SOP 21

**Standard Operating Procedure for**

**Calibration of LPG Provers**[^1]

1 Introduction

1.  Purpose of Test

This procedure may be used to calibrate a volume standard 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, together with numbers, e.g., 1, 2, 3, and 4 to
clarify the various operations described in the procedure. The parts
labeled A, B, and C are hose connections used in meter testing (versus
prover calibrations).

> 1.2 Prerequisites
>
> 1.2.1 Verify the unknown prover has been properly cleaned and vented
> with all petroleum products removed prior to submission for
> calibration to ensure laboratory safety.

2.  Verify that valid calibration certificates are available for the
    standard used in the test.

3.  Verify that the standards to be used have sufficiently small
    standard uncertainties for the intended level of the calibration.

4.  Verify the availability of an adequate supply of clean water (GLP
    10).

5.  Verify that the operator has had specific training in SOP 18, SOP
    19, SOP 21, GMP 3, and SOP 20.

6.  Cylinder of nitrogen or compressed air and a proper pressure
    regulator.

7.  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      | 18 C to 27 C, maximum  | 40 % to 60 %                 |
| Transfer    | change 2.0 C/h         |                              |
|             |                        | ± 20 %, maximum change / 4 h |
+-------------+------------------------+------------------------------+

2.  Field tests

    1.  A "field" calibration is considered one in which a calibration
        is conducted in an uncontrolled environment, such as
        out-of-doors. Calibrations conducted under field and laboratory
        conditions are not considered equivalent.

> 1.3.2 The care required for field calibrations includes proper safety,
> a clean and air-free water supply, measurement control programs, and a
> stable temperature-controlled environment shaded from direct sunshine
> to allow the prover, field standard, and test liquid (water) to reach
> an equilibrium temperature, with minimal evaporation. Environmental
> conditions should be controlled (or selected) to be as close to
> laboratory conditions as possible. All data and appropriate
> environmental conditions must be documented regardless of test
> location.

2.  Methodology

    1.  Scope, Precision, Accuracy

> This procedure is applicable for the calibration of LPG provers with
> capacities of 100 L to 500 L (20 gal to 100 gal) or larger when
> appropriate. Provers of the latter capacity (gal and in^3^ units) are
> encountered most frequently, hence the procedure is written with that
> in mind. The changes necessary for testing 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 100‑gal prover should be within 5 in^3^ (0.02 gal). The 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.

2.  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
these should be minimized, a maximum number of 15 transfers are
permitted to ensure that final calibration uncertainties are
sufficiently small to meet user applications. 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 pressure.

3.  Equipment

    1.  Calibrated standard prover of minimum volume of 10 gal but
        preferably of the same volume as the LPG prover, with recent
        calibration certificate traceable to NIST.

    2.  A funnel and a calibrated 1 gal flask (or other suitable size)
        with recent calibration certificate traceable to NIST, to
        calibrate the neck of prover.

    3.  Calibrated thermometers (2) accurately calibrated to 0.1 C, with
        recent calibration certificate traceable to NIST.

    4.  Meniscus reading device (See GMP 3).

    5.  Timing device (calibration is not required.)

    6.  Supply of clean water, preferably soft water (filtered if
        necessary) (GLP 10).

    7.  Sturdy platform, with appropriate safety conditions, with
        sufficient height to hold standard and to permit transfer of
        water from it to the prover by gravity flow.

    8.  Clean the pipe or tubing (hoses) to facilitate transfer of water
        from the laboratory standard to 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 should be
        minimized to reduce water retention errors. Care must be taken
        during wet-downs and runs to ensure complete drainage and
        consistent retention in all hoses or pipes.

    9.  Compressed nitrogen cylinder or air, suitable regulator, and an
        appropriate pressure gauge. The calibration relies on the
        accuracy of the pressure gauge on the prover. It assumes that
        systematic errors in the prover pressure gauge will be present
        in field applications as well, thus calibration of the
        laboratory pressure gauge is not essential.

4.  Procedure

> 2.4.1 Preliminary Operations

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 most
    direct route to prover.

2.  Position and level the unknown prover where it can be reached from
    the elevated standard by the shortest feasible delivery system.

3.  Remove the plug and relief valve (1) from the top, and extend the
    pipe 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 (2) to provide an air bleed.

> Use the prover inlet line (3) as a gravity drain. If necessary, remove
> the fitting on the end and connect a hose or pipe to make the
> necessary drain line.
>
> Warning: ensure that a check valve is not plumbed into the prover
> inlet line. If it is, remove the check valve, otherwise the prover
> will need to be drained via the plug in the bottom of the lower neck.

