1、Orifice Flow CoefficientEquation ComparisonSTP-TS-084STP-TS-084 ORIFICE FLOW COEFFICIENT EQUATION COMPARISON Prepared by: Casey Hodges CEESI Measurement Solutions, Inc. Date of Issuance: June 27, 2018 This publication was prepared by ASME Standards Technology, LLC (“ASME ST-LLC”) and sponsored by Th
2、e American Society of Mechanical Engineers (“ASME”). Neither ASME, ASME ST-LLC, the author(s), nor others involved in the preparation or review of this publication, nor any of their respective employees, members, or persons acting on their behalf, makes any warranty, express or implied, or assumes a
3、ny legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe upon privately owned rights. Reference herein to any specific commercial product, process, or service by trade
4、 name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by ASME ST-LLC or others involved in the preparation or review of this publication, or any agency thereof. The views and opinions of the authors, contributors and review
5、ers of the publication expressed herein do not necessarily reflect those of ASME ST-LLC or others involved in the preparation or review of this publication, or any agency thereof. ASME ST-LLC does not take any position with respect to the validity of any patent rights asserted in connection with any
6、 items mentioned in this document, and does not undertake to insure anyone utilizing a publication against liability for infringement of any applicable Letters Patent, nor assumes any such liability. Users of a publication are expressly advised that determination of the validity of any such patent r
7、ights, and the risk of infringement of such rights, is entirely their own responsibility. Participation by federal agency representative(s) or person(s) affiliated with industry is not to be interpreted as government or industry endorsement of this publication. ASME is the registered trademark of th
8、e American Society of Mechanical Engineers. No part of this document may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher. ASME Standards Technology, LLC Two Park Avenue, New York, NY 10016-5990 ISBN No. 978-0-7918-7178-
9、2 Copyright 2018 by ASME Standards Technology, LLC All Rights Reserved STP-TS-084: Orifice Flow Coefficient Equation Comparison iii TABLE OF CONTENTS LIST OF TABLES AND FIGURES v FOREWORD . ix EXECUTIVE SUMMARY x ABBREVIATIONS AND ACRONYMS xii 1 DATABASE 1 Flange Tap Database 1 Meter-Run Orifice Pla
10、te Combinations 4 Distribution of Beta Ratios . 9 Corner Tap Database 12 Distribution of Beta Ratios . 14 2 EQUATIONS 16 Flange Tap Equations . 16 2.1.1 ASME MFC-3M 2004 (ISO-RHG) . 16 2.1.2 ISO 5167 1991 (Stoltz) 17 2.1.3 AGA Report Number 3 1990 (AGA-RHG) . 18 2.1.4 PTC 19.5 Appendix 1 (Keyser) 19
11、 2.1.5 Comparison of Equations . 19 Corner Tap Equations . 24 2.2.1 ASME MFC-3M 2004 (ISO-RHG) . 25 2.2.2 ISO 5167 1991 (Stoltz) 26 2.2.3 PTC 19.5 Appendix 1 (Keyser) 26 2.2.4 Comparison of Equations . 27 3 ANALYSIS METHODOLOGY . 32 Example of Methodology . 34 4 RESULTS 36 ASME MFC-3M 2004 (ISO-RHG)
12、 2004 Flange Tap 36 ISO 5167 1991 (Stoltz) Flange Tap 41 AGA Report Number 3 1990 (AGA-RHG) Flange Tap 44 PTC 19.5 Appendix 1 (Keyser) Equation Flange Tap 48 ASME MFC-3M 2004 (ISO-RHG) 2004 Corner Tap 52 ISO 5167 1991 (Stoltz) Corner Tap . 56 PTC 19.5 Appendix 1 (Keyser) Equation Corner Tap . 60 5 E
13、XTRAPOLATION TESTING 64 Methodology 64 Flange Tap Equation Extrapolation 65 5.2.1 6-inch 0.35-0.40 Beta Ratio . 65 5.2.2 10-inch 0.35-0.40 Beta Ratio . 66 5.2.3 6-inch 0.45-0.50 Beta Ratio . 67 5.2.4 10-inch 0.45-0.50 Beta Ratio . 68 5.2.5 6-inch 0.55-0.60 Beta Ratio . 69 5.2.6 10-inch 0.55-0.60 Bet
