a validated model (e.g. finite element, see Figure 47) or a sound empirical database.

Figure 46—Lowest Mode Shape

Figure 47—Typical Branch Connection Finite Element Model

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.2.7.6 Soil-Pipe Interaction

For a buried or partly buried pipe, the soil stiffness makes a significant contribution. Dynamic pipe-soil models have been developed, which use the plane strain approach. These represent linear viscoelasticity of the soil and participation of the soil mass in the vibrations. Test data have shown that neglecting the soil in such situations can lead to high (100 %) discrepancies in mechanical natural frequency; and, as in all soil problems, establishing the soil modulus for different locations at the design stage remains a challenge.

3.2.7.7 Column/Base Flexibility

Some pipe restraints are attached to a plate support, which in turn is supported from a concrete base or column by bolts which act only at the corners. The plate, therefore, has freedom to bend between these bolt supports and can add flexibility to the system, which can lower the natural frequency by 25 % to 40 %. The system model for mechanical analysis should account for this flexibility by an appropriate analysis of the bending flexibility. Ideally, such flexible supports should be avoided, for example, by grouting the entire plate to the concrete column or by using stiffening plates.

3.2.7.8 Compressor Flexibility

The compressor itself is not infinitely stiff. Therefore, to accurately calculate the dynamic behavior of the system around the compressor (and optionally the compressor itself), the dynamic properties (including mass and stiffness of compressor parts such as cylinders and distance pieces) have to be included in the analysis.

It strongly depends on the construction of the machine what parts have to be included in the calculations. In most cases, the distance piece is the most flexible part of the compressor. Finite element models of the compressor can be applied and will improve the accuracy of the calculation. Most of the cylinders can be modeled by means of concentric pipe elements.

Field measurements have shown that the flexibility of the connection of the distance piece with the crosshead guide can have an important effect on the natural frequencies. In Figure 48, a partial detailed finite element model of a compressor is shown.

Figure 48—Example of a Partial Finite Element Model of a Compressor

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




3.2.7.9 Clamps and Supports

Many pipe systems are optimized from the thermal point of view, but not from the dynamic point of view since guide and rest type supports are frequently used. These supports usually are not able to restrain the dynamic motions, and are therefore not advised for systems which are subjected to dynamic loads.

A possible way to achieve dynamic restraint is to ensure that the friction force between the pipe and the pipe support structure (caused by the weight of the pipe) is higher than the pulsation-induced reaction force. Normally, the static loads are much higher than the pulsation-induced forces and it is theoretically possible to design a support, which is both dynamically fixed and statically loose. However, in most cases, the static loads are not known during the mechanical (dynamic) response analysis and it is also possible that the calculated static loads differ from the static loads in the field. This is a reason that rest type weight supports are not advised for systems that are subjected to dynamic loads.

To judge if a guide and/or rest type support restrains a dynamic motion, the definition “dynamically fixed” will be introduced as follows.

A pipe is “dynamically” fixed for one or more translation and/or rotation directions when the construction, which restrains the pipe to the structure, is able to withstand the dynamic loads without movement relative to the supporting structure.

3.2.7.9.1 Clamp Type Pipe Supports

A dynamically fixed support can be achieved by means of a stiff enough pipe support construction that does not allow a dynamic movement and/or rotation of the pipe in a certain direction. This means that no clearance between the pipe and the support construction is allowed.

This can be achieved by the installation of a clamp type support, of which an example is shown in Figure 49. These supports are advised for systems which are subjected to dynamic loads.

3.2.7.9.2 Hold Down Supports

A hold down support is capable of restraining the dynamic loads by means of a friction force and can allow thermal displacement if properly designed. The dynamic restraint in the plane perpendicular to the preload force direction is achieved by applying a friction force between the support and the structure on which the support is mounted. The friction force (Fw) shall be at minimum equal to the pulsation induced reaction force on the support. The minimum required preload (Fn) in the bolts is calculated according to Equation (45). Displacements resulting from thermal loads are sometimes achieved by means of applying a clearance between the bolts and the plate of the support (e.g. pipe shoe) or by slotting the bolt holes. Examples of hold down type supports are shown in Figure 50 and Figure 51. The spring hold-down type of Figure 51 can be applied when a thermal displacement in the vertical direction is required. A disadvantage of these supports is that they require more maintenance because the preload must be maintained. These types of supports do not have the preferred dynamic restraint characteristic of clamp type supports.

Rest supports for existing systems, which are not able to restrain the dynamic motions in one or more directions, can be modified into hold down type supports in such a way that they are able to restrain all translation directions. The dynamically fixed support can be achieved per Equation (45).

(45)

where

Fn is the minimum required preload on the support mounting surface;

Fn

Fw

f------≥

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 49—Typical Dynamically Fixed Clamps

Key1. Clearance

1

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Fw is the pulsation-induced reaction force on the support;

f is the friction coefficient, which depends on the applied materials (normally 0.3 for steel-steel contact).

3.2.7.10 Pipe Shaking Force Analysis Using the Guidelines

A new allowable shaking force criterion for piping has been included in the 5th Edition of API 618. The allowable shaking forces are a function of frequency, pipe diameter, support stiffness and number of supports. All shaking force

Figure 50—Example of a Hold Down Type Support with no Allowance for Thermal Displacement in the Vertical Direction

Key1. Pipe shoe2. Nut3. Washer4. Clearance5. Structural member

1

2

3

45

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




guidelines assume that there is no mechanical resonance. If mechanical resonance occurs, the allowable shaking force drops (essentially to zero), thus requiring that forced response calculations be performed.

The maximum allowable shaking forces are based on a new allowable piping vibration criterion that has been added in Clause 7.9 of the 5th Edition of API 618. This new criterion states that piping vibration levels shall not exceed 0.5 mm peak-to-peak (20 mils peak-to-peak) for frequencies below 10 Hz and 16 mm/s peak (0.625 in./s peak) between 10 Hz and 200 Hz. Note that these vibration limits apply at temperatures normally found on reciprocating compressor systems and may not be appropriate for very high or low extremes.

Figure 51—Example of a Spring Hold Down Type Support which Allows Thermal Motion in the Vertical Direction

Key1. Pipe shoe2. Nut3. Washer4. Spring5. Clearance6. Structural member

12

3

3

4

6 5

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Table 4 was generated using the equation for maximum allowable non-resonant shaking force provided in Clause 7.9 of the 5th Edition of API 618, based on support stiffness.

Table 5 was generated using the equation for maximum allowable non-resonant shaking force provided in Clause 7.9 of the 5th Edition of API 618, based on pipe size.

The maximum piping non-resonant shaking force shall be the lower of those determined from Table 4 and Table 5.

Using the static support stiffnesses provided in Table 4, Figure 52 plots a generic representation of the maximum allowable non-resonant shaking forces, based on pipe size.

Notice in the top plot of Figure 52 that the allowable shaking force increases as the rack stiffness increases, particularly at the lower frequencies. The lower plots show that higher shaking forces can be tolerated when using piers instead of racks due to the increased stiffness of the support structure. At lower frequencies, the stiffness of the pipe has a notable affect on the allowable shaking forces.

Table 4—Generic Piping Shaking Force Criterion from Clause 7.9 of the 5th Edition of API 618

Frequency (Hz)

Allowable Vibration (in. pk-pk)

Allowable Force (lbs)

Elevated Pipe Rack

Elevated Pipe Rack

Concrete Piers

Concrete Piers

Stiffness (lbs/in.) >> 5000 15,000 150,000 250,000

5.0 0.0200 100 300 3000 5000

10.0 0.0200 100 300 3000 5000

16.7 0.0119 60 179 1787 2978

20.0 0.0099 50 149 1492 2487

33.3 0.0060 30 90 896 1494

50.0 0.0040 20 60 597 995

75.0 0.0027 13 40 398 663

100.0 0.0020 10 30 298 497

Table 5—Generic Piping Shaking Force Criterion from Clause 7.9 of the 5th Edition of API — Based on Pipe Size

Nominal Pipe Diameter(in.)

Allowable Force(lbs) peak-to-peak

4 1000

6 1500

8 2000

10 2500

12 3000

16 4000

20 5000

24 6000

30 7500

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 52—Allowable Shaking Forces per API 618, 5th Edition

Frequency (Hz)

5,000 lbs/in. 15,000 lbs/in.

325300275250225200175150125100

755025

00 10 20 30 40 50 60 70 80 90 100

Sha

king

For

ce (l

bf)

API 618 – 5th Ed. Shaking Force AllowablePipe Racks – All Pipe Diameters

Note: Multiply allowable force x number of clamps on piping run (2 minimum) x 0.66 (a dynamic design factor) up to a maximum of 250 x nominal pipe diameter.

Frequency (Hz)

5500500045004000350030002500200015001000

5000

0 10 20 30 40 50 60 70 80 90 100

Sha

king

For

ce (l

bf)

API 618 – 5th Ed. Shaking Force Allowable250,000 lbs/in. Piers


Frequency (Hz)

3500

3000

2500

2000

1500

1000

500

00 10 20 30 40 50 60 70 80 90 100

Sha

king

For

ce (l

bf)

API 618 – 5th Ed. Shaking Force Allowable150,000 lbs/in. Piers


4 in. Dia.10 in. Dia.20 in. Dia






For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




A separate but similar shaking force criterion for pulsation bottles is also included in the 5th Edition of API 618. This criterion is a function of frequency and the number of cylinders per bottle, with an absolute maximum allowable of 45,000 N (10,000 lbf) peak-to-peak.

A minimum axial stiffness requirement has been added for piping restraints and structures per API 618, Annex P.3.2.1. This minimum stiffness requirement is a function of the pipe size, the unit speed, and the number of supports. API 618 does not specify a transverse clamp stiffness, other than to note that the clamp should be stiff enough to create a vibratory node.

If a frequency of pulsation is near or higher than the first mechanical natural frequency, the amount of shaking force that can be tolerated begins to drop significantly. This causes shaking force to govern the design. In other words, because the separation margin has not been met, it is important to ensure that the shaking force can be effectively restrained. Modifications to the pulsation control system are required where shaking forces must be reduced. In practical applications, especially for rack mounted piping, these higher orders of pulsation must be reduced either by using larger volumes for pulsation suppression devices in lower molecular weight applications or by using low-pass filters in higher molecular weight applications. This reduction is not only required because of the magnitude of the shaking force, but also to avoid mechanical resonance, which is a prerequisite for applying the shaking force guideline.

Designers who prefer to apply the greatest amount of acoustic control, will often do so by using a filter system for relatively high mole weight gases, designing the cutoff frequency of the filter to be below one times running speed. For lighter gases, filtering can be impractical, and simple surge volumes and pressure drop elements are utilized. Acoustic control attenuates the amplitude of pulsation transmitted to the piping. When variable speed operation is required, larger volumes may be required.

Three different support structures (rack, beam and pier), representing the three basic structures described in Clause 7.9 of the 5th Edition of API 618 are illustrated in Figure 53.

For review, the design steps can be found either in Clause 7.9 of the 5th Edition of API 618, or in RP 688, Part 2, under API 618 7.9.4.2.5.2 Basic Criteria.

4 Fundamentals of Modeling

4.1 Overview of Acoustic Modeling

The modeling of the acoustic characteristics of a reciprocating compressor piping system within this standard is based upon one-dimensional acoustic theory. The earliest modeling technique for commercial use was an analog simulator. This method uses a “lumped” modeling technique in which the basic acoustic elements of inertance, compliance and damping are represented in an electrical analog.

As computers have evolved, digital techniques have also become widely used. Various types of one-dimensional acoustics mathematical methods can be used as the basis of digital computer codes.

4.1.1 Parameters Considered in Modeling

Regardless of the modeling technique, it is imperative that certain parameters be considered in the simulation. Some of the more important parameters are described in the following paragraphs.

4.1.1.1 Compressor Speed Range

Since acoustic resonances are the primary cause of high pulsation, it is important that the full operating range of the compressor be considered. The modeling techniques should be capable of obtaining an accurate prediction of the

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




system response for high amplification factor responses, i.e. accurate prediction of “on resonance” amplitude is important.

4.1.1.2 Gas Composition

The gas composition, predominantly the gas mole weight, has a significant effect on the acoustic velocity. Since the acoustic velocity has a direct effect on the system’s acoustical resonant frequencies, it is important that the full range of gas composition (encompassing the full range of mole weight) be considered in the speed of sound calculations. The variation in speed of sound is typically considered in the simulation by increasing the speed range of the compressor in the simulation beyond its actual minimum and maximum speeds.

It is also important that some additional variation in the speed of sound (due to possible inaccuracies in the acoustic velocity calculations or piping length) be considered. Therefore, even a constant speed compressor should be evaluated over a varied speed range in the simulation.

For systems incorporating two extremely different gas compositions (e.g. hydrogen and nitrogen), resulting in a large disparity in both speed of sound and density values, separate simulations of the system with each gas should be considered.

Figure 53—Example of Pipe and Support Configurations

120 in.

W8x40Support steel

Clamp wt = 15 lbf

18 in. Diameterconcrete piers(fixed at 48 in.)

Rack Support

120 in.

160 in.

Vibration

Shaking force

8 in. Std. pipe

480 in.

120 in.

Beam SupportPier Support

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




4.1.1.3 Pressure and Temperature

Temperature can have a significant effect on speed of sound. The compression ratio can significantly affect the discharge temperature; therefore, it is important that speed of sound calculations consider the full range of pressures and temperatures over the expected range of operating conditions of the compressor. In addition, the gas density, which is an important parameter of the acoustical modeling, is dependent on pressure and temperature.

4.1.1.4 Flow Control

Unloading of compressor cylinders using valve unloaders or volume pockets can have significant effects on the harmonic content of the flow excitation and resulting pressure pulsation response. The effects of unloaders are important parameters in the simulation procedure.

4.1.2 Acoustic Simulation

4.1.2.1 Technical Basis of Acoustic Simulation

All techniques used (analog and digital) for acoustical simulation of reciprocating compressors, pumps and piping systems are based on the same governing equations, the one-dimensional differential equation of motion (Newton’s Law) and the equation of continuity.

The linearized momentum equation may be written in the form:

(46)

where

Q is the volumetric flow;

P is the pressure;

ρ is the mass density;

A is the pipe area;

t is time;

x is the distance along the pipe;

R is the linearized resistance per unit length.

The linearized continuity equation is:

(47)

where

k is the bulk modulus of the fluid.

The bulk modulus is related to the density and speed of sound by:

(48)

ρA---∂Q

∂t------- ∂P

∂x------ RQ+ + 0=

ΔPQ

-------

∂P∂t------ k

∂QA∂x---------=

k ρa2=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




where

a is the speed of sound.

Both analog and digital techniques are subject to the limitations imposed by the governing equations (linearized for small perturbations, etc.).

Some of the common mathematical formulations for solving the equations of motion and continuity are:

— four-pole method;

— lumped parameter method;

— finite element method;

— finite difference method (method of characteristics).

Note that any of these techniques can be utilized computationally. However, only the lumped parameter technique can be applied to the classical analog simulator which uses no active integrator elements.

4.1.2.2 Electrical Circuit Analog

In the analog simulator, the x-coordinate (distance along the pipe axis) is discretised, i.e. the pipe is divided into sections of length Δx. Referring to Figure 54, this leads to two ordinary differential equations for each pipe section:

(49)

(50)

where

P1 is the pressure at the inlet of the pipe section;

Q1 is the flow at the inlet of the pipe section;

P2 is the pressure at the end of the pipe section;

Q2 is the flow at the end of the pipe section;

L is the acoustic inductance which is analogous to the electrical inductance L;

C is the acoustic compliance which is analogous to the electrical compliance 1/C;

R is the acoustic resistance which is analogous to the electrical resistance R.

The lumped parameter method defines three distinct, independent parameters:

— acoustic inductance

— acoustic resistance

— acoustic compliance

LdQ2

dt--------- RQ2 P2 P1–( )+ + 0=

dP1

dt--------

Q2 Q1–( )C

-----------------------+ 0=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Referring to Figure 54, Equation (49) and Equation (50), the governing equations of continuity and momentum for the analog model, can be written as follows:

(51)

(52)

where

L equals ρl/A;

R is the pressure drop per unit flow;

C equals .

The primary advantage of the lumped parameter method was that it could be applied before the advent of high speed computers using analog simulation techniques. Piping acoustic characteristics can be modeled using a series of pipe elements, each of which contains the inertance, compliance and resistance properties of that particular length of pipe. Figure 54 illustrates a lumped acoustic model of a single pipe element. Many such elements can be combined in a circuit to obtain the piping system analog.

The electrical analog circuit of a pipe section is, therefore, an electrical circuit as is shown in Figure 55.

Another analog approach is to solve both first order differential Equation (49) and Equation (50) by means of electronic integrators. This requires two integrators per pipe section as shown in Figure 56, one for the capacitance and one for the inductance.

This technique became feasible when operational amplifiers became available as an integrated circuit. The advantage of this technique is that it is insensitive for parasitic capacitance and connection resistances. This made it possible to model a pipe system by making connections on a patch board that could be prepared off-line while preserving the important advantage of analog simulation: instantaneous availability of the solution.

Figure 54—Lumped Acoustic Model

Q1 Q2–dP1

dt--------=

P1 P2–LdQ2

dt------------- RQz+=

Alk-----

LegendC = acoustical complianceR = acoustical resistanceL = acoustical inductanceA = pipe areal = length of pipe segmentk = fluid bulk modulus

C R L

l

Q1

P1

Q2

P2

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




4.1.2.3 Digital Analysis

The mathematical formulations for computational simulation of one-dimensional flow were available long before the advent of computers. Beginning in the mid 1980s, digital simulation of compressor piping systems began to compete with analog simulation, and today, is the primary method of simulation.

Digital simulators are based either on time domain integration, using one of the many finite difference schemes, or on a spectral technique, in which the time axis is Fourier transformed to the frequency domain.

Finite Difference (Method of Characteristics)

In the finite difference method, both the x and the t coordinates are discretised, i.e. the pipe axis is divided into sections with a length Δx and the time into steps Δt. For each pipe section, the pressure and flow are calculated at

Figure 55—Analogous Electrical Model

Figure 56—Electronic Analog for One Pipe Section (Simplified Version without Flow Resistance)

LegendC = acoustical complianceR = acoustical resistanceL = acoustical inductancel = length of pipe segment

C

R L

l

Q1

P1

Q2

P2

C L

P toformersection

Q fromformersection

P fromnextsection

Q tonextsection

LegendC = acoustical complianceL = acoustical inductance

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




time t + Δt using the values of pressure and flow at time t. The differential equations are transformed into difference equations, which can be integrated numerically.