1.  Cleanliness Check

> Both the standard and the prover must be internally clean. This should
> be verified by checking that water drains properly from them. If
> necessary, either or both should be cleaned with water and detergent
> (see GMP No. 6) to attain good drainage characteristics.

2.  Neck scale plate verification

    1.  Fill the prover with water from the standard. Check the prover
        levels and adjust if necessary. Check the prover system for
        leaks. This is a wet‑down run.

    2.  Bleed the liquid level down to a graduation near the bottom of
        the upper neck. \"Rock\" the prover to \"bounce\" the liquid
        level, momentarily, to ensure that it has reached an equilibrium
        level. Read and record this setting. This is in preparation for
        calibration of the neck scale.

    3.  Remove the fill hose or pipe from the top and insert a funnel.

    4.  Recheck the scale reading, then add 1 gal of water (or a volume
        equal to approximately ¼ or ^1^/~5~ of the graduated neck
        volume) from a suitable standard; record the scale reading.

    5.  Repeat 2.4.3.4 by successive additions until water is near the
        top of the scale (the neck capacity is usually about 5 gal).
        Record scale readings after each addition. The closer the water
        is to the top of the neck, the harder it may be to \"bounce\"
        the liquid in the gauge.

> A plot of scale readings with respect to volume added should be linear
> and will be a gross check of the validity of this calibration.

6.  Calculate and check accuracy of the neck scale for each interval.
    The error should be less than 0.5 % of the graduated neck volume. If
    more than this, the scale should be replaced or issue the NSCV and
    instructions to user.

7.  The neck scale calibration value is calculated as follows:

> $\text{NSCV} = \frac{V_{w}}{\left( \text{sr}_{f} - \text{sr}_{i} \right)}$
> Eqn. 1
>
> where:

  ---------------------- ------------------------------------------------
  NSCV                   Neck scale calibration value

  V~w~                   Total volume of water added to neck

  $$\text{sr}_{f}$$      Scale reading, final

  $$\text{sr}_{i}$$      Scale reading, initial
  ---------------------- ------------------------------------------------

3.  Body Calibration

    1.  Drain the prover through its inlet valve and the liquid bleeder
        valve. When the liquid reaches the top of the lower gauge glass,
        close the inlet valve and allow the water to drain from the
        interior of the prover into the lower neck for 30 s, while
        controlling the water flow and level with the bleeder valve
        until the liquid meniscus reaches the zero graduation. The
        liquid level should be exactly at the zero graduation and the
        bleeder valve closed simultaneously at the 30 s drain time.
        (Draining with the bleeder valve close to the zero mark should
        be started during the 30 s drain period but should not be
        completed before the end of the drain period.)

> Alternatively, though not recommended, the prover may be completely
> drained with a 30 s drain time and then refilled with a funnel that
> has been wet down, and small volume of water to set the zero mark.
> Errors from this process will result due to the additional drain and
> retention time and other factors associated with the process.

2.  Transfer 100 gal (or other suitable volume) from the standard in the
    usual manner, and record the standard and prover temperature
    readings. If multiple transfers are required, record temperature of
    the standard at the time of each transfer, but that of the prover
    only after the final transfer. \"Rock\" the prover to \"bounce\" the
    liquid in the upper gauge glass before reading. Record the scale
    reading after the nominal volume has been transferred into the
    unknown LPG prover.

> Note regarding temperature measurements: A digital temperature sensing
> device with a long cable can allow insertion of the probe into the
> standard and the unknown to enable direct liquid 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.

3.  Drain the LPG prover as described in 2.4.4.1 and make another test
    run. Record the temperatures of the standard(s) and the unknown and
    final scale reading. Calculate the prover error at 0 psig for each
    run using the appropriate equations in Section 3; these values are
    used to evaluate repeatability of the test only. The error at 0 psig
    for the test runs should agree within 0.02 % of the prover volume or
    approximately one‑half the prover tolerance (i.e., 5 in^3^ on a 100
    gal LPG prover). If the repeatability is larger than 0.02 % of the
    prover volume, continue until replicates agree within these limits,
    taking care to ensure that poor cleanliness, contamination, bubbles
    in hoses, leaking valves or seals are not contributing to poor
    repeatability. Repeatability problems may also be due to poor field
    conditions, such as when calibration is conducted in unstable
    environments. Repeatability problems must be corrected before
    calibration can be completed.

4.  Replace the relief valve and plug in the top of the prover using
    suitable pipe joint compound or tape. Allow water from 2.4.4.3 (the
    second run) to remain in prover.