14、a Ratio . 70 5.2.7 6-inch 0.65-0.70 Beta Ratio . 71 5.2.8 10-inch 0.65-0.70 Beta Ratio . 72 Corner Tap Equation Extrapolation 73 5.3.1 6-inch 0.35-0.40 Beta Ratio . 73 STP-TS-084: Orifice Flow Coefficient Equation Comparison iv 5.3.2 10-inch 0.45-0.50 Beta Ratio . 74 5.3.3 10-inch 0.55-0.60 Beta Rat
15、io . 75 5.3.4 10-inch 0.65-0.70 Beta Ratio . 76 6 SUMMARY AND CONCLUSIONS 78 Flange Tap Equations . 78 Corner Tap Equations . 79 STP-TS-084: Orifice Flow Coefficient Equation Comparison v LIST OF TABLES AND FIGURES Table 1-1: Contribution of Each Testing Facility to the Flange Tap Database 2 Table 1
16、-2: Fluids in the Flange Tap Database . 2 Table 1-3: Location of Meter-Run Testing 3 Table 1-4: 2-inch Meter-Run Plate Combinations . 4 Table 1-5: 3-inch Meter-Run Plate Combination 5 Table 1-6: 4-inch Meter-Run Plate Combinations . 6 Table 1-7: 6-inch Meter-Run Plate Combinations . 7 Table 1-8: 10-
17、inch Meter-Run Plat Combinations . 8 Table 1-9: 24-inch Meter-Run Plate Combinations . 8 Figure 1-1: Beta Ratio Distribution of all Data . 9 Figure 1-2: 2-inch Line Size Distribution of Beta Ratio 9 Figure 1-3: 3-inch Line Size Distribution of Beta Ratio 10 Figure 1-4: 4-inch Line Size Distribution
18、of Beta Ratio 10 Figure 1-5: 6-inch Line Size Distribution of Beta Ratio 11 Figure 1-6: 10-inch Line Size Distribution of Beta Ratio 11 Figure 1-7: 24-inch Line Size Distribution of Beta Ratio 12 Table 1-10: Contribution of Each Testing Facility to the Corner Tap Database . 13 Table 1-11: Fluids in
19、the Corner Tap Database . 13 Figure 1-8: Beta Ratio Distribution of all Data . 14 Figure 1-9: 4-inch Line Size Distribution of Beta Ratio 14 Figure 1-10: 10-inch Line Size Distribution of Beta Ratio 15 Figure 2-1: Equation 1, ASME MFC-3M 2004 (ISO-RHG) Discharge Coefficient Equation 16 Figure 2-2: E
20、quation 2, ISO 5167 1991 (Stoltz) Discharge Coefficient Equation for D 2.3 Inches . 17 Figure 2-3: Equation 3, ISO 5167 1991 (Stoltz) Discharge Coefficient Equation for D 0.65). It is not clear if any or all of this data was used in the regression of any of the equations, but it is important to unde
21、rstand this distribution when analyzing the equations. Figure 1-1: Beta Ratio Distribution of all Data Figure 1-2: 2-inch Line Size Distribution of Beta Ratio STP-TS-084: Orifice Flow Coefficient Equation Comparison 10 Figure 1-3: 3-inch Line Size Distribution of Beta Ratio Figure 1-4: 4-inch Line S
22、ize Distribution of Beta Ratio STP-TS-084: Orifice Flow Coefficient Equation Comparison 11 Figure 1-5: 6-inch Line Size Distribution of Beta Ratio Figure 1-6: 10-inch Line Size Distribution of Beta Ratio STP-TS-084: Orifice Flow Coefficient Equation Comparison 12 Figure 1-7: 24-inch Line Size Distri
23、bution of Beta Ratio Corner Tap Database The Corner Tap Database consists of data collected from the library of Paul LaNasa. The database consists of data collected at nine different laboratory facilities on a total of three fluids. The following laboratories participated: National Engineering Labor
24、atory, East Kilbride, Scotland Primary, Water National Engineering Laboratory, East Kilbride, Scotland Secondary, Air Gasunie, Westerbork, The Netherlands Secondary, Natural Gas Gaz de France, Alfortville, France Secondary, Natural Gas National Institute of Standards and Technology, Boulder, Colorad
25、o Primary therefore, each of the 23,675 data points can be evaluated against each of the four equations. The equations do, however, have different limits of operation. The database data was only analyzed for the published limits of the equation. 2.1.1 ASME MFC-3M 2004 (ISO-RHG) Refer to Figure 2-1.
