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SOP 21

Standard Operating Procedure for

Calibration of LPG Provers1

1 Introduction 

Purpose 

This procedure is used to calibrate a volumetric field standard that is used to test 

systems designed to measure and deliver liquefied petroleum gas (LPG) in the 

liquid state by definite volume, whether installed in a permanent location or 

mounted on a vehicle. A schematic diagram of such a prover is shown in Figure 1, 

with the various system components numbered to clarify the various operations 

described in the procedure. Upon completion of this procedure the prover volume 

is reported to provide the correct volume at the reference temperature of 60 °F and 

reference pressure of 100 psig. Detailed measurement ranges, standards, 

equipment, and uncertainties for this SOP are generally compiled in a separate 

document in the laboratory.

Conformity Assessment

Standards that are calibrated for use in legal weights and measures applications 

should be evaluated for conformance to the appropriate specifications and 

tolerances that apply. LPG provers being calibrated should be evaluated for 

conformance using the checklist provided in NIST Handbook 105-4, Specifications 

and Tolerances for Liquefied Petroleum Gas and Anhydrous Ammonia Liquid 

Volumetric Provers, 2016. Where compliance is required by law, conformity 

evaluations should be conducted prior to performing calibrations. See Section 6.2 

for reporting results.

Prerequisites 

Verify the unknown prover has been properly cleaned and vented with all 

petroleum products removed prior to submission for calibration to ensure 

laboratory safety. The prover and/or pressure gauge must be visually 

inspected to determine that residual products are not present. Smell is not 

necessarily an adequate indicator of cleanliness.

Note: Many laboratories have a policy regarding cleanliness of submitted 

volumetric standards to minimize water contamination with flammable 

petroleum products. Be sure to follow laboratory safety policies for working 

with petroleum products and pressurized vessels.

Verify that valid current calibration certificates with measurement values 

and uncertainties are available for all the standards used in the calibration. 

 1 Non-SI units are predominately in common use in State legal metrology laboratories, and/or the petroleum industry 

for many volumetric measurements, therefore non-SI units have been used to reflect the practical needs of the 

laboratories performing these measurements as appropriate. Most LPG provers in use are 20 gal, 25 gal, and 100 gal 

nominal sizes. The volume of LPG provers is established at reference conditions of 60 oF and 100 psig.
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All calibration values must have demonstrated metrological traceability to 

the International System of Units (SI). Metrological traceability may be to 

the SI through a National Metrology Institute such as NIST.

Verify that the standards to be used have sufficiently small standard 

uncertainties for the intended level of the calibration.

Verify the availability of an adequate supply of clean water complying with 

GLP 10. Conditioning the water to achieve equilibration with the laboratory 

environment, to achieve minimal air entrainment and filtering to ensure 

minimal suspended solids is recommended. Water does not need to be 

distilled or deionized for use in this procedure. The equations used in GLP 

10 for the calculation of water density (air saturated) may be used without 

a significant impact on the measurement results because the density values 

are used as ratios.

Verify that the operator has had specific training in SOP 19, SOP 20, SOP 

21, SOP 31, and GMP 3 and is familiar with the operating characteristics 

and conditioning of the standards and unknown test items being used and 

calibrated.

Ensure that a full cylinder of nitrogen or compressed air, or a regulated air 

source of at least 200 psig, and a proper pressure regulator, connection hose, 

pressure control valves and an appropriately sized pressure relief valve set 

to relieve at no more than 300 psig are available.

Ensure that proper safety procedures are followed for any installation 

requiring that the operator work from an elevated surface; that any fall 

restraints, handrails or other safety related items have been properly 

inspected and are used as required by laboratory policy.

Verify that the laboratory facilities meet the following minimum conditions 

to make possible the expected uncertainty achievable with this procedure:

Table 1. Laboratory environmental conditions.

Procedure Temperature Relative Humidity

Volume Transfer 18 °C to 27 °C

Stable to ± 2.0 °C / 1 h

35 % to 65 %

Stable to ± 20 % / 4 h

The care required for calibrations conducted outside of a permanent 

laboratory includes proper safety, a clean and bubble-free water supply, 

measurement control programs, minimal air movement and a stable 

temperature environment shaded from direct sunshine to allow the prover, 

field standard, and clean calibration liquid (water) to reach an equilibrium 

temperature with minimal evaporation. Environmental conditions must be 

selected to be within stated laboratory conditions during the measurements. 
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All data and appropriate environmental conditions must be documented 

regardless of calibration location. 

2 Methodology

Scope, Precision, Accuracy

This procedure is applicable for the calibration of LPG field standard provers with 

capacities of 100 L to 500 L (20 gal to 100 gal) or larger when appropriate. Provers 

of 20 gal, 25 gal, and 100 gal (with gal and in3 units) are encountered most 

frequently, thus the procedure is written with that in mind. The changes necessary 

for calibrating provers of other capacities will be obvious and are not described in 

this document. The agreement of duplicate measurements made within a short 

period of time on a given LPG field standard prover must agree within 0.02 % of 

the volume. Where the demonstrated standard deviation of the measurement 

process is less than 0.02 % of the volume, replicate values must agree within the 

limits on the standard deviation chart. The calibration accuracy will depend on the 

uncertainty in the volume of the standard, on the care exercised in making the 

various measurements and temperature readings, and on correct application of the

corresponding corrections.