(53)

(54)

Assuming that the velocity of sound is constant in time, the solution procedure can be simplified considerably by choosing . In fact, the difference equations are integrated along the so-called characteristics. Therefore, this technique is called the method of characteristics (MOC).

(55)

(56)

These equations look rather complex, but solving consists, in fact, of two very simple data shift operations. Apart from

the calculation of fw, for each time step, the value of in each section is shifted in the positive x-direction and

the value in the negative x-direction. Note that the wall friction is calculated including the quadratic non-

linearity.

The method gives the pressures and flows in all pipe sections for each time step. The MOC is computationally efficient and includes non-linearities in the model.

There is virtually no limit to the size of the model and many analyses can be made simultaneously on one computer.

Spectral or Frequency Domain Methods

Spectral methods are based on the transformation of the wave equation.

One method is based on the one-dimensional wave equation which is obtained by combining the momentum and continuity equations. The wave equation is defined as follows:

(57)

By Fourier transforming the time to the frequency domain, the following equation is obtained:

(58)

where

(59)

Pi t Δt+( ) Pi t( ) ρa2

A--------–

Qi

12---+

Qi

12---–

–

Δx---------------------------Δt=

Qi t Δt+( ) Qi t( ) Aρ---–

Pi

12---+

Pi

12---–

–

Δx--------------------------Δt

Aρ---fwΔt–=

Δx Δt⁄ a=

P x Δx t, Δt+ +( ) aρA-------Q x Δx t, Δt+ +( )– P x t,( ) a

ρA-------Q x t,( ) fwΔx–+=

P x Δx t, Δt+ +( ) aρA-------Q x Δx t, Δt+ +( )– P x t,( ) a

ρA-------Q x t,( ) fwΔx+ +=

P aρA-------Q+

P- aρA-------Q

∂2Q

dt2--------- AR

ρ------- ∂Q

dt-------+

kρ--- ∂2Q

∂x2---------=

Q x t,( ) C1ej ωt γx–( ) C2ej ωt γx+( )+=

γ jωa

------ 1jARρω---------–=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The pressure as a function of x and t may be determined from the flow Q. This frequency domain solution can be generalized to obtain dynamic pressure and flow throughout the piping network.

4.2 Overview of Mechanical Modeling

The purpose of mechanical modeling is to determine the vibration response characteristics of the compressor system and piping system. Note that vibration response characteristics (mechanical natural frequencies), not vibration response amplitudes, are generally the intent of the modeling. An understanding of the mechanical natural frequencies is necessary and usually sufficient to achieve acceptable vibration response.

4.2.1 Compressor System

The mechanical model of the compressor system is usually performed using a digital computer approach. Classical beam theory and/or finite element techniques, or a combination of both, are used to determine the mechanical natural frequencies. The major components of the model include the cylinders, the associated crosshead guide and distance pieces, the suction and discharge pulsation suppression devices, and the associated piping (usually to first or second clamp). The influence of the flexibility factors associated with branch connections can have a significant influence on mechanical natural frequencies of compressor manifold systems and should be considered in the model.

Normally, calculation of the mechanical natural frequencies, in combination with knowledge of the acoustic forces obtained from the acoustical modeling, is sufficient to obtain a design which will have low and acceptable vibration levels. In some cases, forced response analysis may be utilized to determine the vibration response and stress levels. However, the accuracy of predicted natural frequencies can make response calculations of questionable benefit unless field measurements are available to verify and tune the mechanical analysis.

4.2.2 Piping System

The piping system mechanical analysis is normally treated separately from the compressor manifold system. In most cases, application of basic design guidelines, such as installing supports near concentrated masses (e.g. valves), simple maximum support spacing guidelines can be used to design piping support systems to control vibration of the piping to acceptable levels. Often, this type of analysis is all that can be justified since the piping configuration, support locations, and supporting structure stiffness are not finalized or are unknown at the time of an API 618 acoustical mechanical study.

In some cases, computer based methods may be used to more accurately predict natural frequencies of critical portions of the piping utilizing proprietary or commercially available computer codes. In these cases, detailed knowledge of the support stiffness, clamping techniques, and exact piping configuration are necessary. Experience has shown that in many cases, this level of modeling is not necessary.

Vibration response amplitudes and stress calculations of the piping may also be performed. Response and stress calculations of the piping are rarely required to achieve acceptable piping support, and, as is the case for the compressor manifold, their accuracy can be questionable unless field data are available to “tune” the model.

4.3 Concurrent Acoustical and Mechanical Design

The experienced designer realizes the importance of considering both acoustical and mechanical characteristics concurrently. For example, the mechanical natural frequency of a compressor manifold system can have a significant effect on the strategy used to design the bottles and control bottle unbalanced force characteristics. Likewise, knowledge of the piping support system and the expected range of piping mechanical natural frequencies can also significantly influence the bottle design or the need for the use of acoustic filtering.

Since virtually any change in bottle design to control pulsation characteristics also changes the mechanical model, an iterative and concurrent design procedure is necessary.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




4.4 Design Philosophies For Varying Degrees Of Acoustic And Mechanical Control

Following is a simplified explanation of the differences in design philosophies that are used worldwide. Each of the different philosophies is in compliance with the requirements of API 618; but, because they use different levels of pulsation control and have evolved from different purchaser priorities, they will usually result in different hardware.

The three design philosophies are:

The Acoustic Control (default philosophy of API 618) philosophy primarily focuses on acoustic control to reduce or practically eliminate pulsation and shaking forces in the piping system more than the other philosophies by utilizing acoustic design optimization and acoustic filtering (also called reactive pulsation control).

The Shaking Force Control philosophy primarily focuses on shaking force control instead of pulsation limits to determine bottle sizing (and the use of acoustic filtering). This philosophy sometimes includes prediction of vibration levels in the compressor and piping system to verify that residual pulsation levels will be acceptable and a mechanical restraint analysis is required to provide vibration control. This concept is often used in combination with the acoustic control philosophy.

The Vibration Control philosophy includes sizing and fabrication of pulsation suppression devices prior to final pipe design followed by acoustic and, primarily, mechanical tuning of the piping system during design (using forced response analysis) to ensure that vibration levels and cyclic stresses in the combined system are acceptable. This philosophy has the greatest emphasis of the three on significant mechanical modeling and control.

4.4.1 Acoustic Control

The best approach to minimize the probability of vibration problems is to control pulsation and shaking force levels (especially at higher frequencies) through acoustic optimization techniques. One of the more powerful acoustic optimization techniques is reactive filtering, used most often for higher weight gases. Reactive filtering refers to the electrical analogy used in acoustic modeling. It means that the reactive parameters of inductance and compliance are the primary design variables that are increased to achieve the desired filtering, while simultaneously trying to minimize pressure drop for which the electrical analogy is resistance. Filtering is generally used for higher mole weight gases, while large surge volumes and pressure drop elements are generally used for light gases.

Experience from extensive field testing helped define the maximum pulsation levels that would generally result in acceptable shaking force levels, [see API 618, 5th Edition, Equation (8), paragraph 7.9.2.6.2.2.2], eliminate relief valve “chattering” and reduce flow modulation to prevent check valve slamming.

The corresponding mechanical design focuses on ensuring that the piping mechanical natural frequencies are above the frequency of significant pulsation induced force harmonics (usually the second order of running speed) where acoustic filtering and/or other techniques for pulsation control are most effective. This is not a detailed rigorous process and is accomplished by simply identifying minimum support span lengths, based on pipe diameter, and minimum stiffness values for the clamps.

This philosophy has been successful in providing problem free systems. This methodology emphasizes acoustic control and will generally result in larger bottle designs and more frequent usage of volume-choke-volume filtering than either of the other two philosophies. Because this philosophy emphasizes acoustic control, it is possible to minimize stringent mechanical design to the extent that many users prefer this philosophy where piping layout is not well defined during design. This philosophy requires the least knowledge of the piping structural support details (stiffness and damping) of the three philosophies.

As discharge pressures increase, this philosophy can result in thick-walled vessels with long deliveries, which can often be the critical path of the project schedule. This constraint has caused some users to pursue other options, partially resulting in the evolution of the other philosophies. However, other considerations, such as control of

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




pulsation at pressure relief valves, often make pulsation control imperative. Higher frequency pulsation is more prevalent when operating at high speeds, which would also tend to encourage increased pulsation control.

Another cause for the evolution of the other philosophies is the degree of complexity involved in designing the reactive filtering. This is also a difficult issue to address in a design specification.

4.4.2 Shaking Force Control

It is possible to optimize the system based on shaking forces, while not necessarily meeting pulsation limits in Clause 7.9 of the 5th Edition of API 618. The resulting design usually has smaller bottles, does not always use acoustic filters or larger surge volumes, and frequently employs piping system acoustic and mechanical tuning. Depending on the system, this approach may result in relatively higher shaking force levels than the first philosophy. The success of mechanical tuning is dependent upon an accurate knowledge of the piping support stiffness. Allowing high pulsations in the system not only increases the risk of vibration, but can significantly degrade compressor performance and reduce valve life.

The main difference in these two design philosophies lies in the degree of acoustic control employed to reduce shaking forces in the piping. The choice is also influenced by the designer’s desire to use reactive pulsation control techniques. It should be noted that the “desire to use” is often influenced by the purchaser to minimize the need for the number and size of vessels necessary to provide effective reactive pulsation control.

The philosophy of compliance with the pulsation limit eliminates the need for detailed piping requirements. The shaking force philosophy will generally employ less pulsation control and more mechanical control, necessitating more detailed design of the piping and its support system. However, for both philosophies, it is very rare to arrive at a final design where a forced response analysis is required (Design Approach 3b1 or 3b2 of Clause 7.9 of the 5th

Edition of API 618). This is because the process for designing the pulsation suppression device, the piping and the piping supports can involve iteration between the acoustical and mechanical analyses until the pulsation, shaking force and frequency separation margin criteria are met, thus meeting the requirements of Design Approach 3a of Clause 7.9 of the 5th Edition of API 618. It is important to note that, for variable and high speed machines, there may be more difficulty achieving a good separation margin when reactive filtering is not used.

4.4.3 Vibration Control

If the pulsation suppression device designs are finalized before the piping layout, the shaking forces that result when the complete system is acoustically modeled are applied to a complete mechanical piping model and used to determine optimum modifications of the piping for acceptable dynamic response. This differs from the acoustic control and shaking force methods because there is generally no option to make modifications to the pulsation suppression devices. All design changes usually involve piping and support structure only. Secondly, in this method, a forced response analysis (Design Approach 3b1 and 3b2 of Clause 7.9 of the 5th Edition of API 618) is always done. This latter method has been provided by the consultants to meet the user’s desire for minimum delivery time of the compressor, which has evolved to requiring that the bottles be designed and fabricated before the piping layout is known. Optimizing the piping design based on vibration has been a common practice in the European community since the late 1980s. It is important to consider that if sufficient pulsation control is not achieved with the preliminary bottle design to limit vibration amplitudes, significant piping modifications may be required.

4.4.4 Design Philosophy Summary

When successful, all design philosophies should achieve the same goal of separating significant shaking forces and responsive mechanical vibration modes. The differences in the philosophies come down to the emphasis placed on acoustical versus mechanical control, the extent of the system that is mechanically modeled, and philosophical differences over the accuracies associated with mechanical natural frequency and vibration response modeling.

The generally more conservative piping pulsation and force criteria approach requires more acoustical design emphasis, but less mechanical design. The generally less conservative approach of using shaking forces to optimize

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




design utilizes less acoustical control but more mechanical control. This philosophy requires more detailed focus on the piping system mechanical design. Explicit determination of vibration and cyclic stress from forced response analysis further reduces the need for conservatism in acoustic control, but demands a correspondingly more accurate and detailed mechanical piping model, which can be impractical.

Generally, in the United States, the kind of information and work processes required to generate such a mechanical model are rarely available during the course of the study. Therefore, this detailed type of mechanical study is rarely performed. In Europe, there appears to be a much stronger preference to rigorously model and manage the construction of the piping system, while in the United States, the use of pulsation control, especially in the natural gas transmission, chemical process and refining applications has been the predominant philosophy. In the gas gathering and processing applications in North America, the pulsation and shaking force control philosophies generally have the highest level of support. Users will find that most pulsation and vibration control designers generally have a preferred design philosophy. Although designers have their default preferences, some are capable of designing to the other philosophies if requested.

In general, the design philosophy selected should target an optimum balance between pulsation control, vibration control and compressor performance.

The default philosophy for API 618 is acoustic control, which controls the driving force at its source and reduces the amount of mechanical control that is necessary.

One should note that the other philosophies described above are allowed by API 618, and meet the technical requirements when performed by analysts who understand the conservatism and modeling effort required. When specifying one of the other philosophies, the user should also plan to spend more effort designing the piping and support structure and to ensure that construction processes and quality control provide for replication of piping and support details that have been modeled, to ensure that the predicted pulsation and vibration control is achieved.

4.5 Design Approach and Philosophy Selection Guidelines

This discussion will focus on parameters that might cause one to include more than a Design Approach 2 or less than a Design Approach 3 for situations where deviation from Table 6 requirements in Clause 7.9 of the 5th Edition of API 618 is contemplated.

For 80 % to 90 % of the applications, Table 6 in Clause 7.9 of the 5th Edition of API 618 specifies approximately the same degree of analysis as this process. This information is intended to apply to the 10 % to 20 % not covered by the above.

All of the objective risk factors listed below will have some influence on resulting pulsation and vibration levels. The factors are generally listed in order of most significant to least.

4.5.1 Power per Cylinder

The higher the power per cylinder, the larger the scale of the equipment, and correspondingly, the more necessary it becomes to minimize the risk of problems. This parameter is used in Table 6 in Clause 7.9 of the 5th Edition of API 618 to select the appropriate Design Approach.

4.5.2 Load Steps

Generally, single-acting operation results in higher pulsation at one times running speed, while double-acting operation results in higher pulsation at two times running speed. This lower frequency pulsation can be more difficult to control. However, lower frequency pulsations generally result in lower dynamic forces and easier avoidance of mechanical resonances.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The wider the range of operating conditions, the greater the chance of running into acoustical problems at one or more load steps. Also, the wider the range of flow rates, the harder it is to control pulsation at all conditions while keeping pressure drop reasonable.

4.5.3 Percent of Rated Rod Load

The higher the rod load, the greater the chance of high frequency vibration problems excited by cylinder motion of the compressor itself.

4.5.4 Speed

The wider the speed range, the greater the chance of exciting an acoustical or mechanical resonance.

4.5.5 Discharge Pressure

For system pressures greater than 346 bar (5000 psig), a 3b1 and 3b2 analysis is recommended.

The wider the range of discharge pressures, the greater the chance of running into acoustical problems at one or more load steps. Also, the wider the range, the harder it is to control pulsation at all conditions while keeping pressure drop reasonable.

High pressure typically results in higher pulsation. Also, code requirements for high pressure systems place practical limitations on the size of pulsation bottles. For pressures greater than about 346 bar (5000 psig), additional emphasis should be placed on pulsation control.

4.5.6 Suction Pressure

The wider the range of suction pressures, the greater the chance of running into acoustical problems at one or more load steps. Also, the wider the range, the harder it is to control pulsation at all conditions while keeping pressure drop reasonable.

Controlling pulsation in very low line pressures is difficult, as added pressure drop can significantly affect performance.

4.5.7 Number of Stages/Number of Cylinders

Single nozzle bottles tend to have more mechanical problems, especially on the suction side.

4.5.8 Number of Units On Line

The more units sharing common piping, the greater the chance of pulsation from two or more units adding up to create high pulsation-induced unbalanced forces or high meter error.

4.5.9 Service/Gas

Heavy gases have lower speeds of sound and higher densities. As a result, pulsation problems tend to be more severe, and reactive filtering is needed.

Sour natural gas service may require double distance pieces and heavy walled pulsation supression devices and scrubbers, resulting in more mechanical concerns.

4.5.10 Other Considerations

Some subjective risk factors are listed below. Consideration of one or more of these factors may influence the level of analysis selected for a specific project. The factors are not listed in any particular order of priority.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




4.5.10.1 Location, Ease of Field Fixes

The more remote the site, the greater the difficulty of repairing problems after start-up and the more justifiable the engineering effort in the design stage.

4.5.10.2 Efficiency

High pulsation can degrade compressor performance. Excessive pressure drop, caused by pulsation control devices or due to the dynamic flow characteristics present in pulsating flow, will result in lost capacity.

A detailed acoustical analysis will allow for the best balance of pulsation control and added pressure drop.

Some methods of reporting pressure drop are not indicative of the total power loss through the manifold. It is important that the effects of pressure drop on the predicted power loss due to the pulsation control design be understood.

4.5.10.3 API Pulsation Limits

High pulsation levels at the cylinder flange connection may result in degradation of cylinder performance.

High pulsation levels in the piping may result in high pulsation-induced shaking forces, and hence, high vibration levels.

A detailed acoustical analysis will optimize pulsation levels to meet the guidelines set out in API 618.

4.5.10.4 Vibration Limits

How critical is it that specific vibration guidelines be met?

4.5.10.5 Flow Meter Accuracy

Pulsation can cause meter error. Is there a critical meter (e.g. custody-transfer meter) in the system?

4.5.10.6 Unit Criticality

If the unit goes down, does the plant go down? What will be the impact of lost production? Is there a standby or spared unit?

4.5.10.7 Your Experience

Do you have experience installing a unit of similar power, pressure range, loading and capacity? If so, what is your estimate of the risk and consequences of post start-up problems?

4.5.10.8 Project Profile

Is your reputation or the company’s reputation on the line if the project does not start up on time and without problems? Is this a critical/test case as seen by the customer?