26、The ASME MFC-3M 2004 (ISO-RHG) Equation is the same equation that is in the 2003 ISO 5167. This is the 1998 Reader-Harris Gallagher Equation. There is a typographical error in the term to be added for Line Sizes less than 2.8 inches, as the 0.11 should be 0.011. Figure 2-1: Equation 1, ASME MFC-3M 2
27、004 (ISO-RHG) Discharge Coefficient Equation null null 0.5961 null 0.0261nullnullnull 0.261nullnullnull 0.000521null10nullnullnullnullnullnull.nullnull null0.0188 null 0.0063nullnullnullnull.nullnull10nullnullnullnullnull.nullnull null0.043 null 0.080nullnullnullnullnullnullnull 0.123nullnullnullnul
28、lnullnullnull1 null 0.11nullnull nullnull1null nullnullnull 0.031nullnullnullnullnull0.8nullnullnullnull.nullnullnullnull.nullWhen nullnull71.12 mm null2.8 in.null, the following term shall be added: (U.S. Customary Units) null 0.011null0.75 null nullnullnull2.8 null nullnull Where: nullnullnull/nul
29、l nullnullnull nullnullnullnull nullnullnullnullnullnullnullnull nullnullnullnullnullnull nullnullnullnullnull/null nullnullnullnull nullnullnull/null nullnullnullnull nullnullnullnullnullnull nullnullnullnullnullnullnullnullnullnullnullnullnullnull.nullFor Flange taps: (a) for nullnullmm:nullnullnu
30、llnullnullnullnull nullnullnull.nullnullnull (b) for nullnullin:nullnullnullnullnullnullnull nullnullnullnull STP-TS-084: Orifice Flow Coefficient Equation Comparison 17 The ASME standard sets the limits to this equation as: (a) null null 12.5 mm null0.5 in.null (b) 50 mm null2 in.null null null nul
31、l 1000 mm null40 in.null (c) 0.10nullnullnull0.75 (d) nullnullnull 5000 and nullnullnull 170nullnullnull,nullnull,mmnull (e) nullnullnull 5000 and nullnullnull 4318nullnullnull,nullnull,in.null The uncertainty stated in ASME MFC-3M for this equation is: (a) null null0.7 nullnullnull% for 0.1 null nu
32、ll null 0.2 (b) null 0.5% for 0.2 null null null 0.6 (c) null null1.667null null 0.5null% for 0.6 null null null 0.75 2.1.2 ISO 5167 1991 (Stoltz) Refer to Figure 2-2 and Figure 2-3. The ISO 5167 1991 (Stoltz) Equation utilizes one different term when the diameter is less than 2.3 inches. Figure 2-2
33、: Equation 2, ISO 5167 1991 (Stoltz) Discharge Coefficient Equation for D 2.3 Inches nullnullnull 0.5959 null 0.312nullnull.nullnull 0.184nullnullnull0.09nullnullnullnull1nullnullnullnull null 0.0337nullnullnullnullnull null 0.0029nullnull.nullnull10nullnullnullnullnull.nullnullFigure 2-3: Equation
34、3, ISO 5167 1991 (Stoltz) Discharge Coefficient Equation for D 2.3 Inches nullnullnull 0.5959 null 0.312nullnull.nullnull 0.184nullnullnull 0.039nullnullnull1nullnullnullnull null 0.0337nullnullnullnullnull null 0.0029nullnull.nullnull10nullnullnullnullnull.nullnullThe limits of both Equation 2 and Equation 3 are: nullnullnull 1260nullnullnull 0.2 null null null 0.75 50 nullnull null null null 1000 nullnull null null 12.5 nullnull The uncertainty utilized in this analysis for the ISO 5167 1991 (Stoltz) equation was 0.5 percent.