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4.  Prover Adjustments

    1.  The internal pressure and hence the volume of the prover may
        vary during use. Accordingly, a pressure correction must be made
        using the data of steps 2.4.6.

> To minimize the amount of correction needed when the prover is in use,
> the prover should be adjusted to indicate its nominal capacity when
> 100 psig is applied. (An internal pressure of 100 psig is suggested as
> being convenient.) If the actual volume of the prover is not near a
> convenient whole gallon value and cannot easily be adjusted to a whole
> gallon value, a prover correc­tion value can be computed (see 3.4) and
> added to the pressure correction values to obtain a set of combined
> prover and pressure correction values to be computed. The pressure
> correction is computed in 3.4.

2.  Use a cylinder of nitrogen or compressed air and a proper pressure
    regulator with an integrated pressure gauge.

> Connect the cylinder regulator output to the vapor return fitting (2)
> near the top of the neck. This may require fashioning a connection
> with steel pipe nipples or other appropriate materials and the
> existing fittings.
>
> Caution: Ensure that all piping and fittings are rated for the
> pressures to which they will be exposed.
>
> Make sure all valves are closed except the vapor return valve. Verify
> that the final scale reading has not changed since it was recorded (if
> it has changed it may signal a leak in one of the valves or fittings),
> and then slowly introduce pressure until the installed prover gauge
> reads 100 psig. Lightly tap the gauge to ensure that the gauge needle
> is not sticking. \"Bounce\" the liquid in the neck, then read and
> record the liquid level at this applied pressure.
>
> Return pressure to 0 psig and reapply pressure as above. This reading
> at 100 psig should agree with the above recorded reading within 0.02 %
> of the nominal volume of the prover. Leaking seals or valves may cause
> problems with repeatability of the gauge readings under pressure.

3.  With the pressure in the prover at 100 psig, adjust the upper scale
    to read the nominal volume. This is accomplished by adjusting the
    upper scale so that the water level reading is:

> Desired scale reading = *V~X~*~60~ *-- (V~NOM~ \** 1.00032) Eqn. 2
>
> Take care to use like units in the calculation. The calculation for
> *V~X~*~60~ is given in 3.1, Eqn 5.
>
> Note: The correction factor 1.00032 corrects for the compres­sibility
> of the water at 100 psig. If the upper scale is not adjustable, see
> 2.4.5.4.

4.  For provers with only an adjustable lower scale (or one in which the
    upper scale is not adjustable), a prover correction, *L~C~*~,~ may
    be calculated at 100 psig as follows:

> $L_{C} = V_{X\text{60}} - \left( V_{\text{NOM}} \ast 1\text{.}\text{00032} \right) - sr_{u}$
> Eqn. 3
>
> where:

+---------------+------------------------------------------------------+
| $$L_{C}$$     | # Prover correction at 100 psig                      |
+---------------+------------------------------------------------------+
| *V~X~*~60~    | Volume of unknown prover at 60 F                     |
+---------------+------------------------------------------------------+
| $$V_{         | Nominal volume of prover                             |
| \text{NOM}}$$ |                                                      |
+---------------+------------------------------------------------------+
| $$\t          | Upper scale reading at 100 psig                      |
| ext{sr}_{u}$$ |                                                      |
+---------------+------------------------------------------------------+
| 1.00032       | Correction factor for the compressibility of water   |
|               | at 100 psig                                          |
+---------------+------------------------------------------------------+

> Take care to use like units in the calculation.
>
> If the prover correction is negative, move the bottom scale down to
> increase the prover volume. If the prover correction is positive, move
> the bottom scale up to decrease the prover volume. The distance *h*
> that the bottom scale is to be moved is:
>
> $h = \frac{4\left| L_{C} \right|}{\pi d^{2}}$ Eqn. 4
>
> where:

+----------+-----------------------------------------------------------+
| *h*      | # Dista                                                   |
|          | nce in inches the bottom scale is to be moved, up or down |
+----------+-----------------------------------------------------------+
| $        | # Prover correction at 100 psig in cubic inches           |
| $L_{C}$$ |                                                           |
+----------+-----------------------------------------------------------+
| *d*      | Inside diameter of the lower neck of the prover in inches |
|          | (as noted on identification plate)                        |
+----------+-----------------------------------------------------------+

5.  Pressure Correction

    1.  Return pressure to 0 psig. Record the reading. Slowly introduce
        pressure until the installed prover gauge reads 50 psig. Lightly
        tap the gauge to ensure that the gauge needle is not sticking.
        \"Bounce\" the liquid in the neck, then read and record the
        liquid level at this applied pressure.