Summary 

The procedure is a modification of one described by M.W. Jensen in NBS 

Handbook 99, "Examination of Liquefied Petroleum Gas Liquid- Measuring 

Devices." The LPG prover is calibrated with a known volume of water delivered

into it from a standard prover of calibrated volume. Depending on the respective 

volumes, multiple transfers may be required. While multiple transfers should be 

minimized, a maximum of 15 transfers are permitted to ensure that final calibration 

uncertainties are sufficiently small to meet user applications. The temperature of 

the calibration medium (water) cannot be considered constant during transfers; 

thus, the temperature of the water for each transfer must be measured. Because of 

the large volumes, the difference in thermal expansion of the respective vessels 

must be considered. The LPG prover is pressurized and the liquid level is measured 

at each of several values of applied pressure. The calibration thus defines the 

capacity of the prover over its expected range of operational pressures. Upon 

completion of this procedure the prover volume is reported to provide the correct 

volume, Vref, at the reference temperature of 60 °F and reference pressure of 

100 psig.

Standards and Equipment 

The following are required to properly perform the calibration of a Field Standard 

LPG prover:
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A calibrated standard prover having a minimum volume of 5 gal is 

acceptable for 20 gal and 25 gal LPG provers. A 10 gal standard is 

acceptable for calibrating a 100 gal LPG prover, but a standard that is of the 

same volume as the LPG prover is preferable. 

Note: Standard provers used for calibration may need to have an alternative 

calibration value based on restricted flow delivery as the opening of many 

LPG provers may not be adequate to receive the full flow delivery from the 

reference standard. The calibrated volume of all standards used in this 

procedure must be determined using the same outlet piping as is used for 

LPG prover calibrations.

A funnel to aid in transferring water from calibrated flasks into the unknown 

prover.

Calibrated standards, typically glassware, of suitable sizes to calibrate the 

neck of prover.

Thermometers (2) with resolution and uncertainty better than 0.1 °C.

Note regarding temperature measurements: A digital temperature sensing 

device having a long cable will allow insertion of the probe into the standard 

and the unknown to enable direct liquid temperature measurements at the 

bottom, middle, and top of the provers. If the prover thermometer wells are 

used, ensure that the prover has equalized with the temperature of the water.

Meniscus reading devices (See GMP 3).

Timing device (calibration is not required; the uncertainty of the 

measurement only needs to be less than 5 s for a 30 s pour time).

Sturdy platform, with appropriate safety conditions and complying with 

laboratory policies, with sufficient height to hold standard and to permit 

transfer of water from it to the prover by gravity flow. 

Clean smoothbore pipe or tubing (hoses) to facilitate transfer of water from 

the laboratory standard to the LPG prover. Nearly all LPG provers require 

reducers to be used between normal laboratory piping and the top hole on 

the prover. Pipe and hose lengths must be minimized to reduce water 

retention errors. Care must be taken during wet-downs and calibration runs 

to ensure complete drainage and consistent retention in all hoses or pipes.

Arrange all hoses so that there are no loops or low spots that can hold water. 

Cylinder of compressed nitrogen or air with suitable regulator, as noted with 

prerequisites, and an appropriate pressure gauge.

Pressure Gauges

The accuracy of the prover calibration relies on the accuracy of the pressure 

gauge used to measure the internal prover pressure. When the gauge 

mounted on the prover is used for the measurement, it is assumed that 
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systematic errors in the prover pressure gauge will be present in field 

application and use, thus calibration of the laboratory pressure gauge is not 

essential. However, the prover must be recalibrated if the pressure gauge is 

changed or repaired in the field.

When a laboratory pressure gauge is used to measure the internal prover 

pressure during the calibration, the laboratory gauge and the prover gauge 

must both have current calibration certificates. 

Pipe plugs to seal unused prover ports, and piping and valves needed to 

facilitate gravity draining the prover in a time as similar as possible to the 

time taken to empty the prover using the LPG system pump.

Materials to seal all piping threads to permit pressurization to 200 psig. If 

thread tape is used in place of paste thread sealant, extra care must be 

exercised to ensure that no thread tape debris enters the prover under test.

Procedure 

Preliminary Operations 

2.4.1.1 Install and level the standard(s) on a raised platform with 

appropriate security and safety ensured for the prover(s) and 

operator(s). Provide pipe or tubing for delivery of water by the most 

direct route to the prover. Position and level the unknown prover 

where it can be reached from the elevated standard by the shortest 

feasible delivery system. Replace all valves and piping connected to 

the prover body below the nominal volume line with plugs and 

laboratory owned valves and fittings to eliminate errors that will 

result from leakage or expansion when the prover is pressurized to 

200 psig or more during the calibration. These potential errors 

typically affect only the prover calibration process and have no 

effect during normal use because the prover zero indication is 

established under LPG system pressure. (If there is no significant 

change in system pressure once the zero setting is established during 

a meter test the change in system volume is minimal). Install in one 

lower port a fitting and valve for draining the prover. Plug all other 

ports with sealed plugs of suitable pressure ratings.

2.4.1.2 Remove the plug and/or relief valve (1) from the top of the LPG 

prover, and extend the drain pipe of the standard prover into the 

hole. This may require the use of a reducer and a short length of hose 

(about 1 inch in diameter). If this is a tight fit, open the vapor return 

line valve (connected to 12c) to provide an air bleed.

