August 2005 

Part 3 - 

Small Volume Provers (SVPs): 

Mathematical Determination of Meter Performance Using SVPs

By Diane Lee 

This is the third in a series of articles on small volume provers (SVPs). Part 1 identified the 

various types of pipe provers, which include conventional pipe provers and SVPs and associated 

components, and definitions of the types of pipe provers. Part 2 addressed the history, design, 

and operation of small volume provers. This article, Part 3, addresses the mathematical 

determination of meter performance using SVPs. Please reference Parts 1 and 2 on the WMD 

website at www.nist.gov/owm. 

Calculating Meter Performance 

Calculation of meter performance when using SVPs is mostly automated. These provers are 

typically connected to a pulser driven by the meter and to a prover controller, which can be a 

computer that is capable of dual chronometry pulse interpolation. Dual chronometry, as 

described in part 2 of this series, enhances the pulse output by mathematically interpolating a 

fraction of a flow meter pulse. The use of a "K-Factor," a number that represents the approximate 

number of pulses a given meter generates per unit volume, along with correction factors for 

temperature and pressure, and other prover data allows the controller to calculate a "meter 

factor" that will account for measurement error. 

K-Factor 

There are two K-factors to consider when the prover controller determines the accuracy of a 

meter: the “meter base K-factor” and the “proving K-factor”. As noted above, the K-factor 

establishes a relationship between the pulses generated by the meter and volume shown by the 

indicator. It is important that the prover controller (computer) doing the calculation of the meter 

factor use the same K-factor as the indicator or that the relationship between the pulses it and the 

indictor receives is known if they do not receive pulses from the same source. 

The meter base K-factor is the coarse calibration factor used with the flow computer, which is 

typically supplied by the meter manufacturer. The meter base K-factor is used in the flow 

computer's calculation of the quantity of liquid delivered, so it must be considered during the 

testing of a meter. The proving K-factor (PKF) is used to calculate the correct meter factor 

based on the pulses it receives while a known amount of liquid passes through the SVP. 

Pulses from Same Source 

When both the flow computer and the prover controller receive pulses from the same source, the 

meter base K-factor is equal to the proving K-factor. This practice is common and there is no 

reason to calculate a proving K-factor in such instances; however, it should be confirmed that 

this is the number entered into both units or inaccuracies may result. 
Pulses from Different Sources 

The prover controller may receive pulses from a different pulser than the flow computer. This 

occurs when a separate pulser is hooked up to the meter for proving or when a mechanical 

register, which has no pulser, is tested with an SVP. In some cases, when the pulses used by the 

prover controller are provided by the flow computer, they may already be corrected by some 

factor, either a meter factor or its reciprocal known as a “meter accuracy factor”. In these cases, 

the operator must determine the proving K-factor, which is counting the pulses as product passes 

through the meter. First, a pulse counter must be attached to the pulse source, then both the flow 

computer and the pulse counter are set to zero. A volume of product equal to at least 10,000 

pulses must be passed through the meter. 

The method for determining the proving K-factor is basically the same for all types of SVPs and 

installations, but the calculation must be modified according to the method of correction used by 

the flow computer and where the pulses are being picked up. There are several different 

calculations to determine the proving K-factor for the various flow computers, so the operator 

must consult the specific instructions for the flow computer in use. The following are 

calculations for determining the proving K-factor with many types of flow computers. 

Example 1: 

Meters equipped with mechanical registers OR 

The prover controller receives pulses from a source different than the flow computer, and 

the flow computer provides an indication of volume that has not been corrected with a 

meter factor or meter accuracy factor: 

(These computers divide the total number of pulses received for each run by the gross indicated 

meter volume.) 

PKF = RIP ÷ GMI 

where: 

RIP (Raw Input Pulses) = pulses received directly from the meter; and 

GMI (Gross Meter Indication) = meter indication without automatic temperature compensation 

(ATC) 

Example 2: 

The prover controller receives pulses from a different source and the flow computer 

provides an indication corrected using meter accuracy factors OR 

The pulses received by the prover controller are provided by the flow computer and have 

been corrected using a meter accuracy factor: 

PKF = IP ÷ (GMI x MAF) 

where: 

IP = Input Pulses; 

GMI = Gross Meter Indication; and 

MAF = Meter Accuracy Factor 

Example 3: 
The prover controller receives pulses from a different source and the flow computer 

provides an indication corrected using meter factors OR 

The pulses received by the prover controller are provided by the flow computer, but have 

been corrected using a meter accuracy factor: 

PKF =(IP x MF) ÷ GMI 

where: 

IP = Input Pulses; 

MF = Meter Factors; and 

GMI = Gross Meter Indication 

The proving K-factor should be determined 3 times to obtain an average. The proving K-factor 

used in the calculation of the meter factor is the average of three runs. Agreement of the factors 

to within +/- 0.01% indicates that the pulser/counter system is operating correctly. The proving 

K-factor should be entered into the computer prior to the run 

Temperature and Pressure Corrections 

Corrections must be made for temperature and pressure because the flow meter usually operates 

at conditions that are outside the standard reference conditions to which the SVP was calibrated. 

Temperature and pressure are automatically measured during testing and this information is 

relayed to the prover controller. The prover controller makes corrections for the temperature and 

pressure effect on the prover volume (correction for the effect of temperature and pressure on the 

steel prover parts) and the effect of temperature and pressure on the liquid volume. 

Calculating Meter Error from Proving Data 

The prover controller calculates the meter error from a ratio of the corrected prover volume 

(CPV) to the corrected meter volume (CMV), which is referred to as the new meter factor 

(MFn). 

MFn = CPV÷ CMV 

where: 

CPV = (Certified Prover Volume) x (Temperature and Pressure Corrections for the prover 

volume and liquid volume); 

CMV = Average Number of Pulses x ([Ctlm x Cplm] ÷ PKF); 

Ctlm = corrections for effects of temperature on the liquid in the meter; and 

Cplm = correction for the difference in liquid volume as a result of the difference in pressure 

between the meter and the prover (compressibility correction factor for the meter) 

The new meter factor is the factor that should have been programmed in order to have the flow 

computer indicate the true or corrected volume. If the meter is equipped with a mechanical 

register, the new meter factor multiplied by the meter registration will equal the true unit of 

volume. 

The meter error in terms of percent is calculated by comparing the new meter factor to the 

previously programmed value of the meter factor (Mf). 

Meters equipped with mechanical registers of flow computers: 
Meter Error in % = (1- MNn) x 100 

Meters equipped with other flow computers: 

Meter Error in % = (Programmed Meter Factor - MFn) x 100 

We extend our thanks to Dennis Beattie of Measurement Canada, Emerson Process 

Management, and Marathon Ashland Petroleum for their assistance in the preparation of this 

article. 

The next article in this series will address the use of SVPs in testing commercial measuring 

devices.