    2.  Repeat step 2.4.6.1 at 100, 150, and 200 psig. Other pressure
        points in between those listed may be tested if so desired. (The
        water level should decrease 10 in^3^ to 15 in^3^ for each 50
        psig increase in pressure, although this varies depending on the
        geometry and age of the LPG prover. Water level changes
        significantly greater than indicated may be due to leaking seals
        and/or valves.) Erratic pressure readings may also be due to air
        entrapment based on prover design; repeated pressurizing of the
        prover should eliminate entrapped air. Air entrapment problems
        due to design may need to be investigated and corrected.

    3.  Repeat step 2.4.6.1 as the pressure is bled down to 150, 100,
        50, and 0 psig (atmospheric pressure). The readings should agree
        with those previously obtained within approximately 0.02 % of
        the nominal prover volume. If the data are not linear with
        respect to pressure, repeat the series of measurements above to
        verify the nonlinearity of the readings. Leaking seals or valves
        may cause problems with repeatability of the gauge readings
        under pressure. The cause of repeatability errors must be
        identified and corrected before continuing the calibration.

6.  Final Operations

    1.  Seal the bottom and top scales as specified by laboratory policy
        and as appropriate.

    2.  Drain prover, then remove plug (5) at the lower neck to
        facilitate drainage below the lower gauge. If time permits, let
        the prover drain overnight.

    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.

    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.

3 Calculations

3.1 Single Delivery

3.  

> 3.1.1 Calculate *V~X~*~60~, the volume of the unknown prover at 60 F,
> using the following equation:
>
> $V_{X\text{60}} = \frac{\rho_{1}\left\{ \left( V_{S\text{60}}\text{  } + \text{  }\Delta_{1} \right)\left\lbrack 1 + \text{   }\alpha\left( t_{1} - \text{60}^{\circ}F \right) \right\rbrack \right\}}{\rho_{x}\left\lbrack 1 + \beta\left( t_{x} - \text{60}^{\circ}F \right) \right\rbrack}$
> Eqn. 5

2.  Multiple Deliveries

    1.  Calculate *V~X~*~60~, the volume of the unknown prover at 60 F,
        using the following equation:

$V_{X\text{60}} = \frac{\rho_{1}\left\{ \left( V_{S\text{60}} + \Delta_{1} \right)\left\lbrack 1 + \alpha\left( t_{1} - \text{60}^{\circ}\text{F } \right) \right\rbrack \right\} + \rho_{2}\left\{ \left( V_{S\text{60}} + \Delta_{2} \right)\left\lbrack 1 + \alpha\left( t_{2} - \text{60}^{\circ}\text{F } \right) \right\rbrack \right\} + \text{.}\text{.}\text{.} + \rho_{N}\left\{ \left( V_{S\text{60}} + \Delta_{N} \right)\left\lbrack 1 + \alpha\left( t_{N} - \text{60}^{\circ}\text{F } \right) \right\rbrack \right\}}{\rho_{x}\left\lbrack 1 + \beta\left( t_{x} - \text{60}^{\circ}F \right) \right\rbrack}$
Eqn. 6

**Table 2. Variables for *V~X~*~60~ equations**

+----------+-----------------------------------------------------------+
| Symbols  |                                                           |
| Used in  |                                                           |
| E        |                                                           |
| quations |                                                           |
+----------+-----------------------------------------------------------+
| *V       | volume of the unknown vessel at 60 F                      |
| ~X~*~60~ |                                                           |
+----------+-----------------------------------------------------------+
| *V       | volume of the standard vessel at 60 F                     |
| ~S~*~60~ |                                                           |
+----------+-----------------------------------------------------------+
| $$\rho_  | density of the water in the standard prover where *~1~*   |
| {1},\rho | is the density of the water for the first delivery, *~2~* |
| _{2},\te | is the density of the water for the second delivery, and  |
| xt{.}\te | so on until all N deliveries are completed                |
| xt{.}\te |                                                           |
| xt{.},\r |                                                           |
| ho_{N}$$ |                                                           |
+----------+-----------------------------------------------------------+
| *~1~,    | volume difference between water level and the reference   |
| ~        | mark on the standard where the subscripts 1, 2,\..., N,   |
| 2~,\..., | represent each delivery as above. If the water level is   |
| ~N~*     | below the reference line, 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      |
+----------+-----------------------------------------------------------+
| *t~1~,   | temperature of water for each delivery with the           |
| t~2~,    | subscripts as above                                       |
| \...,    |                                                           |
| t~N~*    |                                                           |
+----------+-----------------------------------------------------------+
|          | coefficient of cubical expansion for the standard in      |
|          | units / ºF                                                |
+----------+-----------------------------------------------------------+
| *ß*      | coefficient of cubical expansion for the prover in units  |
|          | / ºF                                                      |
+----------+-----------------------------------------------------------+
| *t~x~*   | temperature of the water in the filled unknown vessel in  |
|          | units ºF                                                  |
+----------+-----------------------------------------------------------+
| *~x~*    | density of the water in the unknown vessel in g/cm^3^     |
+----------+-----------------------------------------------------------+
| Note:    |                                                           |
| Values   |                                                           |
| for the  |                                                           |
| density  |                                                           |
| of water |                                                           |
| at the   |                                                           |
| re       |                                                           |
| spective |                                                           |
| temp     |                                                           |
| eratures |                                                           |
| may be   |                                                           |
| found in |                                                           |
| Table    |                                                           |
| 9.8 (in  |                                                           |
| NISTIR   |                                                           |
| 6969).   |                                                           |
| It may   |                                                           |
| also be  |                                                           |
| ca       |                                                           |
| lculated |                                                           |
| using    |                                                           |
| the      |                                                           |
| formula  |                                                           |
| given in |                                                           |
| GLP 10.  |                                                           |
+----------+-----------------------------------------------------------+