2.4.1.3 If the prover inlet hose (11) is to be used as a gravity drain, it must 

be disconnected from the bottom of the prover, any check 

valves (12a) installed during normal operationsremoved and a valve 

installed between the prover body and the hose to ensure isolation 

of the hose from the pressurized prover. Failure to insert this 
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isolation valve will result in errors during the pressurized portion of 

the prover calibration. These errors will NOT be offset during use!

Cleanliness Check

Both the standard and the unknown prover must be internally clean. This 

should be verified by checking that water properly drains from them. If 

necessary, either or both should be cleaned with water and non-foaming 

detergent (see GMP No. 6) to attain good drainage characteristics. 

Additional effort may be required to eliminate scaling and contamination 

build-up from the inside of LPG provers. It is a good practice to remove the 

bottom drain plug (13) from the bottom of the prover lower neck to allow 

removal of any debris that may have accumulated in the lower neck of the 

prover.

Neck scale plate calibration

Neck scale plate calibrations are generally conducted only for new or 

damaged volumetric measures, those that have not been calibrated by the 

laboratory in the past, or those for which the calibration data is not available.

See SOP 31 for the neck scale plate calibration procedure. 

Body Calibration

2.4.4.1 Drain the unknown LPG prover through the drain valve installed 

during prover preparations and the connected hose. When the liquid 

reaches the top of the lower gauge glass, close the drain valve and 

adjust the liquid meniscus level to the lower neck zero graduation. 

Record the elapsed time required to drain the prover to the top of the 

neck, ti. Continue adjusting the liquid level until completion of the 

final drain time of 30 s. The liquid level should be exactly at the zero 

graduation and the drain valve closed simultaneously at the end of 

the 30 s drain time. (Final adjustment of the water level close to the 

zero mark should be started during the 30 s final drain period but 

should not be completed before the end of the 30 s drain period).

Alternatively, though not recommended because of resulting errors, 

the prover may be completely drained, given a 30 s final drain time 

and then refilled to the lower zero graduation with a funnel that has 

been wet down by adding the small volume of water needed to bring 

the level to the zero graduation. Errors will result from this process 

due to the extended time between closing the valve and setting the 

zero level and other factors associated with the process and should 

be considered in the uncertainty assessment. These errors can be 

minimized if the prover is refilled to the lower neck zero graduation 

within 30 s of cessation of main flow.

2.4.4.2 Once the zero indication has been properly established, transfer the 

nominal volume from the standard(s) into the LPG prover in the 

usual manner, recording the associated delta (offset of the water 
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level in the standard from nominal) and water temperature reading

in the standard. If multiple transfers are required, record the water 

temperature of the standard at the time of each transfer, but that of 

the LPG prover only after the final transfer. Verify that the LPG 

prover retained its level condition or adjust it to the level condition 

as noted earlier. "Rock" the prover to "bounce" the liquid in the 

upper sight gauge before reading. Record the final scale indication

and prover temperature after the nominal volume has been 

transferred into the unknown LPG prover with 0 psig pressure 

applied, Run 1ATM.

2.4.4.3 Reinstall the plug and relief valve in the top of the prover using an

appropriate sealant to create a leak free installation.

Caution: Ensure that all piping and fittings are rated for the pressures 

to which they will be exposed.

2.4.4.4 Pressurize the prover to 200 psig, hold that pressure for several 

minutes, then return the prover pressure to 0 psig and verify that the 

prover indication has not changed from that previously recorded as 

Run 1ATM. If the prover indication returns to the recorded value,

pressurize the prover to 100 psig and record the prover indication

and temperature, Run 1100.

Note: The prover indication at 0 psig must return to the value 

recorded as Run 1ATM. If it does not, corrective action must be taken 

to correct any causes, i.e., leaks, excessive air entrained in the water. 

Once corrective actions are completed repeat 2.4.1.1 through 2.4.4.3

2.4.4.5 Calculate the effective volume of water delivered into the prover 

using Eqn. 3 or Eqn. 4 as appropriate. Record that value, Run 1 Vref.

2.4.4.6 Calculate the prover volume for Run 1 using Eqn. 6 or Eqn. 7, as 

appropriate. Record the calculated prover volume, Run 1AsFound. The 

calculated prover volume must be within ± 0.2 % of the prover 

nominal volume. 

2.4.4.7 If the indication is not within ± 0.2 % of the prover nominal volume 

the prover must be adjusted (whenever possible) to indicate the Vref

value as described in 2.4.6 Prover Adjustment to Nominal.

2.4.4.8 After completing the prover adjustment process, repeat 2.4.4.1 

through 2.4.4.6 as needed until the “As Left” prover volume is as 

near to the prover nominal as possible. Record the final prover 

volume, Run 1Final.

2.4.4.9 Repeat steps 2.4.4.1 through 2.4.4.6 for Run 2 recording Run 2ATM, 

and Run 2100.
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2.4.4.10 Calculate the effective volume of water delivered into the 

prover using Eqn. 3 or Eqn. 4 as appropriate. Record that value as 

Run 2 Vref.

2.4.4.11 Calculate the prover volume for Run 2 using Eqn. 6 or Eqn. 

7. Record the calculated prover volume for Run 2Final. The calculated 

prover volume must be within ± 0.2 % of the prover nominal 

volume. 

2.4.4.12 The calculated prover volume, Run 2Final, must agree with 

the Run 1Final value within ± 0.02 % of the prover nominal volume

or pass the F-test as shown in Section 3 (use the more stringent limits 

for assessment of repeatability).

