API MPMS 13.3-2016 Manual of Petroleum Measurement Standards Chapter 13.3 Measurement Uncertainty (FIRST EDITION).pdf

1、Manual of Petroleum Measurement Standards Chapter 13.3 Measurement Uncertainty FIRST EDITION, MAY 2016Special 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

2、API nor any of APIs 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

3、use, or the results of such use, of any information or process disclosed in this publication. Neither API nor any of APIs 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

4、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 respo

5、nsibility 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 n

6、ot 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

7、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. Users of this St

8、andard 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

9、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 2016 American Petroleum InstituteForeword This s

10、tandard is in response to the call by industry and regulators for a standardized method to determine the uncertainty associated with various aspects of petroleum measurement. This method is based on the 2008 edition of the International Organization of Standards (ISO) Guide to the Expression of Unce

11、rtainty in Measurement (GUM)- JCGM 100:2008-which was developed to be a guide for the writers of technical standards. Although this document could be used for analysis of an entire system or facility, that use is outside the scope of the document. The uncertainty estimate is only as good as the unde

12、rlying data and engineering judgment. All of the numerical values used and assumptions made must be documented. The statement in Section 3.4 of the ISO GUM reproduced below applies to this standard: “Although this Guide provides a framework for assessing uncertainty, it cannot substitute for critica

13、l thinking, intellectual honesty and professional skill. The evaluation of uncertainty is neither a routine task nor a purely mathematical one; it depends on detailed knowledge of the nature of the measurand and of the measurement. The quality and utility of the uncertainty quoted for the result of

14、a measurement therefore ultimately depend on the understanding, critical analysis and integrity of those who contribute to the assignment of its value.” Nothing contained in any API publication is to be construed as granting any right, by implication or otherwise, for the manufacture, sale, or use o

15、f 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 spe

16、cification. 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

17、 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 Inst

18、itute, 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-ti

19、me 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 re

20、visions are invited and should be submitted to the Standards Department, API, 1220 L Street, NW, Washington, DC 20005, standardsapi.org. iiiContents Page 1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21、. . . . . . . . . . . . . 1 2 Normative References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Terms, Definitions, Acronyms, Abbreviations, and Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . .

22、 . . . . . . . . . . 2 3.1 Terms and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 Acronyms, Abbreviations, and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23、. . . . . . . . . . . . . . . . . . 6 4 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.2 Measurement Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 4.3 True Quantity Value. . . . . . . . . . . . . . . . .

25、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.4 Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.5 Statist

26、ical Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.6 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27、 . . . . . . . . . . . . . . . . 8 4.7 Confidence Level (Confidence Interval) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 4.8 Type A vs Type B Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28、 . . . . . . . . . . . . . . . . . . . . . . 9 4.9 Representative Samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.10 Mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.11 Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.12 Standard Uncertainty . . . . . . . . . .

30、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.13 Degrees of Freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.14 Determinin

31、g Confidence Interval. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.15 Correlation Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32、 . . 13 4.16 Independent and Dependent Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.17 Combining Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33、. . . . . . . . . 13 4.18 Probability Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5 Evaluating Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34、 . . . . . . . . . . . . . . . . . . . . . . 17 5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.2 Determine the Measurement Model . . . . . . . . . . . . . . . . . . . . .

35、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.3 Record Elemental Error Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.4 Create a Primary Uncertainty Table. . . . . . . . . . . . . . . . .

36、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.5 Classify and Evaluate Uncertainty Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.6 Determine Sensitivity Coefficients . . . . . . . . . . . . . . . . .

37、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.7 Determine Correlation Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.8 Determine Combined Standard Uncertainty . . . . . . . . .

38、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.9 Determine Expanded Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.10 Reporting Results . . . . . . . . . . . . . . . . . . . .

39、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Annex A (informative) Monte Carlo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Annex B (informative) Examples . . . . .

40、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Annex C (normative) Formal Proof of Equation 7(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Annex D (informative) Report

41、Significant Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Annex E (normative) Using a Simplified Estimate of Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Bibliography . . . . . . . . . . . . . . . .

42、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 vPage Figures 1 Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43、. . . . 16 2 Triangular Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3 Rectangular Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44、. . . . . . . . . . . . . . . . 17 4 Relationship between Measurement Model and Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5 Relationship between the Uncertainty of the Measurement Model and the Uncertainty of the Inputs. . 19 6 Hierarchal Relationship

45、of all Uncertainty Components of a Measurement Model. . . . . . . . . . . . . . . . . . 19 D.1 Uncertainty of the Transmitter Verification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 D.2 Uncertainty of the Transmitter After Adjustment. . .

46、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Tables 1 t-Distribution Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 D.1 U 95 , Probable Error and Effective

47、 Increment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 E.1 Range to Standard Deviation Conversion Factors, D(n). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 E.2 Student t Factors for Individual Measurements

48、 at Various Confidence Levels. . . . . . . . . . . . . . . . . . . . . 56 Matrices 1 Universe of Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2 Correlation Matrix (Informative). . . . . . . . . . . . .

49、 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 viMeasurement Uncertainty 1 Scope This standard establishes a methodology to develop uncertainty analyses for use in writing API Manual of Petroleum Measurement Standards (MPMS) documents that are consistent with the ISO GUM and NIST Technical Note 1297. 2 Normative References The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (inc