3.  Pressure Corrections

Compute the pressure correction, P~corr~, at each pressure that the
prover was read, after any adjustments, by correcting for the
compressibility of the water. The equation is:

> $\begin{array}{r}
> P_{\text{corr}} = \text{Scale}\ \text{reading}\ @\ \text{100}\ \text{psig} - \text{scale}\ \text{reading}\ @\ X\ \text{psig} \\
>  + \left( \text{water}\ \text{compressiblity}\ \text{factor} \right)\left( \frac{\text{100}\ \text{psig} - X\ \text{psig}}{\text{100}} \right)
> \end{array}$ Eqn. 7
>
> where the water compressibility factor is 7.4 in^3^ or 0.032 gal for a
> 100 gallon prover and 1.8 in^3^ or 0.008 gal for a 25 gallon prover.
> The compressibility value is 0.00032 gal per gallon for 100 psig. The
> compressibility factor is given in both cubic inches and gallons so
> the proper unit can be selected depending upon the unit used for the
> scale readings.
>
> 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. See Appendix A for an
> example of the pressure corrections.

3.4 Prover Volume

> LPG provers are generally adjusted to the nominal value using 100 psig
> as the reference pressure. At 100 psig, the prover reading will be
> lower by at least 0.032 gal/gal than it was at 0 psig due to the
> compressibility of water under pressure. Therefore, a prover of 100
> gal should be set to read the *V~X~*~60~ value at 0 psig minus 7.4
> in^3^. (The water level on the prover's upper scale will be below the
> calculated *V~X~*~60~ reading when pressurized to 100 psig). The
> prover must not be set to read the *V~X~*~60~ value plus the
> compressibility factor at 0 psig because, in addition to
> compressibility of water, the prover expands as pressure is applied.

3.  Measurement Assurance

    1.  If a check standard is used (See SOP 20, SOP 30), repeat the
        process for the unknown prover on the check standard without
        adjustments.

    2.  Plot the check standard volume and verify that it is within
        established limits. Alternatively a *t*-test may be incorporated
        to check the observed value against an accepted value.

    3.  The mean of the check standard values is used to evaluate bias
        and drift over time.

    4.  Check standard values may be used to calculate the standard
        deviation of the measurement process.

    5.  If a check standard is not used, the laboratory will need to
        maintain a Range chart according to SOP 20 to determine the
        repeatability for this procedure.

5 Assignment of Uncertainties

1.  The limits of expanded uncertainty, *U*, include estimates of the
    standard uncertainty of the laboratory volumetric standards used,
    *u~s~*, plus the uncertainty of measurement, *u~m~*, at the 95 %
    level of confidence. See SOP 29 for the complete standard operating
    procedure for calculating the uncertainty.

2.  The standard uncertainty for the standard, *u~s~*, is obtained from
    the calibration report. The combined standard uncertainty, *u~c~*,
    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*.

3.  Neck calibration uncertainty should be estimated based on the
    uncertainty of standards used, errors observed during calibration,
    and the repeatability of the neck calibration.

4.  Standard deviation of the measurement process from control chart
    performance (See SOP No. 20 and SOP 30)

    1.  The value for *s~p~* is obtained by estimation using the range
        from the control chart data for large volume transfer
        procedures.

> Note: 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.