2.4.4.13 If the prover volumes do not repeat within 0.02 % of prover 

nominal volume, or pass the F-test (whichever limit is more 

stringent), corrective action must be initiated and the calibration 

runs repeated until two consecutive calibration runs repeat within 

0.02 % of prover nominal volume or pass the F-test indicating that 

the accepted laboratory process limits are met.

Pressure Correction Curve Determination

2.4.5.1 The internal pressure and thus the volume of the prover may vary 

during use. Accordingly, a pressure correction must be made, using 

the Pressure Correction Calculations given in section 3.3.

2.4.5.2 The calibration status of the pressure gauge mounted on the prover 

MUST be assessed and documented on the calibration certificate.

It is a best practice to permanently mark the mounted pressure gauge 

with a unique identifier that can be included as the gauge 

identification on the prover calibration certificate.

Caution: Ensure that all piping and fittings are rated for the pressures 

to which they will be exposed.

2.4.5.3 Ensure that all valves are closed except the vapor return valve, if 

still installed and being used to apply pressure to the prover.

2.4.5.4 Verify that the final scale indication has not changed since it was 

recorded at the end of Run 2 (if it has changed it may signal a leak 

in one of the valves or fittings), and then bleed off pressure until the 

installed prover gauge reads 0 psig.

2.4.5.5 Apply pressure to the prover until the installed pressure gauge 

indicates 20 psig.

Note: As pressure is applied, the density of the water increases thus 

decreasing the water level inside the prover; the gas in the prover 

heats up and then cools; the prover shape begins to change due to 
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pressure deformation; all resulting in a drifting pressure setting as 

the system comes to equilibrium. Continue adjusting the pressure 

until a stable pressure indication is obtained while lightly tapping 

the gauge to ensure that the gauge needle is not sticking. (Rotating 

the handle of a screwdriver against the side of the pressure gauge is 

a good alternative to tapping on the gauge).

2.4.5.6 "Bounce" the liquid in the neck, then read and record the liquid level 

at this applied pressure, sr20i.

2.4.5.7 Continue increasing the pressure in the prover, setting a stable 

pressure at 50 psig, 100 psig, 150 psig and 200 psig, recording the 

prover indication at each pressure, sr50i, sr100i, sr150i, and sr200i.

Note: The scale indication at 100 psig should be the same as was 

observed for Run 2100.

2.4.5.8 Slowly decrease the prover pressure, setting a stable pressure at 

150 psig, 100 psig, 50 psig and 20 psig, recording the prover 

indication at each pressure, sr150d, sr100d, sr50d, and sr20d.

Note: As the pressure is released the components of the system 

‘relax’ and the gas temperature cools, the pressure drifts as the 

system equilibrates with each pressure change.

2.4.5.9 The prover indication at each corresponding decreasing pressure 

must repeat the increasing pressure indication within 0.02 % of 

nominal prover volume.

2.4.5.10 If any decreasing pressure indication fails to repeat the 

corresponding increasing pressure indication within 0.02 % of 

nominal prover volume the cause for this failure must be determined 

and the calibration performed again until repeatability is obtained.

2.4.5.11 A plot of the scale indications versus the applied pressure 

should be relatively linear. If significant non-linearity is detected it 

may indicate either trapped air or significant deformation of the 

prover body with changes in pressure. 

If the issue is determined to be trapped air, the cause of this air 

entrapment must be corrected and the prover calibration repeated. 

If the problem is determined to be significant deformation of the 

prover body with changes in pressure, the prover must be taken out 

of service and a hydrostatic pressure test scheduled as it may 

indicate failure of the materials from which the prover is made. This 

will likely require replacement of the prover.

Prover Adjustment to Nominal
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2.4.6.1 With the pressure in the prover at 100 psig, the prover volume, 

calculated using the appropriate equation in Section 3, should differ 

from nominal no more than 0.2 % of nominal prover volume.

2.4.6.2 Adjust the LPG prover upper scale to read the calculated Run 1 Vref

value.

2.4.6.3 If the LPG prover scale plate has a 0 indication at nominal, adjust 

the scale plate to indicate Run 1, Vref – Nominal, converting units as 

needed.

2.4.6.4 For provers with only an adjustable lower scale (or one in which the 

upper scale is not adjustable), a prover correction, LC, may be 

calculated at 100 psig as follows:

Nominal Lc = −+ V sr ref u Eqn. (1)

where:

Table 2. Variables used in Eqn. 1.

Variable Description

Lc Prover correction at 100 psig

Nominal LPG prover nominal volume

Vref Volume of water in the unknown prover at 60 °F and 100 psig

u sr Upper scale indication at 100 psig

Note: Take care to use matching units in the calculation.

2.4.6.5 If the calculated prover correction is negative, move the bottom 

scale up to decrease the prover volume. If the calculated prover 

correction is positive, move the bottom scale down to increase the 

prover volume. The linear distance h that the bottom scale is to be 

moved is calculated as:

2

4

d

L

h C

π = Eqn. (2)

where: 

Table 3. Variables used in Eqn. 2.

Variable Description

H Distance in inches the bottom scale is to be moved, up or down

Lc Prover correction at 100 psig in cubic inches

D Inside diameter of the lower neck of the prover in inches (as noted on identification plate)

2.4.6.6 Once the prover is correctly adjusted, repeat the Body Calibration 

process to verify that the adjustment successfully corrected any 

indication errors.
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Final Operations

2.4.7.1 Seal the bottom and top scales as specified by laboratory policy and 

as appropriate.