5 Flow Measurement

5.1 Introduction

A flow is defined as steady if pressure, velocity, density and temperature do not vary enough with time to prevent a flow measurement within the required uncertainty.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




In ISO TR 3313, a steady flow is defined as a flow in which the flow modulation (pulsation) is below 5 % rms of the average flow velocity:

(60)

Pulsations can have a significant impact on the accuracy of flow meters of various measuring principles such as orifice, turbine, or vortex flowmeters, especially in gas flow applications. The impact of flow pulsations on systematic errors in orifice and gas turbine flowmeters has been documented in publications and standards on flow measurement, some of which are found in the references. For other techniques such as ultrasonic flowmeters (aliasing errors), vortex and Coriolis flowmeters (lock-in on pulsation frequency and (sub) harmonics thereof), the systematic errors cannot be quantified in a simple way.

The errors caused by a pulsating flow can over- or under- predict flow. In contrast to the criterion of pressure pulsation, as stated in API 618 for pipe systems in relation to pulsation forces, the flow pulsation amplitude (and frequency) determines the error in reading. For purely sinusoidal pulsations, the systematic error for orifices and gas turbine flowmeters can be quantified in direct relation to flow pulsation amplitude and frequency. This aspect should be taken into account in a pulsation analysis as per API 618 7.9.4.2.3.5. Errors in reading can be estimated based on the flow pulsations calculated in the analyses at the flowmeter location.

In situations where excessive pulsation levels are calculated, the flowmeter location may have to be altered or additional measures to dampen pulsations to acceptable levels will have to be implemented. In most cases, the pulsations caused by compressors are periodic, but not necessarily sinusoidal, so the relation between pulsation levels and meter error cannot be quantified accurately without more complex calculations.

An overview of the impact of pulsations on different metering techniques and references to standards and published literature is shown in Table 6. More detail on the referenced standards can be found in 5.7.

Table 6—Overview of Pulsation Impact on Various Flowmeters

Flowmeter Technique

Gas Application

Liquid Application

Type of Systematic Error

Flowmeter Standards Standards on Pulsation Impact

DP: Orifice, Nozzle and Venturi

++ + Square-root error - ISO 5167

- AGA Report 3

- API MPMS Ch. 14.3

- ISO TR 3313

Gas Turbine ++ Inertia of rotor - ISO 9951 - ISO TR 3313

Liquid Turbine + Inertia of liquid - API MPMS Ch. 5.3 - ISO TR 3313

Gas Ultrasonic + Aliasing error - ISO TR 12765

- AGA Report 9

Liquid Ultrasonic ++ Proving bias - API MPMS Ch. 5.8

Vortex ++ ++ Lock-in - ISO TR 12764 - ISO TR 3313

Gas Coriolis + Lock-in - ISO 10790

- AGA Report 10

Liquid Coriolis ++ Proving bias - API MPMS Ch. 5.6

Electro Magnetic – ++ Unknown

Key– Not applicable ++ Large impact + Minor impact

U'rms

Umean

------------- 0.05≤

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




5.2 Flow Measurement by Measuring Differential Pressure (DP) - Orifice Plate, Nozzle, and Venturi

The flow rate, determined from the differential pressure through a restriction like an orifice, is proportional to the square root of the differential pressure measured between the upstream and downstream taps. This introduces a square root error if the flow, and thus also the differential pressure, shows a periodic pulsation because

In a quasi-steady flow, for low pulsation frequencies and limiting pulsation amplitudes, the square root error for a sinusoidal pulsation can be calculated. In ISO/TR 3313, expressions are derived to estimate the pulsation error, ET, as a function of the flow pulsation and the average flow:

(61)

Expressions are also derived for the pulsation error as a function of dprms and dpmean.

This approach will give accurate results for low amplitude and low frequency pulsations in incompressible flow. Also, other aspects such as the response of the differential pressure sensor and the connecting line length from the taps to the sensor element should be considered with respect to the pulsation amplitude and frequency.

5.3 Flow Measurement by Turbine Flowmeters

A turbine flowmeter has a closely linear relationship between rotational speed and the flow rate, assuming a steady flow. In the case of a pulsating gas flow, the inertia of the rotor, and for liquids, the inertia of the fluid, can cause the rotor speed to lag behind the steady flow in an accelerating flow and to exceed it in a decelerating flow.

The inertia of the rotor results in a positive systematic error, which depends on flow pulsation amplitude, frequency and rotor response parameter. For a sinusoidal gas flow pulsation, the pulsation error can be determined.

A summary of this method and other references are described in ISO TR 3313, Chapter 6.2, Annex C. A sinusoidal flow pulsation of 5 % peak-to-peak results in a maximum pulsation error of less than +0.1 %. The criterion of 5 % peak-to-peak as allowable flow pulsation amplitude for turbine flowmeters is an acceptable limit in most cases.

For large gas flow pulsation amplitudes, positive errors up to +25 % are calculated.

5.4 Flow Measurement by Vortex Flowmeters

In vortex flowmeters, a bluff body is located in the flow at which periodic flow separation occurs, resulting in Von Karman vortices.

The vortex frequency, fv, is determined by the diameter of the bluff body, D, and the flow velocity, U, according to the relationship

(62)

The Strouhal number Str is constant over a large span of the flow, so that the flow velocity, U, is linearly proportional to the vortex frequency, fv. This vortex frequency is registered by measuring pressure fluctuations with a piezo-electric transducer or by measuring alternating forces in the bluff body.

dpmean( )0.5 dp0.5( )mean≠

ET 1U'rms

Umean

-------------

2

+0.5

1–=

fvDU

-------- Str=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




In a pulsating flow, the vortex signal is influenced in two ways:

— The amplitude of the signal is modified by the flow pulsation.

— The vortex frequency, fv, is influenced by the pulsation frequency, fp.

The first effect results in additional frequencies in the vortex signal, corresponding to fv – fp and fv + fp, next to the original vortex frequency, fv. Because of this effect, a number of pulses can be missed, which results in a deviating frequency, fv, indicated by the flowmeter, resulting in a systematic error.

The second effect leads to lock-in. The vortex frequency, fv, couples to the pulsation frequency, fp, but also to subharmonics fp/2 and multiples thereof (0.5fp, fp, 1.5fp, 2fp, and 2.5fp).

In Figure 57, the measuring error is expressed as a change of the vortex frequency, related to the value f0 in a steady, undisturbed flow. This can also be expressed as a change in K-value and thus indicates the uncertainty in the flow measurement.

This graph shows that a vortex meter will have errors up to 60 % if the pulsation frequency is close to the vortex frequency, e.g. if 0.3 < fv/fp < 3. An accurate flow measurement is possible outside of this range.

It should be noted that in addition to pulsation effects, the impact of mechanical pipe vibration on vortex flowmeters could also be large. In addition to pulsation impact, considerable variations have been observed for different vortex flowmeter manufacturers dependent upon sensor type and signal analysis used.

5.5 Flow measurement by ultrasonic flowmeters

In ultrasonic transit flowmeters, the flow velocity is determined by measuring the difference in time of flight between acoustic waves upstream and downstream through the medium. This results in average flow in the pipe. Multiple

Figure 57—Measuring Flow Expressed a Change of the Vortex Frequency

Vortex Frequency Related to Pulsation Frequency (fv/fp)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Erro

r in

Rea

ding

(%)

10

0

-10

-20

-30

-40

-50

-60

50 Hz, 8%50 Hz, 4%100 Hz, 25%100 Hz, 20%100 Hz, 15%294 Hz, 8%290 Hz, 4%

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




beam ultrasonic flow meters are used in custody transfer applications to account for deviating flow patterns resulting from swirl or asymmetry as a result of piping geometry.

Published data indicate that high frequency valve noise is known to be a source of errors in ultrasonic flow metering. Limited documentation is available on the impact of pulsations on ultrasonic flowmeters. It has been shown that low frequency flow pulsations can have a considerable impact on the accuracy of an ultrasonic flowmeter.

Measurement errors can also occur if pulsation frequencies are below the sample frequency.

For flow pulsation amplitudes of 8 % rms, measurement errors between 5 % and 10 % can occur for a 3-in. flowmeter.

5.6 Flow Measurement by Coriolis Flowmeters

ISO 10790, Paragraph 3.4.7 states that “coriolis meters generally are able to perform under pulsating flow conditions.” However, Paragraph 3.3.8 also states that “In environments with high mechanical vibrations or flow pulsations, consideration should be given to the use of pulsation damping devices and/or vibration isolators.”

Coriolis flowmeters measure mass flow by excitation of a fluid conveying tube (U-bend or straight tube) at a resonant frequency. Coriolis forces are developed as a result of the moving fluid in the oscillating tube. The forces produce a distortion of the driven tube motion with the shape of a higher vibration mode, but occurring at the drive frequency. The resonance frequency for the distorted mode is called the Coriolis frequency, fc.

In a steady flow, the mass flow is proportional to the phase difference between the signals from two sensors at different locations along the meter tube. The sensor flow signal is disturbed by mechanical vibration of the tube or flow pulsations in the fluid.

Flow pulsations may beat with the driven motion and produce a signal at fp + fc and fp – fc. Tests have shown that Coriolis flowmeters can give errors in reading as a result of flow pulsations at the Coriolis frequency. Erroneous readings have also been observed for flow pulsation at frequencies corresponding to the difference between drive frequency and Coriolis frequency. A systematic investigation to determine the impact of flow pulsation amplitude and frequency on commercially available flowmeters has not been published in open literature to date.

5.7 References

1) ISO TR 3313, Measurement of fluid flow in closed conduits-Guidelines of the effects of flow pulsations on flow-measurement instruments, 3rd Edition, 1998-08-01.

2) ISO 5167, Measurement of fluid flow by means of pressure differential devices-Part 1: Orifice plates, nozzles and venturi tubes inserted in circular cross-section conduits running full, 1st Edition, 1991-12-15.

3) ISO 9951, Measurement of gas flow in closed conduits-Turbine meters, 1st Edition, 1993-12-01.

4) ISO TR 12765, Measurement of fluid flow in closed conduits-Methods using transit-time ultrasonic flowmeters, 1st Edition, 1998-12-15.

5) AGA Report 9, Measurement of Gas by Multipath Ultrasonic meters, June 1998, Catalogue No. XQ9801.

6) ISO TR 12764, Measurement of fluid flow in closed conduits-Flowrate measurement by means of vortex shedding flowmeters inserted in circular cross-section conduits running full, 1st Edition, 1997-12-01.

7) ISO 10790, Measurement of fluid flow in closed conduits-Guidance to the selection, installation and use of Coriolis meters (mass flow, density, and volume flow measurements), 2nd Edition, 1999-05-01.

8) API MPMS, Chapter 5—Metering, Section 3—Measurement of Liquid Hydrocarbons by Turbine Meters, 4th

Edition, 2000-09-01.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




9) API MPMS, Chapter 5—Metering, Section 6—Measurement of Liquid Hydrocarbons by Coriolis Meters, First Edition, 2002-10-01.

10) API MPMS, Chapter 5—Metering, Section 8—Measurement of Liquid Hydrocarbons by Ultrasonic Flow Meters Using Transit Time Technology, 1st Edition, 2005-02-01.

11) API MPMS, Chapter 14—Natural Gas Fluids Measurement, Section 3—Concentric, Square-Edged Orifice Meters, Part 1—General Equations and Uncertainty Guidelines, 3rd Edition, 2003.

12) API MPMS, Chapter 14—Natural Gas Fluids Measurement; Section 3—Concentric, Square-Edged Orifice Meters, Part 2—Specification and Installation Requirements 4th Edition, AGA Report No.3, Part 2 and GPA 8185-00, Part 2, 2000-04-01.

13) API MPMS, Chapter 14—Natural Gas Fluids Measurement, Section 3—Concentric, Square-Edged Orifice Meters, Part 3—Natural Gas Applications, 2003.

6 Results Reporting Guidelines 3

Complete documentation of the acoustical and mechanical study requires clearly reporting the scope and results of the analysis, as well as presenting the recommendations. Scope includes definition of the analysis method, the operating range, and the extent of the system. Results include the detailed predictions and interpretations of analysis.

The following abbreviated report, with comments, demonstrates what documentation should be provided.

6.1 Scope

This example report is from the forced analysis of a package, which includes two single stage units that operate one at a time. It shows the typical data that should be included to define the scope of the analysis. The compressor configuration is shown in Figure 58. The operating range is shown in Table 7, Table 8, and Table 9.

Each table documents a key element of the study operating range. The unit dimensions, speed and power are shown in Table 7. The study operating conditions are shown in Table 8 and the gas composition in Table 9. Regardless of the format, the above information should be available for careful review to ensure the analysis covers the actual operation of the unit(s).

The guidelines for evaluating predicted results should also be defined. This may be done by reproducing the applicable API 618 formulae. For example, since API 618 designates that the default design philosophy will be acoustic control, the applicable formulae would be for pulsation, pressure drop and pulsation device shaking force. A comparison of study guidelines and predicted results should be provided to confirm compliance.

Finally, schematic or isometric drawings showing the extent and dimensions of the system being studied should be included.

6.2 Results

The sheer volume of data generated by Design Approach 3 makes it impractical to present all predicted results. However, the minimum presentation must include representative results for the recommended design.

Tables and/or graphs may be used to document results. Generally, graphs are more effective for presenting overall results, while tables more concisely present summary or highlight results. The following sample shows both formats.

The model description and predictions are the basic components of the results presentation.

3 The examples in this section are merely examples for illustration purposes only. Each company should develop its own approach. They are not to be considered exclusive or exhaustive in nature. API makes no warranties, express or implied for reliance on or any omissions from the information contained in this document.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The model description serves two purposes. First, the extent of the system analyzed is defined. Second, test points (or nodes) are identified on the model schematic to indicate where predictions are reported. Ideally, overall model correctness can be confirmed by a cursory inspection of the model description. For this reason, dimensioned graphical model descriptions are preferred.

A complete presentation of results would include predictions throughout the model. For brevity, only results from the bottom left corner of the model are shown in Figure 59, Figure 60, and Figure 61.

Table 7—Compressor Geometry

Manufacturer ABC Inc.

Model XYZ-2

Rated Power (HP) 600

Stroke (in) 5.00

Rated Speed (rpm) 1180

Speed Range (rpm) 1180 Fixed

Cylinder 1 2

Pattern CCC CCC

HE Service/Stage 1/1 1/1

CE Service/Stage 1/1 1/1

Bore (in.) 9.500 9.500

Piston Rod Diameter (in.) 2.250 2.250

Connecting Rod Length (in.) 18.000 18.000

Crank Angle w.r.t. Cylinder 1 0 180

Bank Angle w.r.t. Cylinder 1 0 180

HE Base Clearance (% swept) 20.350 20.350

Max. Clearance (% swept) 20.350 20.350

Clearance Device None None

CE Base Clearance (% swept) 23.570 23.570

Max. Clearance (% swept) 23.570 23.570

Clearance Device None None

Table 8—Operating Conditions

Load Step —

Service —

Stage —

Gas Stream —

Suction Pressure (psia) 174.1

Suction Temperature (°F) 122.0

Discharge Pressure (psia) 681.6

Discharge Temperature (°F) 288.0

Flow (MMSCFD) 6.275

Cylinder 1 2

HE Clearance (%) 20.350 20.350

CE Clearance (%) 23.570 23.570

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Table 9—Gas Composition

Gas Stream 1 (mol %)

Methane 69.501

Ethane 14.925

Propane 7.332

n-Butane 1.971

i-Butane 0.969

n-Pentane 0.531

i-Pentane 0.473

Hexane 0.350

Heptane 0.183

Octane 0.074

Nonane 0.023

Decane 0.006

Water 1.023

Carbon Dioxide 0.023

Nitrogen 0.296

Figure 58—Compressor Configuration

Figure 59—Cylinder Nozzle Pulsation (Predicted vs. Guideline)

Driver

Cylinder#1

Cylinder#2

Compressor

1050 1100 1150 1200Speed (rpm)

1250 1300

75

60

45

30

15

0

Pul

satio

n (p

si p

-p) Guideline

Predicted

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




There are two formats for graphical presentation of acoustic predictions. Overall and filtered predictions may be plotted versus run speed and frequency, respectively. The choice of format is dependent on the guideline used to evaluate the acoustic prediction. Cylinder nozzle and piping pulsation guidelines in API 618 are overall and filtered criteria, respectively. Predicted pulsation and force levels should be compared to applicable guidelines. A wider compressor speed range than the actual is typically used during analysis to account for reasonable variations between the model and the real system.

Although applied to an acoustic prediction, the cylinder nozzle pulsation guideline provides a performance criterion related to the affect of pulsations on capacity and power required. As such, along with the predicted pulsation levels, the predicted pressure drop resulting from the pulsation control design is reported to show compliance with the API requirements. In addition, it is customary to generate Pressure versus Volume Diagrams to show the impact of the pulsation and pressure drop predictions on predicted power required.

Similarly, piping pulsation and acoustic force guidelines are actually mechanical vibration criteria. Extrapolating from acoustic response, to either performance or vibration response, involves assessing risk and providing a reasonable margin for data uncertainty. The impact of pulsation is considered acceptable when the acoustic guideline is met. If it has been agreed that the guideline can be exceeded, then the report should indicate by how much, what the impact is upon predicted shaking forces, the assumptions that have been made for support stiffness values and a listing of additional clamps and support stiffening that will be required to meet the separation margin and guidelines where applicable.

Figure 60—Pulsation Suppression Device Line-Side Pulsation (Predicted vs. Guideline)

Figure 61—Pulsation Suppression Device Shaking Force (Predicted vs. Guideline)

0 50 100 150Frequency (Hz)

200 250

10

8

6

4

2

0

Pul

satio

n (p

si p

-p)

Guideline

Predicted

0 50 100 150Frequency (Hz)

200 250

500

400

300

200

100

0

Aco

ustic

For

ce (l

bf p

k)

Guideline

Predicted

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 62 shows a zoomed view of the mechanical finite element model for the compressor system.

Figure 62—Compressor System Finite Element Model with Test Points

Y

Z X

Key Test Points per Table 10 and Table 111. A002. B023. A064. A105. A08

3

4

5

2

1

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




For demonstration, mechanical predictions will be presented in tables rather than graphically. Note that deflected plots could be used to show mechanical natural frequency results. Also, graphs similar to those previously shown for acoustic results could be used to show mechanical forced response predictions.

Table 10 summarizes the lowest mode shape and mechanical natural frequency for the recommended manifold design. Referencing Figure 62, the table indicates a predominately vertical vibration of the suction piping elbow close to the damper. Note that a full presentation would summarize either all modes that do not meet the natural frequency guideline or the lowest mode.