5.  Other standard uncertainties usually included at for this type of
    calibration level include uncertainties associated with the ability
    to read the meniscus, only part of which is included in the process
    variability, viscosity effects, the cubical coefficient of expansion
    for the prover under test, use of proper temperature corrections,
    the accuracy of temperature measurements, water density equation,
    the compressibility of water, round robin data showing
    reproducibility, environmental variations over time, and bias or
    drift of the standard.

    1.  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 "wet-down" 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.

6 Report

1.  Report results as described in SOP No. 1, Preparation of
    Calibration/Test Results, with the addition of the following:

    1.  For LPG provers, the total prover volume and uncertainty,
        reference temperature, 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.\
        \
        The report should also include a pressure correction table or
        chart, along with a note regarding possible differences in
        retention characteristics between water, the calibration medium,
        and LPG products.

**Figure 1.** LPG Prover Schematic

**Appendix A**

**SOP No. 21**

**Recommended Standard Operations Procedure for**

**Calibration of LPG Provers**

1.  Compressibility of Water

The water compressibility factor is calculated based on an equation
given in a paper by Frank E. Jones and Georgia L. Harris, \"ITS-90
Density of Water Formulation for Volumetric Standards Calibration\", as
published in the Journal of Research of the National Institute of
Standards and Technology, Vol. 97, No. 3, 1992.

$$\text{Compressibility  factor } = \text{  }\left( V_{\text{NOM}} \right)\left( \text{ 231 } \right)(kT)(P)$$

where

  -------------------- --------------------------------------------------
  V~NOM~               Nominal volume of Prover in gal

  *kT*                 Thermal compressibility of water in (atm)^-1^

  *P*                  Pressure in atm
  -------------------- --------------------------------------------------

And

$\text{kT} = \text{50}\text{.}\text{83101}x\text{10}^{- 8} - 3\text{.}\text{68293}x\text{10}^{- 9}t + 7\text{.}\text{263725}x\text{10}^{- \text{11}}t^{2} - 6\text{.}\text{597702}x\text{10}^{- \text{13}}t^{3} + 2\text{.}\text{87767}x\text{10}^{- \text{15}}t^{4}$

where k*T* is in (kPa)^-1^ and 1 atm = 101 325 Pa (exactly).

The thermal compressibility of water for the reference temperature 60 F
(15.56 C) is 4.66264002 x 10^-9^/kPa. LPG provers are calibrated at a
nominal reference point at a specified temperature and pressure,
typically 60 F and 100 psig. A pressure of 100 psig correlates to
6.8 atmospheres. The following equation was used to calculate the
compressibility factor:

Compressibility factor = (*V~Nom~*)(231)(*kT*)(*P*)

Compressibility factor = 100 gal (231 in^3^/gal)(4.72442x10^-5^/atm)(6.8
atm) = 7.4 in^3^ or 0.032 gal

1.  Example of Pressure Corrections

The following example is printed from a Lotus 1, 2, 3 program written by
L. F. Eason, Metrologist (NC) to perform calculation for volume
transfer. The program was modified by Georgia Harris (NIST) to provide
calculations and corrections for LPG prover testing.

