A Statistical Meter-Proving Method
Authors: Su Shiaw Y. 
Published: December 2007

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Introduction
The general requirement for meter proving is stated in API Standard 1101:"A positive displacement (PD) meter should be proved in its normalinstallation at the expected operating rate of flow, under the pressure andtemperature at which it will normally operate, and on the liquid which it willmeasure in normal condition.... When a meter is measuring several differentliquids, the meter should be proved on each liquid." Examination of API andother industry procedures for proving meters indicates Tat the procedures forproving meters indicates Tat the accepted ways vary greatly. For example, aminimum of five runs for proving the turbine meter was suggested in APIStandard 2534 and a minimum of two runs was mentioned in API Manual ofPetroleum Measurement Standards for proving the Petroleum Measurement Standardsfor proving the PD meters. In industry, Sohio reported using a PD meters. Inindustry, Sohio reported using a 12-run program to prove some PD meters. SunCo. has used a procedure of repeating proving runs until three consecutive runsare within a prescribed tolerance. Another procedure uses 12 runs, theneliminates the highest and lowest readings. The number of proving runs used inthese procedures seems arbitrarily determined. None of the procedures seemsarbitrarily determined. None of the procedures mentions the use of thestatistical procedures mentions the use of the statistical properties of themeter readings to derive the exact properties of the meter readings to derivethe exact runs required. This observation is supported by Bloser of EmersonElectric Co. He stated, "No standard has been set of the frequency ofproving, though it is related directly to the accuracy of a meter and provingsystem." It is true that too few runs will provide an unacceptable level ofaccuracy. Conversely, too many runs will waste time and delay shipment. Theneed for determining an adequate number of runs is apparent
This study details a simple procedure designed for meter proving todetermine the exact number of proving runs required, based on the statisticalproving runs required, based on the statistical characteristics of the seriesof meter readings. The meter factor derived from these readings will beaccurate to within the desired tolerance with certain confidence.

Analysis of Meter Proving Run Data
Considerable proving-run field data (provided by Sun Pipe Line Co.) wereanalyzed. Some observations based on this analysis follow.The series ofmeter counts (or readings) in each calibration does not show any upward ordownward trend under normal operation. Each series appears to be distributedrandomly around its mean level. Typical examples of the series of meter countsare shown in Fig. 1. The mean and estimated standard deviation of the metercounts, as well as its coefficient of variation, also are shown.Using theKolmogorov-Smirnov Tests to check the normality assumption of the series, thehypothesis is rejected at 5% significance level only in one of 27 cases tested.Thus, the probability distribution of the series of meter counts reasonably canbe assumed as normal.The coefficient of variation is inversely proportionalto the net prover volume. Also, proportional to the net prover volume. Also, increasing the ratio of the net prover volume to the flow through the meterwill reduce the coefficient of variation.

Development of Meter Factor
After each meter calibration, a meter factor is calculated by taking theratio of the adjusted prover volume to the average of meter counts adjusted bya known temperature factor.
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