Forced mechanical response generates vibration and cyclic stress predictions. Table 11 summarizes the recommended design results for the cylinder stretch load case.

A full presentation would report the predictions for all significant load cases.

Lastly, note that the acoustical and mechanical results are typically presented by using a combination of graphs and tables. It is also common practice to show the results for the original unmodified design alongside those of the recommended design.

Recapping, the report should present graphical and/or tabular results applicable to each type of analysis as shown in Table 12.

Table 10—Lowest Mode Shape and Mechanical Natural Frequency

Mode / Frequency (Hz) Direction Test Point Normalized Amplitude

1 / 46.3

X A 08 0.55

Y A 10 0.83

Z A 06 0.04

Table 11—Recommended Design Results for Cylinder Stretch Load Case

Loadcase / Frequency (Hz)

Direction Test PointPredicted Guideline

Vibration (mils p-p)

1 / 19.67

X A 08 0.2

7.1Y A 10 0.3

Z A 00 5.4

Stress (psi p-p)

B 02 348 26600

Table 12—Expected Results

Forced Acoustical

Cylinder nozzle pulsation

Piping pulsation

Acoustic forces

Mechanical Natural Frequency Natural frequencies and mode shapes

Forced MechanicalVibration

Cyclic stress

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




7 Field testing

The purpose of this section is to provide guidance for how and why the purchaser might perform a field test after start-up.

There are a variety of reasons to do a performance test on a reciprocating compressor system. Some of the more common are:

1) confirmation that design requirements have been met;

2) vibration problems;

3) excessive pressure drop;

4) premature valve failure;

5) driver overload;

6) performance degradation.

Each of these will be discussed separately because the techniques employed to identify the problem and solution will vary. With the exception of the proving the design parameters have been met, the user has usually not anticipated that such a test would be required.

7.1 Confirmation that Design Requirements Have Been Met

For critical applications, the purchaser might desire to do testing following startup to confirm that the designer has delivered a system that meets the specified criteria. If such a test is to be done, it should be planned at the design stage of the project to ensure that all of the necessary access points to the process are available for measuring flow, pressure, etc.

This analysis should measure vibration, pulsation and mechanical natural frequencies of main process and associated piping (relief lines, drain lines, oil lines, etc.). Depending upon the scope of the design analysis additional field checks such as pressure drop, meter error, valve dynamics, performance checks and torsional response can also be measured.

Purchaser and vendor should agree prior to the field check on pulsation test point locations, test scope and procedures. The purchaser and vendor should discuss likely operating conditions at start-up. Vendor should indicate which conditions are considered worst case from a pulsation and vibration point of view. Double acting versus single acting operation can result in drastically different pulsation and vibration characteristics, as can high compression ratios versus low compression ratios. To ensure smooth operation over the life of the compressor, a representative range of conditions should be simulated during the startup check.

7.2 Vibration Problems

The procedures for identifying, analyzing and correcting vibration problems in piping systems are described in the paper “Vibration Troubleshooting of Existing Piping Systems,” by J.C. Wachel and D.R. Smith, 1991. The paper may be used as a guide for addressing piping vibration problems and can be accessed on Engineering Dynamics Incorporated (of San Antonio, TX) web page: http://www.engdyn.com/images/uploads/59-vibration_ troubleshooting_of_existing_piping_systems_-_drs&jcw.pdf.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




7.3 Excessive Pressure Drop

When pressure drop exceeds what was expected, it usually manifests itself in one of two ways. Either rod load limits are being approached or the driver power is not enough to handle the load. In either case, it will be necessary to measure the instantaneous pressure at several points in the system. These will usually include the process and compressor side of the pulsation suppression device(s), and the pressure inside the cylinder. All pressures should be measured simultaneously and time synchronized. The measurements are used to determine the pressure drop across the pulsation suppression devices, the pressure pulsation levels on the suction and discharge, and the valve losses. These should be compared to the expected values as discussed in 3.1.3.4, to determine the source of the excess pressure drop.

7.4 Premature Valve Failure

Pulsation frequencies occurring in the internal gas passages adjacent to the valves at higher orders of running speed can coincide with the mechanical natural frequencies of the valve components and the opening and closing of the valves which can cause damage to the valves. High pulsation can contribute to increased loading on the valve, or contribute to “slamming” of the valve on closure. However, the dynamic characteristics of the valve itself, not pulsation, generally control the valve displacement and velocity relative to rotation of the crankshaft, and therefore, the valve impact velocities.

7.5 Driver Overload

3.1.3.4 provides the methodology for determining the driver size. In the event that overload is occurring, it will be necessary to compare the original design to the actual field performance. Pressure measurements at various points as described in 7.3 should be taken and compared to expected design values. One of the more common causes of driver overload is greater than expected pressure drop due to the compressor valves or excessive pressure drop of pulsation control devices. Factors that can increase the gas density, such as higher than expected suction pressure and lower suction and/or interstage temperature(s), will also increase the required power.

7.6 Failure to Deliver Expected Flow

Equation (18) in 3.1.3.4 is used to determine the expected flow rate. If the actual flow is lower than expected, then conditions that would lower the gas density are one of the more common causes. These include lower than expected suction pressure, greater than expected pressure drop across the suction side of the compressor system and higher than expected suction and/or interstage temperatures.

8 Valve Dynamic Performance Analysis

This analysis is used to determine the dynamic response of the valve sealing element, and when agreed upon, interaction with the flow induced pressure pulsations in the piping and cylinder gas passage. The main objective is to select a valve that will be reliable, yet allow the cylinder to operate as efficiently as possible. To achieve this objective, a valve dynamic performance analysis (VDPA) is employed to determine the appropriate lift and spring combination for a given valve at a given set of operating conditions.

8.1 The VDPA Model

The model should include dimensions and mass of the valve elements, spring coefficients, coefficient of restitution, aerodynamic drag coefficient, fluid damping, and physical model of compression chamber.

When it has been specified that the interaction of the flow-induced pressure pulsations be considered, the length and volume of the cylinder gas passages as well as the piping should be included in the compressor system acoustic model to determine the amplitude and frequency of the pulsation at the valve.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




8.2 Valve Reliability and Efficiency

Reliability is usually achieved by using the lowest practicable lift, ensuring that the valve elements close before the piston reaches dead center, and minimizing the impact velocities of the moving elements.

Efficiency is usually achieved by using the highest available lift and light spring rates. This combination normally allows the valve to open quickly and stay open during most of the piston stroke. The effect of lift and springing on efficiency can be observed by calculating the pressure drop across the valves and the attendant horsepower loss.

Since valves depend on differential pressure to operate properly, the design pressure drop should not be too low because this increases the valve’s sensitivity to other forces such as oil stiction and gas passage pulsations.

Reliability and efficiency are competing properties of a valve. Reliability is achieved at the expense of efficiency and vice versa. The key is finding an acceptable balance between the two. Application experience and the VDPA have proven to be the most useful tools to select the best lift and springing combination for a given application.

8.3 Application Of Analysis Results To Valve Selection

When a valve dynamic performance analysis is performed, there are several parameters that should be evaluated to assess the probable reliability of the design. Among these are valve closure timing, valve flutter, power and capacity losses, and impact velocities on the seat and guard.

8.3.1 Valve Closure Timing

A major cause of valve failure is late closing of the moving elements. Pressure drop across the valve opens the moving elements and springs close them. If the springs do not close the elements against the seat before the piston reaches dead center, forces on the valve due to reverse flow can slam the elements closed at elevated impact velocities. Therefore, the first criterion for valve reliability is that there must be sufficient spring force to close the valves on time. The Lift vs. Crank Angle plots in Figure 63 show the valve elements beginning to close before dead center, so the springs are closing the valves properly. An after-bounce may occur just after dead center, but this is normal and will not cause significant reverse flow through the valve.

Valve dynamic performance analysis (VDPA) programs predict valve motion based on compressor characteristics such as bore, stroke, and cylinder clearance, and on operating parameters such as pressure, temperature, and gas composition. Although the results of this analysis provide a reasonable prediction of valve motion, there are factors that can affect the valve motion and valve life that are generally unaccounted for in most VDPA programs.

Some of these factors are liquids, dirt, debris and corrosives. Corrosion is minimized by proper material selection. Liquids and dirt are incompressible substances and must be eliminated for optimal valve life.

Another factor is whether to include the predicted pulsation from the acoustic analysis in the VDPA. Excessive pulsation around the valve can cause the moving elements to remain open longer than predicted and then slam closed against the seat, which may result in excessive impact velocities. API 618 specifies pulsation limits at the cylinder nozzles. For reciprocating compressors, experience has shown that for most applications, if the pulsation levels at the cylinder flanges meet the limits defined in Clause 7.9 of the 5th Edition of API 618, it has not been necessary for the VDPA program to include the predicted pulsation from the acoustic analysis. Generally, pulsation effects do not influence the choice of valve spring stiffness, preload, moving element mass, etc.

The valve shall also be designed to create sufficient pressure drop. Valves that develop very low differential pressure are more likely to have their motion degraded by pulsations.

The term “stiction” is used to describe the viscous adhesion of the moving elements to the guard and, to a lesser degree, the seat. It is another factor to consider when examining the valve closing event. The springs must overcome the stiction force to properly close the valve on time. Excessive oil may cause the elements to close later than predicted by the VDPA program.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Figure 63—Typical Display of Valve Motion versus Crank Angle, Cylinder Pressure versus Volume and Analysis Results Table

Valve Lift - HES

Crank Angle (deg)0 40

Lift

(in.)

80 120 160 200

Crank Angle (deg)0 40 80 120 160 200

0.08

0.06

0.04

0.02

0.00

Valve Lift - HED

Lift

(in.)

0.05

0.04

0.03

0.02

0.01

0.00

Valve Lift - CES

Crank Angle (deg)180 220

Lift

(in.)

260 300 340 380

Crank Angle (deg)180 220 260 300 340 380

0.08

0.06

0.04

0.02

0.00

Cylinder Pressure - HE

Pre

ssur

e (p

sia)

800

600

400

200

0

Cylinder Volume (%)0 20 40 60 80 100

Valve Lift - CED

Lift

(in.)

0.05

0.04

0.03

0.02

0.01

0.00

Cylinder Pressure - CE

Pre

ssur

e (p

sia)

800

600

400

200

0

Cylinder Volume (%)0 20 40 60 80 100

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Field conditions vary, so choosing a spring that closes the valve a little early often eliminates potential reliability problems due to late closing. Choosing a slightly heavier spring may cause the valve to experience flutter, but this is usually not as important as closing the valve on time. If the chosen spring is too light, then the valve will experience high impact velocity when opening. It will also close too late, that is after the piston has reached dead center allowing a flow reversal through the valve.

8.3.2 Valve Flutter

Valve flutter refers to the phenomenon of multiple opening and closing events during one piston stroke. It occurs when the spring rate is too stiff or the preload is to high for the operating conditions. Minimal flutter at the end of the stroke on the VDPA lift diagrams is generally desirable, because it indicates that the springs are overcoming the valve pressure drop early enough to close the valve on time. Flutter should be minimized to enhance efficiency, but not at the expense of reliability. Valve selection would be simplified if perfect valve motion could be predicted by the VDPA program, but this requires perfect prediction of all the factors and forces affecting valve motion, and since this is impossible, some conservatism is often applied in the lift and spring selections. Sometimes, this conservatism is manifested in the form of valve element flutter at the end of the stroke.

8.3.3 Power and Capacity Losses

The calculated power and capacity losses predicted by the VDPA program do not necessarily imply compressor performance. The power losses given in the VDPA output summary are usually used to compare the changes in efficiency resulting from lift and spring changes.

8.3.4 Impact Velocity

The maximum values are often referred to as critical impact velocities. These limits represent the impacts at which the resulting stresses in the elements approach material limits.

8.4 Valve Dynamics Analysis Report

If specified, the valve dynamics performance analysis report should include the following:

a) The impact velocity of each moving element, plate, ring or poppet on the seat and on the guard along with the maximum allowable design values.

b) The power loss caused by the valves.

c) Capacity loss caused by the valves.

d) Equivalent area at full lift, the pressure drop required to lift the moving element off the seat and the pressure drop required to hold the valve fully open.

e) Internal cylinder and cylinder flange pressure versus crank angle and volume diagrams for each cylinder end of the piston.

f) Reasons for selecting the proposed springs, spring forces, lift, valve size and number of valves.

g) The minimum, normal and maximum ranges for all parameters shall be indicated. The assumptions made in the calculating procedure shall be listed and the effect on the program’s output.

h) The natural frequency of the valve element and spring assembly.

i) If specified, the valve dynamic performance analysis shall incorporate the results of the acoustic pulsation analysis to evaluate the influence of the gas pulsations.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on



Pulsation and Vibration Control in Positive Displacement Machinery Systems for Petroleum, Petrochemical, and Natural Gas Industry Services

Part 2: Reciprocating Compressors

1 General

The purpose of this section is to provide the reader with an understanding of the basis for the different design criteria. In the normative text, there are footnotes that qualify the requirements and some limits to be relaxed. The intent of this section is to provide more insight on the guidelines and requirements, and to identify where additional tutorial material can be found in other parts of RP-688.

NOTE Throughout this section, the bolded text has been taken directly from the 5th Edition of API 618, Reciprocating Compressors for General Refinery Services. The bolded paragraphs will also have “618” preceding the paragraph.

2 Comments On API 618, 5th Edition, Clause 7.9 – Pulsation and Vibration Control

618-7.9.1 General

618-7.9.1.1 The objective of the requirements of this clause is to avoid problems with

a) Vibration

b) Performance

c) Reliability, and

d) Flow measuring error caused by acoustical interaction between the compressor and the system in which it operates.

618-7.9.1.2 The basic techniques used for control of detrimental pulsations and vibrations are the following:

a) System design based on analysis of the interactive effects of pulsations and the attenuation requirements for satisfactory level of piping vibration, compressor performance, valve life, and operation of equipment sensitive to flow pulsation.

b) Utilization of pulsation suppression devices, such as: pulsation filters and attenuators; volume bottles, with or without internals; choke tubes; orifice systems; and selected piping configurations.

c) Mechanical restraint design, specifically including such things as: type, location, and number of pipe and equipment clamps and supports.

NOTE Completion of purchaser requirements for pulsation suppressors (Data Sheet page 4, lines 15 through 26, and pages 13 and 14) is essential for the vendor to quote and fabricate these accessories.

618-7.9.2 Alternate Operating Conditions

Operation with alternative gases, alternative conditions of service, or alternative start-up conditions shall be as specified, and pulsation suppression devices shall be mechanically suitable for all specified conditions and gases.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

94




When a compressor is to be operated on two or more gases of dissimilar molecular weights (for example, hydrogen and nitrogen), pulsation levels shall be optimized for the gas on which the unit must operate for the greater length of time.

Pulsation levels shall be reviewed for all specified alternative gases, operating conditions, and loading steps to assure that pulsation levels will be acceptable under all operating conditions. By mutual agreement, the pulsation level criteria of 7.9.4.2.5.2 may be exceeded for alternative conditions; however, the other design criteria of 7.9.4.2.5.2 shall be met.

Note: For the purposes of screening the need for reviewing alternate gases, a significant gas change is one that results in either a 30 % change in the speed of sound, or a molar mass change in the ratio of 1.7:1.

See 4.1.1.2 for more discussion.

618-7.9.3 Multiple Unit Additive Effects

618-7.9.3.1 The purchaser shall specify when the compressor is to be operated in conjunction with other compressor units and their associated piping systems.

In this case, the additive effect of pressure pulsations from multiple units shall be addressed. The scope of the analysis shall be based on agreement between the purchaser and vendor. If the additive effect indicates a requirement for modifications to an existing system to obtain acceptable pulsation levels, such modifications shall be based on agreement between the purchaser and the vendor.

NOTE In some cases, it may be necessary to impose tighter limits for each new compressor than those defined in 7.9.2.6 in order for the combined system to achieve acceptable pulsation levels.

618-7.9.3.2 For preliminary sizing, and, if specified, for Design Approach 1 (7.9.4.2.2), pulsation suppression devices shall have minimum suction surge volume and minimum discharge surge volume (not taking into account liquid collection chambers), as determined from Equation (3), Equation (4), and Equation (5); but, in no case, shall either volume be less than 0.03 m3 (1 ft3).

In SI units:

(3)

(4)

(5)

In USC units:

Vs 8.1 PDkTS

M--------

1 4⁄

×=

Vd 1.6Vs

r1 k⁄-------- ×=

Vs Vd 0.03≥ ≥

Vs 7 PDkTS

M--------

1 4⁄

×=

Vd 1.6Vs

r1 k⁄-------- ×=

Vs Vd 1.0≥ ≥

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




where

Vs is the minimum required suction surge volume, in m3 (ft3);

Vd is the minimum required discharge surge volume in m3 (ft3);

k is the isentropic compression exponent at average operating gas pressure and temperature;

r is the stage pressure ratio at cylinder flanges (absolute discharge pressure divided by absolute suction pressure);

Ts is the absolute suction temperature in K (°R);

M is the molar mass;

PD is the total net displaced volume per revolution of all compressor cylinders to be manifolded in the surge volume in m3/r (ft3/r)

The internal diameter of the surge volume shall be based on the minimum surge volume overall length required to manifold the compressor cylinders. For a single-cylinder surge volume, the ratio of surge volume length to internal diameter shall not exceed 4.0. The inside diameter of spherical volumes shall be calculated directly from the volumes determined by Equation (3), Equation (4), and Equation (5).

Equation (3), Equation (4), and Equation (5) are intended to ensure that reasonably sized pulsation suppression devices are included with the compressor vendor’s proposal and should provide satisfactory sizes for most applications. In some instances, the sizes should be altered according to the simulation analysis employed by Design Approaches 2 and 3. Sizing requirements may be substantially influenced by operating parameters, interaction among elements of the overall system, and mechanical characteristics of the compressor system. The magnitude of the effects of these factors cannot be accurately predicted at the outset.

Some compressor applications require the use of properly designed low-pass acoustic filters. A low-pass acoustic filter consists of two volumes connected by a choke tube. The volumes may be made up of two separate suppressors or one suppressor with an internal baffle. A procedure for preliminary sizing of low-pass acoustic filters is presented in Annex O. The design must be confirmed by an acoustic simulation.