+---------+---------+-------+-------+---------+-----+-------+------+
| *       |         |       |       |         |     |       |      |
| *VOLUME |         |       |       |         |     |       |      |
| T       |         |       |       |         |     |       |      |
| RANSFER |         |       |       |         |     |       |      |
| CALI    |         |       |       |         |     |       |      |
| BRATION |         |       |       |         |     |       |      |
| ‑ METAL |         |       |       |         |     |       |      |
| LPG     |         |       |       |         |     |       |      |
| P       |         |       |       |         |     |       |      |
| ROVER** |         |       |       |         |     |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+
| DATE:   |         |       |       |         |     |       |      |
| 0       |         |       |       |         |     |       |      |
| 4/09/91 |         |       |       |         |     |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+
| COMPANY |         |       | Han   |         |     |       |      |
| NAME:   |         |       | dbook |         |     |       |      |
|         |         |       | 145   |         |     |       |      |
| A       |         |       | Ex    |         |     |       |      |
| DDRESS: |         |       | ample |         |     |       |      |
|         |         |       |       |         |     |       |      |
| CITY,   |         |       | 12321 |         |     |       |      |
| STATE:  |         |       | Some  |         |     |       |      |
|         |         |       | S     |         |     |       |      |
|         |         |       | treet |         |     |       |      |
|         |         |       |       |         |     |       |      |
|         |         |       | Anyw  |         |     |       |      |
|         |         |       | here, |         |     |       |      |
|         |         |       | USA   |         |     |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+
| NOMINAL |         |       | 100   |         |     |       |      |
| VOLUME  |         |       | GA    |         |     |       |      |
| OF      |         |       | LLONS |         |     |       |      |
| PROVER: |         |       |       |         |     |       |      |
|         |         |       | 100‑  |         |     |       |      |
| PROVER  |         |       | 234LP |         |     |       |      |
| SERIAL  |         |       |       |         |     |       |      |
| NO:     |         |       | Pr    |         |     |       |      |
|         |         |       | overs |         |     |       |      |
| MANUFA  |         |       | Unli  |         |     |       |      |
| CTURER: |         |       | mited |         |     |       |      |
|         |         |       |       |         |     |       |      |
| NUMBER  |         |       | 1     |         |     |       |      |
| OF      |         |       | (     |         |     |       |      |
| DEL     |         |       | 0‑15) |         |     |       |      |
| IVERIES |         |       |       |         |     |       |      |
| RE      |         |       |       |         |     |       |      |
| QUIRED: |         |       |       |         |     |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+
| DATA    |         |       |       |         |     |       |      |
| FOR     |         |       |       |         |     |       |      |
| IND     |         |       |       |         |     |       |      |
| IVIDUAL |         |       |       |         |     |       |      |
| S       |         |       |       |         |     |       |      |
| TANDARD |         |       |       |         |     |       |      |
| DEL     |         |       |       |         |     |       |      |
| IVERIES |         |       |       |         |     |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+
| DROP    | VOL     | METAL | EXP   | TEMP    | T   | WATER | D    |
|         |         |       |       |         | EMP |       | ELTA |
| NO      | (GAL)   | (M    | COEF  | DEG C   |     | DE    |      |
|         |         | S/SS) |       |         | DEG | NSITY | (CU  |
|         |         |       |       |         | F   |       | IN)  |
+---------+---------+-------+-------+---------+-----+-------+------+
| 1       | 100     | stai  | 0.    | 15.55   | 59  | 0.9   | 0    |
|         |         | nless | 00003 |         | .99 | 99013 |      |
+---------+---------+-------+-------+---------+-----+-------+------+
| TYPE OF |         |       |       |         | m   |       |      |
| METAL   |         |       |       |         | ild |       |      |
| FOR THE |         |       |       |         | st  |       |      |
| U       |         |       |       |         | eel |       |      |
| NKNOWN: |         |       |       |         |     |       |      |
|         |         |       |       |         | 0.0 |       |      |
| COEF    |         |       |       |         | 000 |       |      |
| FICIENT |         |       |       |         | 186 |       |      |
| OF      |         |       |       |         | /°F |       |      |
| EXP     |         |       |       |         |     |       |      |
| ANSION: |         |       |       |         | 15  |       |      |
|         |         |       |       |         | .55 |       |      |
| WATER   |         |       |       |         | C   |       |      |
| TEMPE   |         |       |       |         |     |       |      |
| RATURE: |         |       |       |         | 59  |       |      |
|         |         |       |       |         | .99 |       |      |
| WATER   |         |       |       |         | F   |       |      |
| D       |         |       |       |         |     |       |      |
| ENSITY: |         |       |       |         | 0.  |       |      |
|         |         |       |       |         | 999 |       |      |
| GAUGE   |         |       |       |         | 013 |       |      |
| AT 0    |         |       |       |         | g   |       |      |
| PSIG:   |         |       |       |         | /cm |       |      |
|         |         |       |       |         | ^3^ |       |      |
| GAUGE   |         |       |       |         |     |       |      |
| AT 50   |         |       |       |         | 0   |       |      |
| PSIG:   |         |       |       |         | .09 |       |      |
|         |         |       |       |         | gal |       |      |
| GAUGE   |         |       |       |         |     |       |      |
| AT 100  |         |       |       |         | 0   |       |      |
| PSIG:   |         |       |       |         | .02 |       |      |
|         |         |       |       |         | gal |       |      |
| GAUGE   |         |       |       |         |     |       |      |