2.4.7.2 Drain the prover, then remove the plug (13) at the lower neck to 

facilitate complete drainage of the prover. If time permits, let the 

prover drain overnight. If it is not possible to remove the plug, other 

means, such as siphoning or vacuuming, must be used to remove all 

water from the bottom of the prover.

2.4.7.3 With the nitrogen cylinder or compressed air connected, blow 

nitrogen or air through the prover to remove remaining moisture. Be 

sure to blow out the drain line and any other portions of the system 

that may have become contaminated with water. Flushing the prover 

with 1 or 2 gallons of ethanol will aid in complete removal of the 

water.

2.4.7.4 If water has entered the pump-off system, pour several gallons of 

alcohol into the prover and pump the alcohol through the system to 

remove the water to prevent it from freezing in the pump when LP 

gas is used. This will not be an issue if the recommendations of 

removing all user connections from the prover body described in 

Preliminary Operations have been followed. 

3 Calculations

Single Delivery 

Calculate the effective volume of water delivered to the unknown prover at 60 °F

and 100 psig, Vref, using Eqn. 3:

{( ) ( ) }

( )

1 60 1 1 1 60 F 1

1 60 F

S

ref

x x

V t

V

Pf t

ρ α

ρ β

  +∆ + −       =   + −    



 Eqn. (3)

Multiple Deliveries

Calculate the effective volume of water delivered to the unknown prover at 60 °F

and 100 psig, Vref, using Eqn. 4:

{( ) ( ) } {( ) ( ) } {( ) ( ) }

( )

1 60 1 1 2 60 2 2 60 + 1 60 F + 1 60 F ... + 1 60 F 1

1 60 F

S S nS N N

ref

x x

Vt V t V t

V

Pf t

ρ αρ α ρ α

ρ β

∆ + − + ∆ + − ++ ∆ + − = + −

                 

 



Eqn. (4)
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These equations correct the volume of water in the unknown prover for the effects 

of temperature on the density of the water, the thermal expansion and contraction 

of the standard and unknown provers, and the compressibility of water at 100 psig.

Table 4. Variables for Vref Equations 3 and 4.

Variable Description

Vref

Effective volume of water delivered to the unknown prover corrected to 60 °F and 

100 psig.

VS60

Volume of the standard vessel at 60 °F and atmospheric pressure (If the standard has 

been calibrated at a different reference temperature, i.e., 20 °C (68 °F) for glassware, that 

temperature must be used in the calculation of the temperature correction in Eqn. 3 and 

Eqn. 4, taking care to make coefficients of expansion units).

P Internal LPG prover pressure at a specific data point; psig

Pf

Pressure factor to be used at:

0 psig: 1.000 000

20 psig 1.000 064 

50 psig: 1.000 161

100 psig: 1.000 322

150 psig: 1.000 483

200 psig: 1.000 644

These factors are the ratio between the water density at 60 °F and 0 psig and that at 60 °F 

and the given pressure, using the equations in GLP 10.

ρ1, ρ2, ...ρN

Density of the water in the standard prover where ρ1 is the density of the water for the first 

delivery, ρ2 is the density of the water for the second delivery, and so on until all n

deliveries are completed

∆1, ∆2,..., ∆n

Volume difference between the water level and the reference mark on the standard where 

the subscripts 1, 2,..., n, represent each delivery as above. If the water level is below the 

reference line, delta (∆) is negative. If the water level is above the reference line, ∆ is 

positive. If the water level is at the reference line, ∆ is zero

Note: units must match volume units for the standard. For slicker-plate type standards, the 

∆ is zero.

tS1, tS2,..., tSn Temperature of water for each delivery with the subscripts as above

α Cubical coefficient of expansion (also CCE) for the standard: /oF

ß Cubical coefficient of expansion (also CCE) for the LPG prover: /oF

tx Temperature of the water in the filled unknown vessel: oF

ρx Density of the water in the unknown vessel: g/cm3 using GLP 10.

Pressure Correction Calculations

Compute the pressure correction, Pcorr, at each pressure that the prover was 

read by correcting for the compressibility of the water using Eqn. 5:

100 ( ) 100 1.000322

100 corr X N N

psig x psig P sr rs P P     − = × −        +

 − Eqn. (5)
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where the water compressibility factor at 60 °F and 100 psig is 1.000322.

Caution: Be certain to match the pressure correction units to those of the 

prover scale plate indications.

Table 5. Variables used in Eqn. 5.

Variable Description

Pcorr Correction to scale indication resulting from prover pressure: x psig

sr100 Prover Scale Plate reading at 100 psig

srx Prover Scale Plate reading at x psig

Pn Nominal volume of prover

Plot the pressure corrections. If the corrections versus the pressure are 

linear, make a straight line best fit of the data and interpolate to obtain the 

pressure corrections for any desired pressure. If the data is nonlinear, then 

perform a straight-line interpolation between adjacent pressure readings to 

obtain pressure corrections at any desired intermediate pressures. 

Alternatively, a best fit curve can be drawn for the nonlinear data and the 

pressure corrections interpolated from the graph for intermediate pressures.

Eqn. 5 can also be used to generate a pressure correction table for the prover 

across the range of 20 psig to 200 psig.