The use of Equation (3), Equation (4), and Equation (5) ensures that quotations for the pulsation suppression devices are based upon the same size and amount of material. However, it is not uncommon for the acoustic analysis to cause the bottle design changes and/or addition of secondary volumes. For more information about the use of volumes and low-pass filters, refer to 3.1.4. The maximum length to diameter (L/D) ratio is utilized to ensure that mechanical natural frequency of the pulsation suppression device stays above 2.4 times the maximum continuous speed of the compressor. The reason that a designer might wish to use a higher L/D ratio is that it would enable the compressor to sit lower which might result in a smaller foundation and support structure.

618-7.9.4 Design and Documentation

618-7.9.4.1 Design Approach Selection

618-7.9.4.1.1 Unless otherwise specified, Table 6 shall be utilized to determine the Design Approach. For applications above an absolute pressure of 350 bar (5000 psia), the purchaser and the vendor shall agree on the criteria for pulsation suppression.

Refer to Section 4.5 for discussion about specific considerations if the default design approach selection is not going to be followed.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




618-7.9.4.1.2 The purchaser shall specify if the analysis is to be performed by the vendor or a third party. If a third party is selected to perform the analysis, the compressor vendor shall provide the necessary information required for the third party vendor to complete the analysis.

Some purchasers prefer to use a third party vendor because they feel that it will ensure that their preferred design philosophy will be utilized without compromise. Others prefer to have accountability for acceptable design and performance assigned to a single vendor, such as the Compressor Manufacturer, the Engineering and Construction Contractor or the Packager. Both methods are acceptable if the Purchaser, Compressor Manufacturer, and Engineering Contractor(s) clearly define and agree upon the expectations, roles, responsibilities, and accountabilities prior to contract award.

618-7.9.4.2 Design Approaches

618-7.9.4.2.1 General

The design approach choices are:

a) Design Approach 1–Empirical Pulsation Suppression Device Sizing;

b) Design Approach 2–Acoustic Simulation and Piping Restraint Analysis;

c) Design Approach 3–Acoustic Simulation and Piping Restraint Analysis plus Mechanical Analysis (with Forced Mechanical Response Analysis if necessary).

Unless otherwise specified, each subsequent Design Approach includes all of the elements of preceding approaches that are not superseded by more comprehensive methods. Elements of the various design approaches are summarized in 7.9.4.2.2, 7.9.4.4, and 7.9.4.5. Flowcharts detailing work processes for each Design Approach can be found in Annex M.

NOTE A detailed description of the three design approaches is given in 7.9.4.2.

NOTE API RP 688 provides a discussion of the different operating and mechanical parameters that should be taken into account when considering a Design Approach that is different from that indicated by Table 6, especially if less analysis is contemplated.

Refer to 4.5 for discussion about specific considerations if the default design approach selection is not going to be followed.

Table 618-6—Design Approach Selection

3 3 3200 bar ≤ P < 350 bar

(3000 psi ≤ P > 5000psi)

Ab

solu

te D

isch

arg

e P

ress

ure2 3 3

70 bar ≤ P <2 00bar

(1000 psi ≤ P < 3000 psi)

2 2 335 bar ≤ P < 70 bar

(500 psi ≤ P < 1000 psi)

1 2 2 P < 35bar

kW/cyl < 55

(HP/cyl < 75)

55 ≤ kW/cyl < 220

(75 ≤ HP/cyl < 300)

220 ≤ kW/cyl

(300 ≤ HP/cyl)

Rated Power per CylinderFor

Committe

e Ball

ot 54

81

Not For

Genera

l Dist

ributi

on




618-7.9.4.2.2 Design Approach 1—Empirical Pulsation Suppression Device Sizing

Pulsation suppression devices shall be designed using proprietary and/or empirical analytical techniques to meet line side pulsation levels required in 7.9.4.2.5.2.2.1, and the maximum pressure drop allowed in 7.9.4.2.5.3.1, based on the normal operating condition. Acoustic simulation analysis is not performed when using this design approach.

As shown in Figure 4 of API 618, Design Approach 1 is only recommended for small scale applications. Since no acoustic simulation is performed, this design is usually based upon previous designs for similar applications.

618-7.9.4.2.3 Design Approach 2—Acoustic Simulation and Piping Restraint Analysis

618-7.9.4.2.3.1 General

Design Approach 2 is pulsation control through the use of pulsation suppression devices and proven acoustic techniques in conjunction with mechanical analysis of pipe runs and anchoring systems (clamp design and spacing) to achieve control of vibrational response. This approach includes the evaluation of acoustic interaction between the compressor, pulsation suppression devices and associated piping, including pulsation effects on compressor performance and an evaluation of acoustic shaking forces in the pulsation suppression devices. This evaluation is accomplished by modeling the compressor system and the piping and then performing an acoustic simulation to determine the response.

Refer to 4.1 for an explanation of acoustic simulation techniques and 3.2.7.2 for discussion about mechanical analysis of pipe runs and anchoring systems.

618-7.9.4.2.3.2 Compressor System Model

Pulsation suppression devices (or dampers) are initially sized using Design Approach 1, and analyzed using acoustic simulation. The compressor system model normally includes piston and valve kinematics, cylinder passages, pulsation suppression device(s) and terminates at the line side nozzle flange. This model is only used for the acoustic simulation. There is no mechanical modeling of the compressor system to evaluate mechanical resonances in Design Approach 2.

Refer to 3.1 and 4.1 for an explanation of pulsation concepts and their application to the compressor system model.

618-7.9.4.2.3.3 Piping System Model

For applications where the piping system is not defined, the acoustic simulation can be performed with the piping system initially modeled with an infinite length, acoustically non-reflective line. The allowable design limits of 7.9.4.2.3.4 apply. This is called a Pre-Study and is also referred to as a “bottle check” or “damper check.” For applications where the piping system is defined, the pre study does not have to be performed. The piping model replaces the acoustically non-reflective line in the simulation model.

There is no mechanical modeling of the compressor system to evaluate mechanical resonances in Design Approach 2.

Refer to 3.1 and 4.1 for an explanation of pulsation concepts and their application to the piping system model.

618-7.9.4.2.3.4 Pre-Study

When the acoustic simulation is performed prior to completion of the piping system model, the maximum allowable pressure pulsation level at the pulsation suppression device line-side nozzle flange shall be 80 % of the allowable value defined by Equation (8) for single pulsation suppression devices, and 70 % of the

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




allowable value defined by Equation (8) when two or more pulsation suppression devices are attached to common piping.

It is possible that the maximum allowable pulsation levels (80 % of the allowable value defined by Equation (8) of API 618 for single pulsation suppression devices and 70 % of the allowable value defined by Equation (8) of API 618 for two or more pulsation suppression devices) will not be sufficient to ensure that pulsation levels meet API 618 guideline with piping attached. Additional pulsation and/or vibration control may be required.

NOTE A single pulsation device means a device that is not connected to another by common piping. Examples include: a single cylinder first stage suction device of a single unit; a single cylinder discharge pulsation device of a single unit; and, single unit first stage suction or final stage discharge device that manifolds all the cylinders that generate pulsation in the particular piping system. Examples of two or more pulsation suppression devices attached by common piping are: interstage devices (even with intercoolers); single units with multiple pulsation suppression devices for first stage suction or for final stage discharge piping systems; and multiple units attached to common piping systems.

In order to meet contract delivery, all parties should cooperate to schedule the design of the pulsation suppression device, the pulsation analysis, and piping design. Ordering components after the pre-study can facilitate the procurement of long delivery components of the pulsation suppression devices, such as end caps, nozzles and cylindrical sections. However, the final length, nozzle orientation, and need for vessel internals cannot be optimized until the piping system is added to the acoustic model. Therefore, it should be noted, that if the pulsation suppression devices are fabricated prior to finalizing the piping configuration, the only remaining system design optimization methods available to the designer are the installation of orifices, piping modifications and stiffening of the piping system. This sometimes leads to the need to order different pulsation suppression devices to provide an adequate system, with a consequent negative impact on schedule.

In many cases, in order to reduce the shaking forces to acceptable levels, it is necessary for the acoustic design to provide pulsation levels well below the API guideline (See Equation (8) in 7.9.2.6.2.2.2 of the 5th Edition of API 618). The exact amount can only be determined when the acoustic simulation can be applied to the pipe layout. If the pulsation suppression devices have already been fabricated and do not meet the need defined by the acoustic simulation of the piping, the only option is to apply additional mechanical control to the piping system.

618-7.9.4.2.3.5 Acoustic Simulation

When the layout and sizing of the piping system is completed, an acoustic simulation of the complete system shall be performed to confirm compliance with the requirements of 7.9.4.2.5 or to identify changes necessary to achieve compliance.

618-7.9.4.2.3.6 Mechanical Review and Piping Restraint Analysis

A mechanical review shall be performed using span and basic vessel mechanical natural frequency calculations to avoid mechanical resonance. This review shall result in a table of various pipe sizes that indicates the maximum allowable span (based on the maximum compressor operating speed) between piping supports as a function of pipe diameter, and the separation margin requirements of 7.9.4.2.5.3.2.

NOTE 1 In the piping design, when clamps are used to avoid mechanical resonances, the thermal flexibility effects should also be considered.

However, thermal flexibility analysis is not considered to be in the scope of an acoustic simulation.

NOTE 2 To accurately predict and avoid piping resonances, the supports and clamps must dynamically restrain the piping. Piping restraints are only considered to be dynamically restraining when they have either enough mass or stiffness to enforce a vibration node at the restraint. This requirement is difficult to achieve with overhead piping and/or the use of simple supports, hangers, and guides.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




Basic vessel mechanical natural frequency calculations are performed to determine the first mode of the vessel and make sure that the length to diameter ratio is low enough so that the first natural frequency is greater than 2.4 times the running speed.

See 3.2.7.9 for recommendations on restraint design.

618-7.9.4.2.4 Design Approach 3—Acoustic Simulation and Piping Restraint Analysis Plus Mechanical Analysis – (With Forced Mechanical Response Analysis if Necessary)

618-7.9.4.2.4.1 General

This approach is identical to Design Approach 2, with the addition of a mechanical analysis of the compressor cylinder, compressor pulsation suppression devices and associated piping systems, including interaction between acoustic and mechanical system responses. Forced mechanical response is included when necessary. Both acoustic and mechanical methods are used to arrive at the most efficient and cost effective plant design.

Design Approach 3 has been separated into Steps 3a, 3b1, and 3b2. Design Approach 3 is considered complete at the end of any of the steps if the design criteria are met.

In Step 3a, the focus of the analysis is on identifying compressor system natural frequencies and shaking forces that occur at or near those same frequencies. If redesign is not possible to achieve the desired separation margins, then Step 3b1 is followed to perform a forced response analysis on the Compressor System to ensure that cyclic stresses are within acceptable limits.

Step 3b2 provides the criteria for performing a forced response analysis of the piping system. For designers who utilize the acoustic control philosophy to ensure that pulsation limits are met at the line side nozzles of the pulsation suppression devices, Step 3b2 is rarely required. In the 3rd Edition of API 618 when the Design Approach concept was first introduced, the authors envisioned that the application of forced response analysis would only apply to highly stressed compressor components and the nozzles connecting the cylinders to the pulsation suppression devices. These were the areas where users had experienced failures which the 3rd and 4th Editions were addressing.

618-7.9.4.2.4.2 Step 3a—Mechanical Natural Frequency Analysis of the Compressor and Piping System to Avoid Coincidence with Significant Shaking Forces

a) The starting point of the mechanical model is defined as either the crankcase-to-foundation interface or the crosshead guide-to-crankcase interface. For modeling accuracy, this location must be relatively rigid when compared to the rest of the compressor mechanical model and/or it must be accurately described by a 6 degree of freedom spring. The compressor mechanical model end point is defined as the second pipe clamp on the suction and discharge piping moving away from the line side nozzles of the pulsation suppression devices. The factors that can influence the accuracy of the model are discussed in more detail in API RP 688. If specified, this modeling will also include an analysis of the stresses found in the pulsation suppression device internals in accordance with 7.9.5.1.22 and 7.9.5.1.23.

Note 1: The intent is to avoid mechanical resonance of the compressor cylinders, pulsation suppression devices, and piping system at frequencies where high shaking forces also exist.

Note 2: In some cases the compressor frame, crosshead guides and cylinders, mounted on a concrete foundation, can be considered to be relatively rigid, and could be modeled using rigid elements.

Note 3: The compressor and pulsation suppression device mechanical model was formerly known as the compressor manifold model.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




b) An analysis of the compressor and piping system shall be done to predict the mechanical natural frequencies. The mechanical and acoustic system shall be designed to meet the separation margin criteria of 7.9.4.2.5.3.2 and the shaking forces shall not exceed the limits found in 7.9.4.2.5.2.3.

Note: Geometrically-complex areas of the system such as: cylinders; distance pieces; crosshead guides; frames; pulsation suppression device nozzles; and piping, where span calculations cannot be applied accurately, are analyzed to determine mechanical natural frequencies, usually with vendor proprietary methods, shop measured data, or finite element methods; with the intent of avoiding mechanical resonances at frequencies where significant shaking forces also exist.

In the event that the requirements of 3a cannot be met, the two options are to redesign acoustically or move on to forced response analysis. The default philosophy of acoustic control (and therefore resulting in shaking force control) will generally cause acoustic redesign to be employed, eliminating the need for forced response analysis due to the mechanical modeling uncertainties (see 3.2.7.3 through 3.2.7.8) and the effectiveness of acoustic control in eliminating all higher frequency excitation mechanisms.

618-7.9.4.2.4.3 Step 3b1—Forced Mechanical Response Analysis of the Compressor Mechanical Model

When the excitation frequency separation margins or the shaking force amplitude guidelines for pulsation suppression devices cannot be met, a forced-mechanical-response analysis of the compressor mechanical model to the pulsation-induced forces and cylinder-gas load forces shall be performed. The allowable cyclic stress criteria in 7.9.4.2.5.2.5 shall apply. The compressor vendor shall supply the allowable vibration criteria for compressor components such as cylinders, distance pieces and crankcases.

NOTE The allowable compressor vibration levels are generally the limiting design criteria. This analysis predicts the cyclic stress in the pulsation suppression devices and associated piping. It is not intended that analysis of the cyclic stresses in the compressor components be included in this design approach. The compressor components are included in the model only for the purpose of enabling the analysis of the effects of their flexibility and dynamic movement on the pulsation suppression devices. The compressor manufacturer is expected to provide vibration criteria to ensure that no fatigue failures or premature wear of compressor components occur, in accordance with 6.1.1.

See the commentary following 7.9.4.2.5.2.5 later in this section on compliance with the cyclic stress criteria.

618-7.9.4.2.4.4 Step 3b2—Forced Mechanical Response of the Piping System

When the excitation frequency separation margins or the shaking force amplitude guidelines for the piping system cannot be met, a forced-mechanical response analysis of the piping system to acoustic shaking forces shall be performed. The allowable vibration and cyclic stress criteria per 7.9.4.2.5.2.4 and 7.9.4.2.5.2.5, respectively shall apply. The model end points shall be defined by the analyst in agreement with the purchaser but will generally include all of the piping that was included in the acoustic model. The factors that can influence the accuracy of the model are discussed in more detail in API 688.

When forced-mechanical-response analysis of the piping system is performed without doing a forced-mechanical-response analysis of the compressor mechanical model, the starting point of the piping system is at the compressor cylinder flanges, which are assumed to be rigid.

NOTE As with Step 3b1, the vibration criteria will generally be the limiting design criteria, because when the vibration levels are within the recommended allowable limits, the allowable stress levels will usually not be approached. The exception is where high concentrations occur at large diameter reductions such as nozzle connections and weldolets for small piping on significantly larger piping.

See 3.2.7.1 through 3.2.7.8 for the above referenced factors that can influence the accuracy of the model.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




618-7.9.4.2.5 Design Criteria

618-7.9.4.2.5.1 General

Pulsation suppression devices and techniques applied in accordance with Design Approaches 1, 2, and 3 shall satisfy the basic criteria in 7.9.4.2.5.2, and the other criteria in 7.9.4.2.5.3.

618-7.9.4.2.5.2 Basic Criteria

To evaluate compliance with the basic criteria, the following hierarchy applies:

1. Preliminary pulsation suppression device sizing. Determine pressure drop across the pulsation suppression device. The criteria as described in 7.9.4.2.5.2.2.1 and 7.9.4.2.5.3.1 shall be met. Design Approach 1 is complete.

For Design Approaches 2 and 3:

2. Pre-study of pulsation suppression devices (if required). Determine pulsations at the compressor cylinder flanges and at the line side of the pulsation suppression device. The criteria as described in 7.9.4.2.5.3.1, 7.9.4.2.5.2.1 and 7.9.4.2.5.2.2.2 de-rated as in accordance with 7.9.4.2.3.4 shall be met. The criteria for pulsation suppression device non-resonant shaking force are described in 7.9.4.2.5.2.3.3.

3. After the layout of the piping system is completed, pulsation analysis of the complete pipe system is undertaken. The criteria for maximum pressure drop and pulsations are described in 7.9.4.2.5.3.1, 7.9.4.2.5.2.1, and 7.9.4.2.5.2.2.2. The criteria for pulsation suppression device non-resonant shaking force are described in 7.9.4.2.5.3.3.

If these criteria are met and Design Approach 2 is specified, then Step 4 shall be performed. If Design Approach 3 is specified, then proceed directly to Step 5.

4. Specify maximum piping spans and determine vessel mechanical natural frequencies utilizing piping tables and basic vessel calculations. The minimum allowable mechanical natural frequencies are given in 7.9.4.2.5.3.2.

If the criteria for Step 3 and Step 4 are met, Design Approach 2 analysis is complete. If the criteria under Steps 3 or 4 are not met, then either a redesign or Steps 5 and 6 shall be performed:

5. Develop a mechanical model and determine mechanical natural frequencies; the minimum separation margins are in 7.9.4.2.5.3.2.

6. Determine the maximum allowable shaking forces in accordance with 7.9.4.2.5.2.3 and check whether these are higher than the acoustic shaking forces calculated by acoustic simulation.

If criteria for Step 5 and Step 6 are met, Design Approach 3a analysis is complete.

For the compressor system, if criteria in Step 5 or Step 6 are not met, either a redesign or Step 8 shall be performed.

For the piping system, if the criteria in Step 5 or Step 6 are not met, either a redesign or Step 7 shall be performed.