| AT 150  |         |       |       |         | ‑0  |       |      |
| PSIG:   |         |       |       |         | .05 |       |      |
|         |         |       |       |         | gal |       |      |
| GAUGE   |         |       |       |         |     |       |      |
| AT 200  |         |       |       |         | ‑0  |       |      |
| PSIG:   |         |       |       |         | .10 |       |      |
|         |         |       |       |         | gal |       |      |
| D       |         |       |       |         |     |       |      |
| ELIVERY |         |       |       |         | ‑0  |       |      |
| VOLUME  |         |       |       |         | .16 |       |      |
| AT 60   |         |       |       |         | gal |       |      |
| °F:     |         |       |       |         |     |       |      |
|         |         |       |       |         | 10  |       |      |
| UNKNOWN |         |       |       |         | 0.0 |       |      |
| PR      |         |       |       |         | 000 |       |      |
| OVER\'S |         |       |       |         | *V  |       |      |
| ERROR   |         |       |       |         | ~X~ |       |      |
| AT 100  |         |       |       |         | *~6 |       |      |
| PSIG:   |         |       |       |         | 0~, |       |      |
|         |         |       |       |         | g   |       |      |
|         |         |       |       |         | all |       |      |
|         |         |       |       |         | ons |       |      |
|         |         |       |       |         |     |       |      |
|         |         |       |       |         | 4.2 |       |      |
|         |         |       |       |         | in  |       |      |
|         |         |       |       |         | ^3^ |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+
| ADJ     |         |       |       |         |     |       |      |
| USTMENT |         |       |       |         |     |       |      |
| INSTR   |         |       |       |         |     |       |      |
| UCTIONS |         |       |       |         |     |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+
| To      |         |       |       |         |     |       |      |
| adjust  |         |       |       |         |     |       |      |
| prover  |         |       |       |         |     |       |      |
| to      |         |       |       |         |     |       |      |
| deliver |         |       |       |         |     |       |      |
| exactly |         |       |       |         |     |       |      |
| 100     |         |       |       |         |     |       |      |
| gallons |         |       |       |         |     |       |      |
| at 60   |         |       |       |         |     |       |      |
| F,      |         |       |       |         |     |       |      |
| adjust  |         |       |       |         |     |       |      |
| scale   |         |       |       |         |     |       |      |
| to read |         |       |       |         |     |       |      |
| -0.032  |         |       |       |         |     |       |      |
| gallons |         |       |       |         |     |       |      |
| or ‑7.4 |         |       |       |         |     |       |      |
| in^3^,  |         |       |       |         |     |       |      |
| at 100  |         |       |       |         |     |       |      |
| psig.   |         |       |       |         |     |       |      |
| Move to |         |       |       |         |     |       |      |
| ‑0.032  |         |       |       |         |     |       |      |
| gals,   |         |       |       |         |     |       |      |
| ‑7.4    |         |       |       |         |     |       |      |
| in^3^,  |         |       |       |         |     |       |      |
| by 0.34 |         |       |       |         |     |       |      |
| inches  |         |       |       |         |     |       |      |
| if 4\"  |         |       |       |         |     |       |      |
| lower   |         |       |       |         |     |       |      |
| scale.  |         |       |       |         |     |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+
| PROVER  |         |       |       |         |     |       |      |
| P       |         |       |       |         |     |       |      |
| RESSURE |         |       |       |         |     |       |      |
| CORR    |         |       |       |         |     |       |      |
| ECTIONS |         |       |       |         |     |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+
|         | psig    | P~    | P     | Prover  | Vol |       |      |
|         |         | corr~ | rover | Error   | ume |       |      |
|         |         |       | Error |         | of  |       |      |
|         |         |       |       |         | the |       |      |
|         |         |       |       |         | Ad  |       |      |
|         |         |       |       |         | jus |       |      |
|         |         |       |       |         | ted |       |      |
|         |         |       |       |         | Pro |       |      |
|         |         |       |       |         | ver |       |      |
|         |         |       |       |         | (g  |       |      |
|         |         |       |       |         | al) |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+
|         | 0       | ‑     | ‑     | ‑0.090  | 99. |       |      |
|         |         | 0.108 | 0.108 |         | 829 |       |      |
|         | 50      |       |       | ‑0.036  |     |       |      |
|         |         | -     | ‑     |         | 99. |       |      |
|         | 100     | 0.054 | 0.054 | 0.018   | 946 |       |      |
|         |         |       |       |         |     |       |      |
|         | 150     | 0.000 | 0.000 | 0.052   | 1   |       |      |
|         |         |       |       |         | 00. |       |      |
|         | 200     | 0.034 | 0.034 | 0.096   | 000 |       |      |
|         |         |       |       |         |     |       |      |
|         |         | 0.078 | 0.078 | Not     | 1   |       |      |
|         |         |       |       | Adj.    | 00. |       |      |
|         |         |       | Adj.  |         | 034 |       |      |
|         |         |       |       |         |     |       |      |
|         |         |       |       |         | 1   |       |      |
|         |         |       |       |         | 00. |       |      |
|         |         |       |       |         | 078 |       |      |
+---------+---------+-------+-------+---------+-----+-------+------+

![](media/image2.wmf)

[^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. The majority of LPG provers in use are
    20 gal, 25 gal, and 100 gal nominal sizes. The volume of LPG provers
    is established at 60 ºF and 100 psig.