Prover Volume 

LPG provers are generally adjusted to the nominal value using 100 psig as 

the reference pressure and a 60 °F reference temperature. Because the 

calibration medium, water, compresses thereby decreasing in volume by 

0.00032 gal/gal at 100 psig, the prover indication must be adjusted to 

indicate the decreased water volume to correctly indicate the volume of 

LPG at 100 psig. The value calculated as Vref correctly represents the 

volume of water delivered at atmospheric pressure after pressurizing to 100 

psig.

For an LPG prover having a scale plate that directly indicates the total 

volume delivered the prover volume is calculated as:

100 Prover volume Nominal V sr ref =− + Eqn. (6)

For a prover having a ‘0’ graduation marking at the nominal volume 

delivered, with a scale plate that indicates a volume above and below that 

graduation as a positive or negative value, the prover volume is calculated 

as:

100 Prover volume V sr ref = − Eqn. (7)

For either type scale plate the prover should be adjusted so that the prover 

indicates the effective volume of water delivered: Vref.
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Calculate the within process standard deviation, sw, for the replicate runs. For two 

runs, the degrees of freedom will be one.

Calculate the F statistic to compare the observed within process standard deviation, 

sw, to the accepted (pooled) within process standard deviation for the measurement 

process. (See NISTIR 6969, Sections 8.4 and 8.9.2, for more information on 

pooling standard deviations and F-tests).

2

Accepted

2

Observed

w

w

s

s F = Eqn. (8)

The calculated F statistic must be less than the F value obtained from an F table at 

95 % confidence level (Table 9.12, NISTIR 6969) to be acceptable. The F value is 

obtained from the F table for one degrees of freedom for the numerator and the 

degrees of freedom for the denominator is equal to the number of degrees of 

freedom in the pooled within process standard deviation. If the data fails the F-test 

and the source of the error cannot be determined conclusively and corrected, the 

measurement must be repeated.

Calculate and report the mean volume of the volumetric standard at 60 °C and 

100 psig. 

If adjustments were made during replicate runs, report the “as found” volume or 

the mean of “as found” volumes and the “as left” volume or mean of “as left” 

volumes, as applicable, at 60 °F and 100 psig. (I.e., do not calculate a mean value 

by combining “as found” and “as left” values when adjustments are made).

4 Measurement Assurance

Due to the cost of obtaining an LPG prover for use as a check standard it will be 

unlikely that a laboratory will have one in place. Instead a standard deviation chart 

is used to monitor the within process standard deviation.
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A standard deviation chart is used for measurement assurance through the 

evaluation of replicate measurements. The standard deviation of each combination 

of Run 1 and Run 2 is calculated and the pooled standard deviation over time may 

be used to estimate the short-term variability in the measurement process. A 

standard deviation chart for unknown provers represents the variability in condition 

of test measures submitted for calibration as well as the short-term repeatability of 

the measurement process but does not monitor the stability of the reference standard 

or represent the variability or potential systematic errors associated with meniscus 

readings. The range of the calibration runs must repeat to within 0.02 % of the 

volume, or the standard deviation must be less than applicable control/action limits 

on standard deviation charts, or the observed standard deviation must pass the Ftest statistics (as applicable).

For unknown standards that are adjusted, do not combine an “as found” value with 

an “as left” value for the two runs recorded in the chart; use the adjusted value from 

Run 1 and the value from Run 2, both at the applicable reference temperature and 

pressure, when entering values in a standard deviation or range chart.

5 Assignment of Uncertainties

The limits of expanded uncertainty, U, include estimates of the standard uncertainty of the 

laboratory volumetric standards used, us, plus the standard deviation of the process, sp, and 

the additional items noted below and in the uncertainty budget table, Table 4, at the 95 % 

level of confidence. See SOP 29 for the complete standard operating procedure for 

calculating the uncertainty. 

The standard uncertainty for the standard, us, is obtained from the calibration 

certificate. The combined standard uncertainty, uc, is used and not the expanded 

uncertainty, U, therefore the reported uncertainty for the standard will usually need 

to be divided by the coverage factor k. 

Note: See NISTIR 6969, SOP 29 for the complete standard operating procedure for 

calculating the uncertainty when multiple deliveries or multiple standards are used

to correctly calculate correlated uncertainties. Fifteen is the maximum 

recommended number of deliveries from a laboratory standard to a prover under 

test to minimize calibration uncertainties to the levels identified previously. 
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The standard deviation of the measurement process sp, is taken from a standard 

deviation chart for LPG provers (and not from charts for a refined fuel check 

standard) (See SOP 17, SOP 20 and SOP 30). Check standards are not normally 

available. 

Neck calibration uncertainty should be estimated based on the uncertainty of 

standards used, errors observed during calibration, ability to read the meniscus of 

all standards involved (see GMP 3), and the repeatability of the neck calibration

(See SOP 31). 

Other standard uncertainties usually included at this calibration level are:

1) uncertainties associated with the ability to read the meniscus, only part of which 

is included in the process variability due to parallax and visual capabilities, and 

2) uncertainties associated with temperature corrections that include values for the 

cubical coefficient of expansion for the prover under test, the accuracy and 

gradients associated with temperature measurements in the provers. Additional 

factors that might be included are: data showing reproducibility, environmental 

variations over time, and bias or drift of the standard as noted in control charts.

Factors that are usually insignificant are uncertainties associated with viscosity of 

the water as a calibration medium and uncertainties associated with the 

compressibility of water.