7. Determine pipe vibrations based on the maximum calculated acoustic shaking forces. Criteria for maximum allowable pipe vibrations are in 7.9.4.2.5.2.4.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




If the vibration criteria in Step 7 are not met, either a redesign or Step 8 shall be performed:

8. Calculate dynamic stresses in the compressor system or piping system, as required. Maximum allowable cyclic stresses are in 7.9.4.2.5.2.5. For the compressor system, also compare the vibration levels calculated to those supplied by the compressor vendor.

If criteria for Step 7 or Step 8 are met, Design Approach 3b analysis is complete. If the criteria are not met redesign is required.

NOTE The calculations to determine the criteria for allowable shaking forces, in Step 6 of this clause, can be ignored if the piping vibration analysis is performed according to Step 7 directly after Step 5.

See also the work flow charts in Annex M of API 618.

618-7.9.4.2.5.2.1 Maximum Allowable Compressor Cylinder Flange Pressure Pulsation

Unless other criteria (such as loss of compressor efficiency) are specified, the unfiltered peak-to-peak pulsation level at the compressor cylinder flange, as a percentage of average absolute line pressure, shall be limited to the lesser of 7 % or the value computed from Equation (6).

(6)

where

Pcf is the maximum allowable unfiltered peak-to-peak pulsation level, as a percentage of average absolute line pressure at the compressor cylinder flange.

R is the stage pressure ratio.

NOTE 1 Where maximum pulsation levels exceed these values and reasonable modifications are used, higher limits may be agreed on by the purchaser and the compressor vendor.

NOTE 2 The frequencies, phase relationships, and amplitudes of pressure pulsation at the compressor valves can significantly affect compressor performance and valve life. Pulsation levels measured at the compressor cylinder flange will usually not be the same as those levels existing at the valves. Experience has shown, however, that pulsation limits at the cylinder flanges, as specified above, result in compressor performance within the tolerances stated in this standard.

See 3.1.3.4.3 for insight on the impact of cylinder flange pulsation on compressor performance and 8.3.1 discussion about pulsation interaction with valve performance.

618-7.9.4.2.5.2.2 Maximum Allowable Pulsation Limits At and Beyond Line-side Nozzles of Pulsation Suppression Devices

618-7.9.4.2.5.2.2.1 Pulsation suppression devices used in accordance with Design Approach 1 shall limit peak-to-peak pulsation levels at the line side of the pulsation suppression device to a value determined by Equation (7).

In SI units:

(7)

Pcf 3 R%=

P14.1

PL( )1 3⁄----------------%=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




And in USC units:

where

P1 is the maximum allowable peak-to-peak pulsation level at any discrete frequency, expressed as a percentage of average mean absolute pressure.

PL is the average mean absolute line pressure, in bar (psia).

618-7.9.4.2.5.2.2.2 Unless otherwise specified for Design Approaches 2 and 3, based on normal operating conditions, the peak-to-peak pulsation levels in the initial suction, interstage and final discharge piping systems beyond pulsation suppression devices shall satisfy the requirements specified in a) and b).

a) For systems operating at absolute line pressures between 3.5 and 350 bar, (50 and 5000 psia), the peak-to-peak pulsation level of each individual pulsation component shall be limited to that calculated by Equation (8).

(8)

In USC units:

where

P1 is the maximum allowable peak-to-peak level of individual pulsation components corresponding to the fundamental and harmonic frequencies, expressed as a percentage of mean absolute line pressure.

a is the speed of sound for the gas in m/s (ft/s).

PL is the mean absolute line pressure in bar (psia).

DI is the inside diameter of line pipe in mm (in.).

f is the pulsation frequency in Hz.

The pulsation frequency f is derived from Equation (9).

(9)

where

N is the shaft speed in r/min.

z is the 1, 2, 3,… corresponding to the fundamental frequency and higher order frequencies.

P110

PL( )1 3⁄----------------%=

P1a

350---------

400

PL D1× f×( )0.5----------------------------------- =

P1a

1150------------

300

PL D1× f×( )0.5----------------------------------- =

fN z×

60------------=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




b) For absolute pressures less than 3.5 bar (50 psia), the peak-to-peak levels of individual pulsation components need only meet the levels calculated for an absolute pressure of 3.5 bar (50 psia).

NOTE At pressures below 3.5 bar (50 psia), it is impractical to impose the stringent requirements of Equation (8).

1. Comments on Equation (8)—Experience has shown that higher pulsation levels may be acceptable for gases that have higher sonic velocities. Lower pulsation levels are necessary for gases with lower sonic velocities.

(SI units) or (USC units) has been added to Equation (8) in the 5th Edition.

2. Comments for over 350 bar (or 5000 psia)—Since P1 is a percentage of the line side pressure, as the line side pressure increases, P1 decreases. However, P1 does not decrease linearly with increasing PL; so, the absolute value of the peak-to-peak pressure pulsation is about 19 times greater when PL is 350 bar than when PL is 1 bar. For this reason, as PL increases, the shaking force that the allowable pulsation can generate becomes more likely to the governing factor in the overall design. Applications above 350 bar (or 5000 psia) require criteria that are mutually agreed upon by the purchaser and vendor to ensure that the residual shaking forces in the system are acceptable.

3. Why adherence to the pulsation limits defined in this paragraph is the default design process for API 618 is explained in 4.4.1.

618-7.9.4.2.5.2.2.3 If mutually agreed between the purchaser and vendor, the pulsation levels may exceed the limits defined by 7.9.4.2.5.2, provided that requirements in 7.9.4.2.5.2.3 through 7.9.4.2.5.2.5 are satisfied, as noted in 7.9.4.2.5.2.1.

NOTE The default design philosophy is based on minimizing pulsation and pressure drop utilizing proven acoustic control techniques. For applications where the user may desire to relax the criteria, API 688 should be used as guidance to understand the risks and benefits that might be encountered.

This paragraph allows purchasers who desire, to deviate from the default philosophy of acoustic control. Other philosophies are explained in 4.4.2 and 4.4.3. The techniques utilized for additional mechanical control (which will be necessary) are reviewed in 3.2.

618-7.9.4.2.5.2.2.4 If specified, flow pulsations in systems which include elements sensitive to such phenomena shall be limited to mutually agreed criteria; for example, flow meters, check valves, and cyclone separators. Allowance for the presence of any such sensitive elements outside the vendor’s scope of supply shall be as specified.

Section 4 provides guidance on the impact of flow pulsations on various types of flow measuring devices.

618-7.9.4.2.5.2.3 Maximum Allowable Acoustic Shaking Force

618-7.9.4.2.5.2.3.1 General

The maximum allowable non-resonant shaking force based on the design vibration guideline is calculated with Equation (10).

(10)

where

SFk is the non-resonant shaking peak-to-peak force guideline relative to static structural stiffness in N (lbf).

keff is the effective static stiffness along the piping or pulsation suppression device axis where the shaking force acts in N/mm (lbf/in.).

V is the design vibration peak-to-peak guideline in mm (in.) (see Figure 4).

a 350⁄ a 1150⁄

SFk keff V×=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The shaking force guideline (SFk) applies to non-resonant vibration; therefore, shaking forces near resonance must be reduced well below the above shaking force guideline. This guideline is simplified from a complex analysis, contains many inherent assumptions, and needs to be applied with care. See Annex P for conventions and a more detailed discussion of the maximum allowable shaking forces.

Various support types provide peak-to-peak ranges of support stiffness approximately as follows:

Elevated Un-braced Rack Supports 900 – 2700 N/mm

(5000 – 15000 lbf/in)

Grade Level Typical Supports and Clamps 2700 – 27000 N/mm

(15000 – 150000 lbf/in)

Grade Level Heavy Supports and Clamps 27000 – 45000 N/mm

(150000 – 250000 lbf/in)

See 3.2.7 for calculation methods.

618-7.9.4.2.5.2.3.2 Maximum Allowable Piping System Non-resonant Acoustic Shaking Force

The maximum allowable piping non-resonant shaking forces shall be the lower of the values calculated from Equation (10) or from Equation (11).

In SI units:

(11)

In USC units:

where

SFpmax is the maximum piping non-resonant shaking peak-to-peak force guideline based on support strength in N (lbf).

NPS is the nominal pipe size in mm (in.).

618-7.9.4.2.5.2.3.3 Maximum Allowable Cylinder Mounted Pulsation Suppression Device Non-resonant Shaking Force

The maximum allowable non-resonant shaking forces for cylinder mounted pulsation suppression devices shall be the lower of the values calculated from Equation (10) or from Equation (12). For Design Approach 2, since the shaking force levels are not evaluated using Equation (10), the maximum allowable level shall be 10 % of Equation (12). For frequencies within ±20 % of the calculated pulsation suppression device mechanical natural frequency, the maximum allowable level shall be 1 % of Equation (12).

In SI units:

(12)

SFpmax 45 NPS×=

SFpmax 250 NPS×=

SFdmax 45,000=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




In USC units:

where

SFdmax is the maximum pulsation suppression device non-resonant shaking peak-to-peak force guideline based on structural strength in N (lbf).

Note 1: The shaking force criteria are intended as design criteria for shaking forces that act along the pulsation suppression device axis. Other shaking forces that can be affected by the pulsation suppression device design such as (but not limited to) those acting parallel to the compressor cylinder nozzles and those acting within the cylinder internal passages must also be evaluated. Evaluation criterion relative to the cylinder varies and should be mutually agreed upon by the purchaser and compressor manufacturer.

Other shaking forces that contribute to cylinder vibration and cylinder nozzle stresses are discussed in 3.2.6.3 and 3.2.6.4.

618-7.9.4.2.5.2.4 Piping Design Vibration Criteria

The predicted piping vibration magnitude shall be limited to the “design level” in Figure 618-4. The diagram in Figure 618-4 is based on the following:

a) constant allowable vibration amplitude of 0.5 mm peak-to-peak (20 mils peak-to-peak) for frequencies below 10 Hz (the frequency of 10 Hz is also according to ISO 10816);

b) constant allowable vibration velocity of approximately 32 mm/s peak-to-peak (1.25 in./s peak-to-peak) for frequencies between 10 and 200 Hz.

The limits in Figure 618-4 are intended as a design trigger point for analysis in accordance with 7.9.4.2.5.2.1. These values should not be used as field acceptance criteria.

NOTE The requirements in this subclause are considered to be conservative. There are, however, situations in which high stress risers and un-braced small diameter attached piping can pose a problem even though the main pipe exhibits acceptable vibration limits. There are no criteria conservative enough to be used without a significant understanding of vibrational mechanics.

618-7.9.4.2.5.2.5 Maximum Allowable Cyclic Stress

618-7.9.4.2.5.2.5.1 For Design Approach 3, Steps 3b1 and 3b2, pulsation and/or mechanically induced vibration shall not cause a cyclic stress level in the piping and pulsation suppression devices in excess of the endurance limits of materials used for components subject to these cyclic loads. For example, carbon steel pipe with an operating temperature below 370°C (700°F), the peak-to-peak cyclic stress range shall be less than 180 N/mm2 (26000 psi) considering all stress concentration factors present and with all other stresses within applicable code limits.

It is not considered necessary to demonstrate compliance with this clause for Design Approaches 1 and 2.

This stress criterion, in its original form (in 618 3rd Edition, 13.2), was intended to be applied to the pulsation suppression devices. With the 4th edition and the addition of Appendix M, this criterion was then also applied to the Piping System Dynamic Stress Analysis (M.7).

Experience has shown that fatigue failures in reciprocating compressor piping systems are generally limited to pulsation suppression device nozzles which are connected to the cylinders, to small bore appurtenances on pulsation suppression devices near the compressor themselves and less frequently to small bore appurtenances off main

SFdmax 10,000=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




process piping. Seldom do actual fatigue failures occur in the main process piping. The major concern in the piping distant from the compressor is degradation and failure of piping supports, and overall vibration levels. Piping vibration levels causing failure of the main process piping would be extremely high, and likely violate all standard vibration severity chart guidelines. Although maximum piping stress levels are specified below 26,000 psi peak-to-peak, this criterion will usually not be the limiting design guideline in main process piping.

618-7.9.4.2.5.2.5.2 If specified, a piping system flexibility analysis that predicts forces and stresses resulting from thermal gradients, thermal transients, pipe and fitting weights, static pressure, and bolt-up strains shall be performed. The specified piping code shall provide the design criteria.

Modeling should include frame growth and component properties.

This is the relocation of M.11 from Appendix M of 618, 4th Edition.

618-7.9.4.2.5.3 Other Criteria

618-7.9.4.2.5.3.1 Maximum Allowable Pressure Drop

For all Design Approaches:

a) Unless otherwise specified, the pressure drop for each operating case, based on steady flow through a pulsation suppression device at the manufacturer’s rated capacity, shall not exceed 0.25 % of average absolute line pressure at the device, or the percentage determined by Equation (13), whichever is higher. These limits shall be increased by a factor of two when the pressure drop is calculated using the total flow, where total flow is the sum of the steady flow plus dynamic flow components, provided that the static component still meets the above criteria.

(13)

Figure 618-4—Piping Design Vibration at Discrete Frequencies

Vibr

atio

n G

uide

line

(mm

, p-p

)

Vibr

atio

n G

uide

line

(in.,

p-p)

0.1 2.5

0.5

0.25

0.025

0.02

200

0.01

1Frequency (Hz)

API 618 Design Vibration Guideline

10 100 10000.001

ΔP 1.67R 1–

R------------%=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




where

ΔP is the maximum pressure drop based on steady flow through a pulsation suppression device expressed as a percentage of mean absolute line pressure at the inlet of the device.

R is the stage pressure ratio.

b) When a moisture separator is an integral part of the pulsation suppression device, the pressure drop for each operating case, based on steady flow through such a device at the manufacturer’s rated capacity, shall not exceed 0.33 % of the mean absolute line pressure at the device, or the percentage determined by Equation (14), whichever is higher. These limits shall be increased by a factor of two when the pressure drop is calculated using the total flow, where total flow is the sum of the steady flow plus dynamic flow components.

(14)

c) Pressure drops specified in this clause may be exceeded by mutual agreement between purchaser and vendor, when this is the consequence of the preferred solution to piping resonance problems. The effects of dynamic interaction between compressor cylinders, pulsation suppression devices and attached piping on cylinder performance are evaluated and pulsation-induced power and capacity deviations are determined for the recommended design. This analysis should optimize pulsation related compressor performance.

See 3.1.3.4.4 for more discussion about the effects of pressure drop on compressor performance.

618-7.9.4.2.5.3.2 Separation Margins

Unless otherwise specified, both of the following guidelines are to be used together to avoid coincidence of excitation frequencies with mechanical natural frequencies of the compressor, pulsation suppression devices and piping system.

a) The minimum mechanical natural frequency of any compressor or piping system element shall be designed to be greater than 2.4 times maximum rated speed.

Note 1: The intent is to be above twice running speed, because there is almost always sufficient excitation energy at the first and second orders to excite resonances to a dangerous level.

Note 2: In certain compressor configurations, there can be significant excitation energy at higher orders of running speed and the system design shall take this into account. When the minimum mechanical natural frequency guideline is not met or when there is significant excitation energy at higher orders, the separation margins as defined in b) shall be maintained.

b) The predicted mechanical natural frequencies shall be designed to be separated from significant excitation frequencies by at least 20 %.

Note 1: The intent is that at least 10 % separation for the actual system is achieved, and due to modeling limitations, if 20% is used for predicted designs, then 10 % for the actual system will generally be attained.

Note 2: The ability to accurately predict resonance and, therefore, separation margin is greatly affected by the stiffness of the system. Elevated rack-mounted piping systems will be inherently less stiff than grade-mounted pipe on concrete sleepers. In general, the stiffer the system, the lower the sensitivity of the model to stiffness variability, and therefore, the more accurate the prediction of the natural frequencies and avoidance of coincidence with excitation frequencies.

ΔP 2.17R 1–

R------------%=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




The requirement for 20 % separation of significant excitation frequencies from predicted mechanical natural dictates that all significant excitation above 3× maximum rated speed shall be attenuated because of the overlap of successive multiples of running speed, even for fixed speed compressors. For example, to avoid 3× running speed, all frequencies from 2.4× to 3.6× running speed need to be avoided. To avoid interference with 4× running speed, all frequencies from 3.2 to 4.8 need to be avoided. Thus, the low range of 4 times running speed overlaps with the high range of 3× running speed. Therefore, robust pulsation control is especially important at frequencies above 2×running speed.

618-7.9.4.2.5.3.3 Flow Measurement Error

Unless otherwise specified, for flow meters located in the specified piping system, the maximum flow measurement error caused by pulsation shall not exceed the following:

a) For non-custody transfer meters 1.00 % error.

b) For custody transfer meters 0.125 % error.

NOTE See API RP 688 for a discussion on flow measurement error.

See Clause 4 for more details about flow measurement error.

618-7.9.4.2.6 Documentation Requirements

A written report on the control of pulsation and vibration shall be furnished to the purchaser. Compliance with the requirements of Clause 7.9 for the specified Design Approach shall be documented.

The documentation requirements of API 618 are clearly defined in a large clause only briefly summarized above. See Clause 5 for more details about reporting of analysis results.

618-7.9.5 Pulsation Suppression Devices

A significant number of paragraphs in Clause 7.9.5 deal with design and construction requirements for the pulsation suppression devices that do not affect pulsation and vibration control. Only those paragraphs that directly affect pulsation and vibration control are reprinted here with additional discussion regarding recommended practice.

618-7.9.5.1.5 All flanged branch connections shall be reinforced so that the reinforcement provides a metal area equal to the cut-away area removed from the shell or head regardless of the metal thickness in the branch connection wall. Stress concentration factors shall be considered to assure compliance with 7.9.4.2.5.2.5.

The reinforcement described in this paragraph is primarily required to provide adequate pressure rating for the pulsation suppression device. Additional reinforcement to meet the cyclic stress requirements, such as gusseting, is described in API 618, 7.9.5.1.12.

618-7.9.5.1.6 Suction pulsation suppression devices, not provided with an integral moisture removal section, shall be designed to prevent trapping of liquid.

