Orifice Coefficients For Critical Flow Provers
Authors: Stinson D.L. 
Published: December 2007

Publication Rights Reserved
This paper is to be presented at the 39th Annual Fall Meeting to be held in Houston, Tex., on Oct. 11–14, 1964, and is considered property of the Society of Petroleum Engineers. Permission to publish is hereby restricted to an abstract of not more than 300 words, with no illustrations, unless the paper is specifically released to the press by the Editor of the Journal of Petroleum Engineers or the Executive Secretary. Such abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in JOURNAL OF PETROLEUM TECHNOLOGY or SOCIETY OF PETROLEUM ENGINEERS JOURNAL is granted on request, providing proper credit is given that publication and the original presentation of the paper.
Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.

Abstract
The critical flow prover has been found to be a rugged accurate instrument, well adapted for determining gas flow rates under field conditions. During some twenty-five years of extensive use, only one set of orifice coefficients has been generally used, apparently without a critical examination of their values. Several of the suggestions of the original authors, Rawlins and Schellhardt, have been ignored in many of the applications of these coefficients. A brief investigation of the inter relations of these coefficients by means of their discharge per unit area indicates differences of approximately five per cent between the expected values and the actual coefficients. These differences indicate that the values of these coefficients should be redetermined, or that the nature of critical flow through such orifices is much more complicated than has been generally accepted.

Introduction
The critical flow prover has long been recognized as a valuable tool for determining gas flow rates. Because it is relatively insensitive to obstructions in the flow line and to turbulence, it is suitable for use at the wellhead or near the separator on temporary installations where it would be inconvenient to use a conventional orifice meter. The flow through a critical flow prover does not depend upon the differential pressure or down stream pressure once the upstream pressure is high enough with respect to the downstream pressure. Accordingly, it is inherently a more accurate method of measuring gas flow rates than a conventional orifice meter, since it involves the determination of one less factor.
In 1935 Rawlins and Schellhardt completed their work on "Back-Pressure Data on Natural-Gas Wells and Their Application to Production Practices". Included in this publication were the designs of two critical flow provers and tables of the average coefficients which they obtained during the evaluation of these provers. In the ensuing years these tables have been copied, converted, and used throughout the oil and gas industry without considering their origin or some of the original authors' recommendations. Considering the effort involved in checking or improving upon this original work, it is not surprising that these coefficients have not been checked. However, in view of the wide spread applications of these tables it is desirable to point out their limitations.