To properly evaluate uncertainties and user requirements (tolerances), assessment 

of additional user uncertainties may be required by laboratory staff. Through proper 

use of documented laboratory and field procedures, additional uncertainty factors 

may be minimized to a level that does not contribute significantly to the previously 

described factors. Additional standard uncertainties in the calibration of field 

standards and their use in meter verification may include: how the prover level is 

established, how delivery and drain times are determined, the use of a proper “wetdown” prior to calibration or use, whether gravity drain is used during calibration 

or whether the volume of water is eliminated by pumping, the cleanliness of the 

prover and calibration medium, prover retention characteristics related to inside 

surface, contamination or corrosion, and total drain times, and possible air 

entrapment in the water. Systematic errors may be observed between laboratory 

calibration practices where a gravity drain is used and field use where the pumping 

system is used. 

Example components to be considered for an uncertainty budget table are shown in 

the following table. Multiple values of some items may need to be considered (e.g., 

multiple drops from the standard, multiple meniscus readings, and multiple 

temperature readings).
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Table 6. Example uncertainty budget table.

Uncertainty Component Description Symbol Source Typical Distribution

Uncertainty of the standard (5.1) us

Calibration certificate; 

may be multiplied or 

added based on 

dependencies

Expanded divided by 

coverage factor

Accepted standard deviation of the 

process (5.2) sp

Standard deviation chart

(or control chart) Normal

Uncertainty or uncorrected error 

associated with a neck calibration (5.3) un SOP 31 Rectangular 

Ability to read the Meniscus in S (5.4) um

None if using a slickerplate type standard; 

GMP 3

Triangular

Ability to read the Meniscus in X (5.4) um GMP 3 Triangular

Water temperature (S) (5.4) uts

Consider accuracy, 

resolution, and gradients Rectangular

Water temperature (X) (5.4) utx

Consider accuracy, 

resolution, and gradients Rectangular

Cubical Coefficient of Expansion 

(CCE) on S (5.4) uCCE

5 % to 10 % of the CCE 

(EURAMET CG-21) Rectangular

Cubical Coefficient of Expansion 

(CCE) on X (5.4) uCCE

5 % to 10 % of the CCE 

(EURAMET CG-21) Rectangular

Uncertainty associated with the 

pressure gauge

upsig

Handbook 105-4, 5 psig 

increments; use 2.5 psig Rectangular

Uncertainty of bias, drift, or variability

of standards (5.2) ub

From calibration history 

of reference standards Rectangular

Uncertainty of drain time (insignificant 

if closely following the procedure) ud From experimental data Normal

Uncertainty Evaluation

Where applicable, uncertainties for volume calibrations that are assessed for 

conformity must meet decision rule criteria in the applicable documentary 

standards.

6 Calibration Certificate

Report results as described in NISTIR 6969, SOP No. 1, Preparation of Calibration

Certificates, with the addition of the following:

For LPG provers, calculate and report the mean final prover volume and its 

associated uncertainty, reference temperature, reference pressure, material, 

coefficient of expansion (assumed or measured), any identifying markings, 

tolerances (if appropriate), laboratory temperature, water temperature, barometric 

pressure, relative humidity, out-of-tolerance conditions, and the total drain time 

from opening of the valve, including the 30 s drain after cessation of flow, 

identification and calibration status of the mounted pressure gauge and if the gauge 

is uncalibrated a Note stating the requirement that the prover be recalibrated if the 

gauge is repaired or replaced.
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The certificate should also include temperature and pressure correction tables or 

chart, along with a note regarding possible differences in retention characteristics 

between water, the calibration medium, and LPG products.

The SI unit of volume is m3

, so a conversion factor must be included on the report 

in the notes section when other units are used.

Conformity Assessment

Evaluate compliance to applicable tolerances as needed or required by the customer 

or by legal metrology requirements. Compliance assessments must note the 

applicable documentary standard and which portions of the standard were or were 

not evaluated. The uncertainty for volume calibrations must be less than the 

tolerances published in the applicable documentary standards. For volume 

calibrations where the unknown standard can be adjusted, it is standard practice to 

adjust the standard or leave the scale plate in a position close enough to its nominal 

volume to ensure that the absolute value of the measurement result plus the 

uncertainty is less than the applicable tolerance. Where the unknown standard 

cannot be adjusted, and a portion of the uncertainty band from the error exceeds 

tolerance limits, it is not appropriate to state compliance with the tolerances unless 

additional decision rules are communicated with and agreed to by the end user. 

Correction values (measurement results) may need to be used by the end user in 

such cases.

Table 7: Data recorded.

Variable Type Data Step

ti Initial drain time 2.4.4.1

Run 1ATM Scale indication 2.4.4.2

Run 1100 Scale Indication 2.4.4.4

Run 1 Vref Calculated value Eqn. 3 or 4 2.4.4.5

Run 1AsFound Calculated value Eqn. 6 or 7 2.4.4.6

Run 1Final Calculated value Eqn. 6 or 7 2.4.4.8

Run 2ATM Scale indication 2.4.4.2

Run 2100 Scale Indication 2.4.4.4

Run 2 Vref Calculated value Eqn. 3 or 4 2.4.4.10

Run 2Final Calculated value Eqn. 6 2.4.4.11

Pass/Fail Run 1Final - Run 2Final < 0.02 % Nominal 2.4.4.12

Pressure Gauge Identifier 2.4.5.2

sr20i Scale Reading at 20 psig increasing 2.4.5.6

sr50i Scale Reading at 50 psig increasing 2.4.5.7

sr100i Scale Reading at 100 psig increasing 2.4.5.7

sr150i Scale Reading at 150 psig increasing 2.4.5.7

sr200i Scale Reading at 200 psig increasing 2.4.5.7

sr150d Scale Reading at 150 psig decreasing 2.4.5.8

sr100d Scale Reading at 100 psig decreasing 2.4.5.8

sr50d Scale Reading at 50 psig decreasing 2.4.5.8

sr20d Scale Reading at 20 psig decreasing 2.4.5.8

Pass/Fail Repeat all pressure point indications 2.4.5.10
SOP 21 

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Figure 1. Representative LPG Prover Schematic
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Appendix A: Data Recording Sheet