Heat tracing the suction pulsation suppression device and the piping connecting it to the suction scrubber is one technique that can minimize the formation of liquid. The piping should also slope towards the suction scrubber. However, even when these techniques are employed, the configuration of internals and the nozzle that connects to the cylinder must be arranged so that pockets of liquid cannot accumulate. Paragraph API 618, 7.9.5.1.10 provides for connections for draining. If a slug of liquid is ingested into the cylinder, it can result in a catastrophic failure of the cylinder that includes loss of containment of the process gas.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




618-7.9.5.1.8 The nozzle length from the shell of the pulsation suppression device to the cylinder flange shall be held to a minimum that is consistent with thermal flexibility and pulsation requirements. The nozzle area shall be at least equal to the area for the nominal compressor cylinder flange size. Adequate space shall be allowed for access to and maintenance of the cylinder’s working parts.

The shortest possible nozzles are generally preferred for acoustic and mechanical design, but can cause interference with the pulsation suppression device during valve maintenance. This issue must be considered by the designer during the acoustic analysis.

618-7.9.5.1.10 A DN20 (3/4 NPS) pressure test connection shall be provided at each pulsation suppressor inlet and outlet nozzle. An external drain connection of at least DN25, (1 NPS) shall be provided for each compartment where practical. Where multiple drains are impractical, circular notched openings in the baffles that are located at the low point of the vessel wall may be used with the purchaser’s approval. The effect of such drain openings on the performance of the pulsation suppression device must be considered. Arrangement of internals shall ensure that liquids will flow to drain connections under all operating conditions.

Care must be taken when providing connections on pulsation suppression devices. While it is necessary to make such connections to facilitate draining, pressure and temperature measurement, etc., they can also be the source of piping fatigue failures if not properly designed. API 618, 7.9.5.1.12 provides the requirement for gussets and API RP 688, 2.2.6.6 provides more details for these suggested methods of bracing and support.

618-7.9.5.1.12 Flanged connections DN25, (NPS 1) and smaller, although reinforced in accordance with 7.9.5.1.5, shall be designed to minimize overhung weight and shall be gusseted back to the main pipe or reinforcing pad in at least two planes to avoid breakage resulting from vibration.

618-7.9.5.1.18 All internals of pulsation suppression devices shall be designed, fabricated, and supported considering the possibility of high acoustic shaking forces. Dished baffles in lieu of flat baffles shall be used. The same welding procedures as applicable to external welds shall be followed. Full penetration welds shall be used for the attachment of the baffles to the pulsation suppressor shell.

The acoustic shaking forces internal to the pulsation suppression devices should be determined during the design for each of the operating cases specified to ensure that the cyclic baffle loads are not excessive. If in doubt, then specify the dynamic and static stress analysis described in API 618, 7.9.5.1.22.

618-7.9.5.1.22 If specified, the dynamic and static stresses on the pulsation suppression device internals that result from pulsation-induced shaking forces and pressure-induced static forces shall be analyzed to confirm compliance with 7.9.4.2.4.

618-7.9.5.1.23 If required by the specified pressure vessel code, such as ASME Section 8, Division 2, a low cycle fatigue analysis shall be performed to predict the stresses from thermal gradients, thermal transients, and pressure cycles on the pulsation suppression devices and internal components.

618-7.9.6 Supports for Pulsation Suppression Devices

If specified, supports for the pulsation suppression devices and vendor-supplied piping shall be furnished by the vendor. The supports shall be designed considering static loading (including piping loads), acoustic shaking forces, and mechanical responses; and shall not impose harmful stresses on the compressor, piping system, or pulsation suppression devices to which they are attached. In calculating stress levels, the compressor frame growth and the flexibilities of the frame, crosshead guide, distance piece, flange, and branch connection shall be considered.

Compliant (resilient) supports having inherent vibratory dampening characteristics are preferred to accommodate thermal expansion. Loading of compliant supports shall be adjustable. Noncompliant

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




supports shall be designed to allow adjustment by the purchaser while in operation. Spring supports shall not be used unless specifically approved by the purchaser.

NOTE To the extent possible, the foundation of the supports should be integral with the compressor foundation. When noncompliant adjustable supports are used, they should be adjusted by the purchaser at normal operating conditions.

Pulsation suppression device support design is an integral part of the overall compressor and piping mechanical system design. The purchaser and vendor should ensure that the design assumptions for initial and ongoing adjustment are well understood and documented so that they can be maintained throughout the operating life of the compressor system.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on



API 618 Annex M(informative)

Design Approach Work Process Flowcharts

The work processes used in Design Approaches 1, 2 and 3 described in 7.9.4.2 are illustrated in Figures M-1, M-2 and M-3 respectively. The steps in the hierarchy of the Basic Criteria described in 7.9.4.2.5.2 are shown with circled numbers in each figure.

Figure M-1—Design Approach 1

Shows the step in 7.9.2.6.2

Preliminary Pulsation Suppression Device Sizing per 7.9.2.3. If specified, minimum volume shall be per

7.9.1.4

1

Pulsation Criteria in 7.9.2.6.2.2.1 and Pressure Drop Criteria in 7.9.2.6.3.1

Met?

Design Approach 1 Analysis Complete

Revise Design

Yes No

X

Preliminary pulsationsupression device

sizing per 7.9.4.2.2. Ifspecified, minimumvolume shall be per

7.9.3.2.

Pulsation criteria in7.9.4.2.5.2.2.1 and pressure

drop criteria in 7.9.4.2.5.3.1 met?

No

Revisedesign

YesDesign approach 1analysis complete

Shows the step in 7.9.4.2.5.2

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

113




NOTE In the event that pulsation suppression device design is fixed, it may be necessary to accept higher pressure drop or perform a Design Approach 3 analysis.


Shows the step in 7.9.2.6.2Preliminary PulsationSuppression DeviceSizing per 7.9.2.3. Ifspecified, minimump

7.9.1.4

PreliminaryPi i

Complete?

PerformPre-Study

per 7.9.2.4.4

Perform AcousticSimulation per 7.9.2.4.5

Yes

No

Pulsation Criteria7.9.2.6.2.1 and7 9 2 6 2 2pressure drop criteria

7.9.2.6.3.1 and CompressorSystem shaking force

criteria 7.9.2.6.2.3.2M t?

Complete Maximum PipingSpan Table and Vessel

Mechanical NaturalFrequency Calculations per

7.9.2.4.6Yes

ReviseDesign

No (seeNote)

1

2

3

4

X

ReviseDampener

Design

7.9.2.4.4 and7.9.2.6.2.3.2Criteria Met?

Yes

No

Is Separation MarginCriteria in 7.9.2.6.3.2

met?

No Yes

Design Approach 2 iscomplete. No furtheranalysis is required.

Is PulsationSuppression Device

design to be completeand final before

completion of pipinglayout?

Yes

No

Pulsation SuppressionDevice design is final andreleased for order. Future

design changes can only bemade to the piping system.

Complete pipingsystem design

and layout.

Preliminary pulsationsuppression device

sizing per 7.9.4.2.2. Ifspecified, minimum volume shall be per

7.9.3.2

Preliminary pipinglayout complete?

No

Yes

Perform acousticsimulation per 7.9.4.2.3.5

Pulsation criteria7.9.4.2.5.2.1 and pressuredrop criteria 7.9.4.2.5.3.1and compressor system

shaking force criteria7.9.4.2.5.2.3.3.

Revise design

No (see Note)

No

Yes

Complete maximum pipingspan table and vessel

mechanical naturalfrequency calculations per

7.9.4.2.3.6.

Complete pipingsystem design

and layout.

Is pulsationsupression device

design to be completeand final before

completion of pipinglayout?

Yes

No

Shows the step in 7.9.4.2.5.2

Yes

7.9.4.2.3.4 and 7.9.4.2.5.2.3.3criteria met?

No

Performpre-study

per 7.9.4.2.3.4

Revisedampener

design

Pulsation suppressiondevice design is final andreleased for order. Future

design changes can only bemade to the piping system.

YesIs separation margincriteria in 7.9.4.2.5.3.2

met?

Design approach 2 iscomplete. No furtheranalysis is required.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on





Preliminary pulsation suppression device sizing per7.9.4.2.2. If specified, minimum volume shall be per

7.9.3.2.

Shows the step in 7.9.4.2.5.2X

YesPerform acoustic

simulation per 7.9.4.2.3.5

Revisepulsation

suppressiondevice or

pipingsystemdesign

(see Note 3)

Pulsation criteria7.9.4.2.5.2.1 and 7.9.4.2.5.2.2.2

and pressure drop criteria7.9.4.2.5.3.1 met?

No

Yes

Preliminary pipinglayout complete?

No

No

Is the pulsationsuppression device

design to becompleted before

completion ofpreliminary piping

layout?

Yes

Yes

No7.9.4.2.3.4 and7.9.4.2.5.3.1ccriteria met?

Performpre-study per

7.9.4.2.3.4

Revisedampener

design

Completepipingsystemdesign

andlayout.

Pulsationsuppression

device design isfinal and releasedfor order. Future

design changes canonly be made to

the piping system.

No YesHas allowance to

exceed the pulsationcriteria in 7.9.4.2.5.2.1 or

7.9.4.2.5.2.2.3 beenagreed upon?(see Note 1)

No

Yes

Can the pulsationcriteria be met by

exceeding the pressure drop criteria

in 7.9.4.2.5.3.1c?(see Note 2)

No

Has allowance toexceed the pressure

drop criteria in7.9.4.2.5.3.1c been

given to enablecompliance with thepulsation criteria?

Yes

And

Step 3amechanical analysis

of compressor systemand piping system per

7.9.4.2.4.2

Revise pulsationsuppression

device and/orpiping system

and/or structuralsupport design(see Note 3)

NoYes

Piping systemseparation

margin criteria7.9.4.2.5.3.2 met?

YesNo

Piping systemshaking force

criteria7.9.4.2.5.2.3.3 met?

(see Note 4)

Or

Step 3b2Perform forced mechanical response

analysis on piping system per 7.9.4.2.4.4

Revisedesign

Yes

No

Piping systemvibration criteria

7.9.4.2.5.2.4 met?

Yes No

Cyclic stress criteria7.9.4.2.5.2.5.1 met?

Yes

Design approach 3 is complete. Nofurther analysis is required.

No

Vibration and cyclic stresscriteria 7.9.4.2.5.2.5.1 met?

(see Note 5)

Step 3b1Perform forced mechanical response

analysis on compressor mechanical modelper 7.9.4.2.4.3

And And

Yes

Yes

No

No

Or

Compressorsystem

separationmargin driteria

7.9.4.2.5.3.2 met?

Compressorsystem shaking

force criteria7.9.4.2.5.2.3.3 met?

(see Note 4)

Revisepulsation

suppressiondevice and/orpiping system

and/orstructuralsupport

economically feasible to

; ,

,

,

7.9.4.2.4.4

Note 1—The default design philosophy ispressure pulsation control unless otherwisespecified. However, when evaluating theneed for possible modification to the pipingand/or pulsation suppression devices,consideration should be given to acoustical-shaking forces and the effect of pulsations oncompressor performance. Also, pulsationlevels (expressed as a percentage of linepressure) should not be used as the solecriterion for making modifications.

Note 2—For some applications that havevariable operating parameters such as speedor gas composition, it may not be technicallypossible or economically feasible tosimultaneously comply with the pulsation andthe pressure drop limitations for all operatingconditions. The purchaser and designershould mutually agree upon the mostappropriate compromise.

Note 3—When design revisions are complete,the flowchart indicates that the acoustic simulation is run again. In practice, if the revisions (for example, structural supportchanges) do not impact the acousticsimulation, then the previous simulation is stillvalid. In this case, the evaluation of the design change would begin with Step 3a; but,the designer is responsible for ensuring thatthe acoustic simulation is still valid. Also, notethat not all options for design revisions listed(for example, modifying the pulsationsuppression device) will be availabledepending upon decisions that have alreadybeen made.

Note 4—The requirement to analyze theshaking forces in Step 6 is waived if thecompressor vendor analyzes the pipingsystem vibration in Step 7 per 7.9.4.2.4.4. If theshaking forces are not analyzed, then “No” isselected and analysis proceeds to Step 7.

Note 5—The compressor vendor shall supplythe allowable vibration criteria for compressor components such as cylinders, distancepieces and crankcases. Due to the variabilityand complexity of compressor systems, it isnot possible to provide vibration criteria that,when met, eliminate the need to calculatestress.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on



API 618 Annex N(informative)

Guideline for Compressor Gas Piping Design and Preperation for an Acoustic Simulation Analysis

N.1 General

N.1.1 Any reciprocating compressor in conjunction with a piping system forms an interactive dynamic system that cannot be accurately analyzed as two separate systems. Therefore, it is virtually impossible for the pulsation system designer and the piping system designer to arrive at proposed designs on an independent basis that can be guaranteed to work in the final analysis and be cost effective.

N.1.2 This annex gives guidelines for the piping system designer which will help to minimize problems that can occur at the time of the acoustic simulation and it also outlines the information that must be available at the time of this interactive analysis. Communication between the piping system designer, the compressor vendor and the pulsation control system designer during the course of a project is important to minimize problems and develop the best overall compressor system installation. The key times of interaction are at the post order coordination meeting (see 9.1.3), early in the project, and during the interactive acoustic simulation/mechanical analysis.

N.1.3 The purchaser may elect to perform an in-house acoustic simulation, to use equipment vendor services or to use the services of a third party.

N.2 Acoustic Consideration in Piping DesignsN.2.1 The interaction of the compressor, pulsation devices and piping system produces potentially harmful pulsations when there is resonant interaction between the various elements in the system. The system designer can help to minimize this interaction by avoiding resonant lengths of pipe. When resonant lengths of pipe are used and the resonant frequency matches compressing frequency, one can expect major changes to the system as a result of the acoustic simulation analysis. The resonant length of various piping configurations is given in Equation (N-1). It is recommended that lengths of these configurations be avoided in a ±10 % band for the first four harmonics of compressor speed. The piping areas where this is most important are the sections of piping between the first major volume on the suction side and the first major volume on the discharge side. In piping areas outside major volumes, or those far enough away from the compressor(s) the potential for harmful pulsation buildup is considerably reduced.

N.2.2 For piping sections open at both ends or closed at both ends the length to be avoided can be calculated from the following:

(N-1)

where

LH is the pipe length to be avoided in meters (feet);

C is the velocity of sound in gas in meters/second (feet/second);

n is the harmonic number (1, 2, 3 and 4);

N is the compressor speed in revolutions per minute.

Examples of this are lengths between major volumes, length of headers, etc.

LH30cnN--------=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

116




N.2.3 For pipe sections open at one end and closed at the other end, the lengths to be avoided can be calculated from the following:

(N-2)

where

LQ is the pipe length to be avoided in meters (feet);

C is the velocity of sound in gas in meters/second (feet/second);

n is the harmonic number (1, 2, 3 and 4);

N is the compressor speed in revolutions per minute.

Examples of this are relief valve lines and bypass lines.

NOTE A pipe can be considered to have an open end if the diameter increases by a factor of 2 to 1 or more. Similarly, a pipe can be considered to have a closed end if the diameter is reduced by a factor of 2 to 1 or more.

N.2.4 The acoustic simulation should be carried out after a piping static stress analysis has demonstrated that the location and design of the piping restraints result in acceptable piping static stresses.

N.2.5 For variable speed compressors and/or those with varying gas composition and/or varying pressures and temperatures, the separation of resonances is more difficult to calculate and can only be handled properly with an acoustic simulation study.

N.3 Acoustic simulation studyN.3.1 The extent of the piping system to be analyzed by acoustic simulation techniques is usually defined as all associated piping systems to a point where piping changes will have only insignificant effects on the parts of the system under study and in determining the acoustic characteristics of the design. Typically, these requirements are satisfied by beginning the simulation with the inlet of a major process vessel or volume on the suction side of the compressor unit(s), continuing through all interstage systems (if any) and terminating the study at the outlet of a major process vessel or volume on the discharge side of the unit(s). Included are branch connections to or from this system, such as relief valve lines and bypass lines.

N.3.2 When major volumes do not exist or are very remote from the compressor, suitable piping lengths are included in the simulation, such that the pulsation levels are sufficiently low so as to minimize the potential of pulsation driven vibration problems.

N.4 Information requiredN.4.1 The acoustic simulation requires a considerable amount of information in order to be properly performed. The purchaser and the vendor should agree upon who is responsible for the development and compilation of the following information:

N.4.1.1 Data sheets showing all compressor operating conditions, analysis of all gases to be compressed, and all unloading steps.

N.4.1.2 Isometric drawings showing all lengths (between bends, valves, diameter changes, etc.) and line sizes and schedules for the complete piping system, including all branch lines and relief valve lines. If a mechanical study is included, the distance between the supports and the type of support and clamp used at each location must be shown on the isometrics. A detailed drawing of each type of support and clamp is required.

LQ15CnN----------=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




N.4.1.3 Piping and instrument diagrams (P&ID’s) are required to ensure that all piping and equipment that may effect the study are included.

N.4.1.4 Layout drawings are required to help determine the practicality of any proposed modifications. Reproducible drawings are useful since they can be marked up and copies can be included in the report.

N.4.1.5 Complete information must be supplied on all of the piping up to and including the first large volume in the suction, the interstage and the discharge piping. Every branch must be included up to a shutoff valve or a large volume.

N.4.1.6 Any orifice or other flow-resistive device must be shown and complete details provided.

N.4.1.7 Detailed drawings of each vessel, showing the location of all nozzles, the internal diameter and the length, as well as details of any vessel internals are required. Normal liquid levels and design pressure drops in these vessels must be shown.

N.4.1.8 TEMA data sheets, or their equivalent, must be provided for all heat exchangers. The data sheets must show whether gas is through the tubes or in the shell; the number, length and gauge of tubes; whether the tubes are plain or finned; the number of passes; the I.D. of the shell; the gas temperature in and out; the gas pressure drop; and the dimensions of the header. A dimensional drawing is preferred.

N.4.1.9 If there are different gas routings, a complete description must be included to show the relative positions of all the valves for each routing. If different process gases are involved, the description must show which routings apply to which gases. Flow from/to any sidestream must be shown, including gas analysis, flow rate and direction.

N.4.1.10 If gas filters are used, the type of filter, internal diameter, length and element pressure drop must be supplied. A dimensional drawing is desirable.

N.4.1.11 When two or more compressors are connected to the same piping system, a clear description of how they will operate (such as unloading steps, speed differences, etc.) is required.

N.4.1.12 Detailed dimensional drawings on each suppressor showing the location of all nozzles, lengths, internal diameters and details on suppressor internals, if any.

N.4.1.13 The information in Table N.1 is required from the compressor vendor.

N.4.2 It is highly recommended that a piping system design representative who is familiar with the piping system be present at the acoustical simulation analysis, in order to make piping changes as the need arises.

Table N-1—Compressor Data Required for Acoustic Simulation

Compressor Data Design Approach2, 3a, 3b1, 3b2

Compressor dataHead end fixed clearance volumeHead end unloader volume(s)Crank end fixed clearance volumeCrank end unloader volume(s)

Casting drawingsCompressor cylinder (internal passage)Distance piece (inertia and stiffness)Crosshead guide (inertia and stiffness)

Assembled cylinder weight

XXXX

X

XXXX

XXXX

Support drawingsCylinder support drawingsCrosshead guide support drawingsDistance piece support drawingsPulsation suppressor support drawings

XXXX

Compressor Dynamic Valve Analysis Results XCrank angles between manifolded cylinders X

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on



API 618 Annex O(informative)

Guidelines for Sizing Low Pass Acoustic Filters

O.1 General

The general configuration for an acoustic filter is shown in Figure O-1.

The lowest acoustic resonant frequency of the filter system, is referred to as Helmholtz frequency (fH). An accepted generalized equation for Helmholtz frequency is

(O-1)

where

fH is the Helmholtz frequency in Hertz;

c is the velocity of sound in gas in meters per second (feet per second);

V1 is the volume in cylinder bottle (chamber) in cubic meters (cubic feet);

V2 is the volume in filter bottle (chamber) in cubic meters (cubic feet);

μ is the acoustic conductivity in meters or feet.

where

A is the internal cross-sectional area of choke in square meters (square feet);

Lc is the actual length of choke in meters (feet);

Figure O-1—Nonsymetrical Filter

fHc

2π------ μ

V1

----- μV2

-----+

12---

=

μ ALc 0.6Dc+------------------------- A

L---= =

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

119




L is the acoustic length of choke in meters (feet);

Dc is the diameter of choke in meters (feet).

The filter cut-off frequency (fco), which is the frequency above which pulsation attenuation is achieved, is usually defined as follows

The acoustic filter can be either symmetrical or non-symmetrical. As shown in Figure O-1 and Equation (1), the non-symmetrical filter can have different volumes (lengths and diameters) and a different length of choke. For a symmetrical filter, the volumes are equal and the acoustic length of the choke L is equal to the length of each volume that is Lc = L. This is valid when Lc is much larger than Dc. This also means that the diameter of each volume is equal.

Substituting into Equation (O-1), the Helmholtz frequency for a symmetrical filter becomes:

(O-2)

where

DB =inside diameter of pulsation suppression devices in meters (feet).

O.2 GuidelinesThe following guidelines may be used for the preliminary sizing of acoustic filters.

O.2.1 Selection of Helmholtz Frequency (fH)

The preferred Helmholtz frequency is:

where

s is the compressor speed in r/min.

Only when conditions are such that it is uneconomical, or physically impractical, should a higher Helmholtz frequency be considered, that is, only when pressure drop is very critical—as in the case of low suction pressure, or when space is limited by the compressor system layout. In that instance, a higher Helmholtz frequency may be chosen. Generally, the Helmholtz frequency should not be higher than

unless the acoustic simulation proves otherwise. For compressor speeds above 500 rpm, the Helmholtz frequency should not exceed:

fco 2( )fH=

fH1

2------- c

π---

Dc

LDB

----------=

fHs

85------=

fHs

45------=

fHs

85------=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




O.2.2 Relationships of Filter Element Diameters

For acoustic considerations, the diameter of the cylinder bottle (chamber) V1 should be equal to, or greater than, two times the diameter of the cylinder connection (flange). Larger ratios generally improve acoustic characteristics but may result in unacceptable mechanical characteristics. The final design ratio must be determined by both acoustic and mechanical analysis.

The diameter of the filter bottle (chamber) V2 should be equal to, or greater than, three times the diameter of the line piping.

O.2.3 Relationship of Filter Element Lengths

The preferred filter system is with equal lengths of cylinder bottle (chamber), choke tube and filter bottle (chamber) that is L1 = Lc = LZ. In cases where the physical restrains (piping layout) and the required sizes do not permit equal lengths, the next best alternative is with equal length of choke and filter (chamber) L1 Lc = L2.

O.2.4 Sizing of the diameter of the choke tube (DC)

Unless otherwise specified, calculate the maximum allowable pressure drop per the applicable Equation (13) in 7.9.4.2.5.2.3.2. Using maximum allowable pressure drop and appropriate pressure drop relationship, calculate the minimum diameter choke tube which can be used considering all operating conditions expected.

O.2.5 Acoustic Simulation of the Preliminary Design

These sizing guidelines cannot be used to determine the final dimensions of the filter elements without an acoustic simulation. Once the preliminary design of the filter is completed, an acoustic simulation must be performed to evaluate the unbalanced shaking forces within the components of the filter and the pulsation levels at the nozzles. Adjustments to the filter component dimensions are almost always made during the acoustic simulation.

≠

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on



API 618 Annex P(informative)

Piping and Pulsation Supression Device Shaking Force Guidelines

P.1 General

Shaking force guidelines provide an alternative evaluation tool to determine the need for forced mechanical response analysis. The foundation for deriving appropriate shaking force guidelines is knowledge of stiffness and acceptable vibration for the structure. Knowledge of the structure’s stiffness may be based on experience with similar structures, or based on calculation varying in precision from assuming minimum stiffness values to stiffness determined by detailed structural simulation. Similarly, knowledge of acceptable vibration may be experience based or determined by detailed structural modeling.

The adopted shaking force guidelines work in concert with the separation margin and the design vibration guidelines. The simplification to a non-resonant shaking force guideline requires simultaneous compliance with both the shaking force and separation margin guidelines.

Figure P-1 shows the piping non-resonant shaking force guideline versus a corresponding shaking force guideline accounting for resonance. The non-resonant shaking force guideline results in acceptable vibration when the separation margin guidelines are met. Meeting both the minimum natural frequency guideline and the non-resonant shaking force guideline ensures acceptable vibration for the first and second orders of compressor speed. Meeting both the 20 % separation margin from natural frequencies and the non-resonant shaking force guideline will also ensure acceptable vibration at higher orders of compressor speed. Therefore, the piping non-resonant shaking force guideline applies when the separation margin guidelines are met. When the separation margin guidelines are not met, much lower piping shaking forces are required to ensure acceptable vibration.

Figure P-2 shows the pulsation suppression device non-resonant shaking force guideline versus a corresponding shaking force guideline accounting for typical resonance. As with the piping, the pulsation suppression device non-resonant shaking force guideline applies when the separation margin guidelines are met. When the separation margin guidelines are not met, much lower pulsation suppression device shaking forces are required to ensure acceptable vibration.

Figures P-1 and P-2 demonstrate the importance of meeting the separation margins when applying the non-resonant shaking force guidelines.

P.2 Orientation of Shaking Forces

P.2.1 Piping Orientation

The piping non-resonant shaking force guideline applies to shaking forces acting along the piping axis, as shown in Figure P-3, which cause non-resonant vibration. The piping non-resonant shaking force guideline cannot be applied when resonant vibration occurs in either the run containing the shaking force or in adjoining perpendicular piping.

P.2.2 Cylinder Mounted Pulsation Suppression Device Orientation

The pulsation suppression device non-resonant shaking force guideline applies to shaking forces acting along the pulsation suppression device axis, as shown in Figure P-4, which cause non-resonant vibration.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

122




P.3 Determination of Effective Static Stiffness

P.3.1 General

Suggested equations for effective stiffness of piping and pulsation suppression devices are provided in P.3.2 and P.3.3. In addition, meeting the minimum mechanical natural frequency guideline can be used to establish a required minimum effective static stiffness. Equations for minimum effective static stiffness of piping and pulsation suppression devices are also given below.

Figure P-1—Non-dimensional Piping Shaking Force Guidelines

Figure P-2—Non-dimensional Pulsation Supression Device Shaking Force Guidelines

0.01

0.1

1

0.1 1 10

Non-resonant Resonant

SF K

n ks V (2)

Frequency / 1st Transverse Natural Frequency

0.01

0.1

1

0.1 1 10

Non-resonant Resonant

SF K

kt V (2)

Frequency / 1st Pulsation Suppression Device Natural Frequency

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




P.3.2 Piping Effective and Minimum Static Stiffness

P.3.2.1 The effective axial stiffness of piping is usually determined by the axial stiffness of the supports as shown in Equation (P-1).

(P-1)

Figure P-3—Shaking Forces along the Piping Axis

Figure P-4—Shaking Forces along the Pulsation Supression Device Axis

TransverseVibration

Axial Vibration

Axial Shaking Force,Axial Stiffness

Shaking Force, Vibration


Cylinder

Suction PulsationSuppression Device

Discharge PulsationSuppression Device

Cylinder



keff 0.66 n ks××=For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




where

keff is the effective static stiffness along the piping where the shaking force acts in N/mm (lbf/in.);

0.66 is the dynamic design factor to account for reduced stiffness as resonance is approached (see Figure P-1);

n is the number of active axial supports (see P.2.1.1 when supports are not collinear with the pipe run where the shaking force is acting);

ks is the axial static support stiffness in N/mm (lbf/in.).

To satisfy the minimum natural frequency guideline (see clause 7.9.4.2.5.3.2), the active axial support stiffness must at least meet the minimum ks defined in Equation (P-2). Equation (P-2) satisfies the minimum required support stiffness for all practical piping configurations with maximum acceptable spans (see P.2.1.2 and P.2.1.3 regarding lumped masses and equipment).

(P-2)

where

CKS is the constant dependent on support stiffness units (SI units: 1/130; USC units: 25);

A is the pipe cross-sectional metal area in mm2 (in.2);

= π/4 × (OD2 – ID2);

I is the pipe cross-sectional area moment of inertia in mm4 (in.4);

=π/64 × (OD4 – ID4);

OD is the pipe outer diameter in mm (in.);

ID is the pipe inner diameter in mm (in.);

fn,T is the minimum transverse natural frequency in Hz (see P 3.2.5);

n is the number of active supports (or n = 2 as a minimum, see P 3.2.7).

The actual value of ks should be determined and compared to the minimum ks requirement. When the actual ks is greater than minimum ks there is sufficient support stiffness to constrain higher shaking forces [up to the limit defined by Equation (10) in 7.9.4.2.5.2.3.2 and P.1]. When the actual ks is lower than minimum ks, the minimum mechanical natural frequency separation margin guideline will not be met, and the possibility of operating on resonance within the first two orders of compressor speed must be considered.

The actual and minimum ks values should also be compared with the range of typical support stiffness values found in Note 2 of 7.9.4.2.5.2.3. The actual ks should fall within the range of the corresponding support type. When the minimum ks required exceeds the range of the corresponding support type, the actual ks must be carefully determined and either a sufficiently stiff type of structure must be used or the shaking force guideline must be reduced.

P.3.2.2 When supports are not collinear with the pipe run where the shaking force is acting (such as the middle section of U, Z or 3D bends), the perpendicular pipe sections clamped by the supports may be more flexible than the supports, and keff must correspondingly be reduced. Flexibility of the perpendicular pipe section should be considered when the support is offset greater than 25 % of the maximum acceptable span length.

minimum k s CKS A0.75 I0.25 fn,T 1.5 n 1– n⁄( )×××=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




P.3.2.3 The calculation of minimum ks does not include lumped masses, but results in a conservative shaking force criteria when the separation margin minimum natural frequency guideline is satisfied. To ensure the separation margin criteria are satisfied, the support requirements of each lumped mass, such as valves, must additionally be provided.

P.3.2.4 The calculation of minimum ks is based on the minimum number of supports required to satisfy the minimum mechanical natural frequency guideline. When more than the minimum number of supports are present, the minimumks can be reduced by the ratio of the minimum number required divided by the number of active supports.

P.3.2.5 The minimum transverse natural frequency (fn,T) required is dependent on the frequency of the shaking force. For example, to comply with the first part of the separation margin criteria, it is typically chosen as 2.4 times maximum rated speed. In higher speed compressors, this is not always practical to achieve, however Equation (P-2) can still be used to determine the minimum support stiffness required for the given fn,T.

P.3.2.6 The minimum axial support stiffness requirements of vessels and equipment (such as secondary pulsation dampeners, separators, cooler sections and heat exchangers) should be determined directly from the equipment mass to meet the separation margin criteria.

P.3.2.7 The number of active supports include all axial restraints along the run containing the shaking force and restraints offset from the run less than 25 % of the maximum acceptable span length.

P.3.2.8 Vessels and equipment may also be restraints. See examples in Figure P-5.

P.3.2.9 Pipe wall thickness is specified based on design pressure using applicable design codes and is not increased as a method to control vibration.

P.3.3 Cylinder Mounted Pulsation Suppression Device Effective and Minimum Static Stiffness

The effective axial stiffness of cylinder mounted pulsation suppression devices is the result of a complex interaction between many structures requiring detailed analysis or field measurement to determine. Expressed in the same form as the effective stiffness for piping yields Equation (P-3).

(P-3)

Figure P-5—Examples of Shaking Force Restraints

L = Lspan / 4

n = 3

L = Lspan / 4

n = 3

L = Lspan / 4

n = 3

Shak

ing

Fo

rce

Shak

ing

Fo

rce

Shak

ing

Fo

rce

keff 0.66 kt×=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




where

keff is the effective static stiffness along the pulsation suppression axis where the shaking force acts in N/mm (lbf/in.);

0.66 dynamic design factor to account for reduced stiffness as resonance is approached (see Figure P-2);

kt is the pulsation suppression device axial static support stiffness in N/mm (lbf/in.).

Noting that the cylinder assembly stiffness is a critical component of the pulsation suppression device stiffness, and considering reasonable supporting of typical cylinder assemblies, a minimum kt can be established based on the number of cylinders as shown in Equation (P-4).

where

kmin is the minimum pulsation suppression device axial static stiffness per cylinder nozzle (SI units: 50 × 103 N/mm; USC units: 3 × 105 lbf/in.);

ncyl is the number of cylinders attached to pulsation suppression device.

Caution—Long cylinder nozzles, double compartment and small cross-section distance pieces may not provide the minimum axial stiffness.

Also, on higher speed units, larger and higher pressure cylinders may require greater than the minimum axial stiffness to meet the minimum natural frequency guideline. Cylinders heavier than shown in Table P-1 may require additional supporting.

The maximum cylinder assembly weight for compressor speeds not shown in the Table P-1 can be obtained using Equation (P-5).

where

Wcyl is the maximum cylinder assembly weight in N (lbf);

Cc is the constant dependent on weight and stiffness units (SI units: 8.0 × 109; USC units: 1.8 × 109);

S is the compressor rotational speed in r/min.

P.4 Evaluation of Shaking Forces

Making modifications to reduce predicted shaking forces is referred to as shaking force control (see API 688 for a complete discussion of the various control methods). As a minimum, shaking force control is required for all cylinder

Table P-1—Cylinder Assembly Weights Possibly Requiring Strengthening

Maximum Compressor Speed (rpm) 300 600 900 1000 1200 1500

Cylinder Assembly Weight (N) 89000 22000 9800 8000 5500 3500Cylinder Assembly Weight (lbf) 20000 5000 2200 1800 1250 800

minimumkt kmin n× cyl=

Wcyl Cc S2⁄=

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on




mounted pulsation suppression devices. When the purchaser agrees, shaking force control may be used in place of piping pressure pulsation guidelines.

The first step in the shaking force control method is to determine the shaking force guidelines using the equations and methods shown in 7.9.4.2.5.3 and Annex P. Then, the predicted shaking forces are compared to the shaking force and separation margin guidelines. When predicted shaking forces do not meet these guidelines, then one or more of the following actions must be taken to obtain acceptable results:

— modify system acoustics to reduce predicted shaking forces;

— modify support structure to meet separation margin guidelines;

— perform forced mechanical response analysis and satisfy vibration guideline.

Combinations of the above options are often employed in an iterative fashion to arrive at acceptable predicted shaking forces for the entire system.

For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

API Monogram®

Licensing Program Sales: 877-562-5187

(Toll-free U.S. and Canada)(+1) 202-682-8041(Local and International)

Email: [email protected]: www.api.org/monogram

API Quality Registrar (APIQR®)• ISO 9001• ISO/TS 29001• ISO 14001• OHSAS 18001• API Spec Q1®

• API Spec Q2®

• API QualityPlus®

• Dual RegistrationSales: 877-562-5187


Email: [email protected]: www.api.org/apiqr

API Training Provider Certification Program (TPCP®) Sales: 877-562-5187


Email: [email protected]: www.api.org/tpcp

API Individual Certification Programs (ICP®) Sales: 877-562-5187


Email: [email protected]: www.api.org/icp

API Engine Oil Licensing andCertification System (EOLCS)Sales: 877-562-5187


Email: [email protected]: www.api.org/eolcs

Motor Oil MattersSales: 877-562-5187


Email: [email protected]: www.motoroilmatters.org

API Diesel Exhaust Fluid Certification Program Sales: 877-562-5187


Email: [email protected]: www.apidef.org

API Perforator Design Registration Program Sales: 877-562-5187


Email: [email protected]: www.api.org/perforators

API WorkSafe®

Sales: 877-562-5187(Toll-free U.S. and Canada)(+1) 202-682-8041(Local and International)

Email: [email protected]: www.api.org/worksafe

API-U™


Email: [email protected]: www.api-u.org

API Data®


Service: (+1) 202-682-8042Email: [email protected]: www.APIDataNow.org

API Publications Phone: 1-800-854-7179

(Toll-free U.S. and Canada)(+1) 303-397-7956 (Local and International)

Fax: (+1) 303-397-2740Web: www.api.org/pubs

global.ihs.com

API Standards Sales: 877-562-5187


Email: [email protected]: www.api.org/standards

THERE’S MOREWHERE THIS CAME FROM

REQUEST AQUOTATIONwww.api.org/quote



For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

Product No. C68801



For Com

mittee B

allot

5481

Not For

Genera

l Dist

ributi

on

Pulsation and Vibration Control in Positive Displacement ......API Standards Department, telephone...

Documents

Transcript of Pulsation and Vibration Control in Positive Displacement ......API Standards Department, telephone...