LPG Prover Calibration Page 1 of 2

Laboratory Information

Metrologist Date

Location Temperature

Date Relative Humidity

Vessel Identification Barometric Pressure

sp of Process Degrees of Freedom

Unknown Prover Information

Owner Manufacturer

Address Serial

Material

Cubical Coefficient of Expansion (β)

Phone Reference Temperature

Unknown prover graduations Applicable Specifications and 

Tolerances

Initial Drain time, ti, (s)

(Time to drain full prover to Zero) Maximum Permissible Error (MPE)

Pressure Gauge Identification Is Pressure Gauge Calibrated?

Upper Neck Inside Diameter Lower Neck Inside Diameter

Volume standard(s) data:

Identification (ID)

(Note ID of 

Standards)

Reference 

Temp.

Nominal 

Volume

Volume 

Correction

Expanded Unc:

From Cal. 

Cert.

Unc:

k factor

Cubical 

Coefficient of 

Expansion (α)

S1

S2

S3

S4

Run 1: Data for volumes delivered from the standards:

DROP 

#

Reported Volume 

(gal) Material (MS/SS/) Water Temperature (°C)

(Must be ≥ 0.5 °C and < 40 °C)

Offset from 

Nominal ∆

(in3)

1

2

3

4

5

Observations Calibration Data

Run 1 Variable Indication 

(Left scale)

Units ( )

Indication

(Right scale)

Units ( )

Prover Water 

Temperature (°C)

Run 1ATM 

Run 1100

Run 1 Vref

Run 1AsFound

Run 1Final

Within MPE? Pass / Fail Pass / Fail
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Appendix A: Data Recording Sheet

LPG Prover Calibration Page 2 of 2

Run 2: Data for volumes delivered from the standards:

DROP 

#

Reported Volume 

(gal) Material (MS/SS/) Water Temperature (°C)

(Must be ≥ 0.5 °C and < 40 °C)

Offset from 

Nominal ∆

(in3)

1

2

3

4

5

Observations Calibration Data

Run 2 Variable

Indication 

(Left scale)

Units ( )

Indication

(Right scale) Units ( 

)

Prover Water 

Temperature (°C)

Run 2ATM 

Run 2100

Run 2 Vref

Run 2AsFound

Within MPE? Pass / Fail Pass / Fail

Observations Pressure Calibration Data

Pressure Setting

Indication 

(Left scale)

Unit ( )

Indication

(Right scale)

Unit ( )

Pressure Setting

Indication 

(Left scale)

Unit ( )

Indication

(Right scale)

Unit ( )

sr20i sr150d

sr50i sr100d

sr100i sr50d

sr150i sr20d

sr200i

Repeatability Evaluation (Run 1 to Run 2)

Repeatability error 

< 0.02 % Nominal Pass Fail

Prover Volume (Average of Run 1Final and Run 2Final)

Left scale

Units ( )

Right scale

Units ( )

Prover Volume 

at 60 °F and 100 psig

Uncertainty

k
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Appendix B

Example Temperature Correction TableA

Example for a 100 gallon prover and 60 °F reference temperature.

CCE Mild Steel

1.86 x 10-5 / °F

Stainless Steel

2.65 x 10-5 / °F

Temperature °F in3 gal in3 gal

-20 -34 -0.149 -49 -0.212 

-15 -32 -0.139 -46 -0.199 

-10 -30 -0.130 -43 -0.186 

-5 -28 -0.121 -40 -0.172 

0 -26 -0.112 -37 -0.159 

5 -24 -0.102 -34 -0.146 

10 -21 -0.093 -31 -0.133 

15 -19 -0.084 -28 -0.119 

20 -17 -0.074 -24 -0.106 

25 -15 -0.065 -21 -0.093 

30 -13 -0.056 -18 -0.079 

35 -11 -0.047 -15 -0.066

40 -9 -0.037 -12 -0.053 

45 -6 -0.028 -9 -0.040 

50 -4 -0.019 -6 -0.026 

55 -2 -0.009 -3 -0.013 

60 0 0.000 0 0.000 

65 2 0.009 3 0.013 

70 4 0.019 6 0.026 

75 6 0.028 9 0.040 

80 9 0.037 12 0.053 

85 11 0.046 15 0.066 

90 13 0.056 18 0.080 

95 15 0.065 21 0.093 

100 17 0.074 24 0.106 

105 19 0.084 28 0.119 

110 21 0.093 31 0.133 

115 24 0.102 34 0.146 

120 26 0.112 37 0.159 

CCE = coefficient of cubical expansion 

A Provide only the applicable coefficient of cubical expansion for the prover under test.