**SOP No. 15**

**Recommended Standard Operations Procedure for**

**Calibration of Intermediate and Large Volume Standards**

**Gravimetric Method**[^1] **Using an Equal-Arm Balance**[^2]

1.  Introduction

    1.1 Purpose of Calibration

This procedure is applicable to calibrations where high accuracy is
needed, or where the volumetric transfer method is not possible. It is
especially useful for the capacity range of 5 gal to 100 gal (or larger)
using an equal-arm balance and the double substitution weighing method
as described in SOP 4. It may also be used for smaller volumes with an
equal-arm balance. If an electronic balance is used, see SOP 14.

2.  Prerequisites

    1.  Verify that valid calibration certificates are available for the
        standards used in the test.

    2.  Verify that the standards to be used have sufficiently small
        standard uncertainties for the intended level of calibration.
        Reference standards should not be used for gravimetric
        calibration.

    3.  Verify that the balance used is in good operating condition with
        sufficiently small process standard deviation as verified by a
        valid control chart, or preliminary experiments to ascertain its
        performance quality when a new balance is put into service. The
        accuracy of the balance and weighing procedures should be
        evaluated to minimize potential bias in the measurement process.

    4.  Verify that the operator is experienced in precision weighing
        techniques and has had specific training in SOP 2, SOP 4, SOP
        29, and GMP 1, GMP 3, GMP 10, and gravimetric calibrations.

    5.  Verify that the laboratory facilities meet the minimum
        conditions shown in Table 1 to meet the expected uncertainty
        achievable with this procedure.

    6.  Verify that an adequate supply of distilled or deion­ized water
        (see GLP 10) is available.

# Table 1. Laboratory environmental conditions

+-----------+------------------------------------+--------------------+
| Procedure | Temperature                        | #                  |
|           |                                    |  Relative Humidity |
+-----------+------------------------------------+--------------------+
| Gr        | 20 °C to 23 °C, a set point ± 2    | 40 % to 60 %       |
| avimetric | °C,\                               |                    |
|           | maximum change 1 °C/h              | ± 10 % max change  |
|           |                                    | / 4 h              |
+-----------+------------------------------------+--------------------+

2 Methodology

2.1 Summary

> This procedure may be used to determine three calibration values:

1.  The contained volume, *V~C~*, which is the volume of water required
    to fill the vessel at a specified temperature (usually 60 °F for
    petroleum products).

2.  The delivered volume, *V~D~*, which is the volume of water that may
    be poured or drained from the vessel at a specified temperature
    (usually 60 °F for petroleum products) under specified conditions
    (see note 1).

3.  The neck scale calibration value, *NSCV*, which relates the true
    volume of the neck to the value indicated by the neck scale.

The mass of water required to fill the vessel is measured at an observed
temperature. The known density of water and coefficient of expansion of
the vessel are used to calculate the volume of the vessel at a reference
temperature.

The precision attained will depend on the sensitivity of the balance and
on the care exercised in carrying out the various operations of the
procedure. Cleanliness of the vessel and strict adherence to the
prescribed drainage procedure are critical for high precision. The
accuracy of calibration depends on all of the above plus the
uncer­tainties of the various weighings, accuracy in reading a meniscus
(where present), the volumetric temperature equilibration and
corrections, the proper correction for air buoyancy, and the purity of
the water used as the standard. The metrologist must critically consider
all of the above factors when assigning uncertainty limits to the
calibrated volumes.

With careful observance of good measurement practices, an overall
relative uncertainty of ± 0.02 % should be attainable.

1.  Apparatus

    1.  Equal‑arm balance of adequate capacity and sensitivity (standard
        deviation of 500 mg or better for 5 gal level).

    2.  Weights (meeting ASTM Class 2 or 3 specifications) as
        appropriate for the accuracy requirements.

    3.  Calibrated thermometer accurate to ± 0.1 °C with recent
        calibration values that are traceable to NIST to determine water
        temperature.[^3]

    4.  Calibrated thermometer accurate to ± 0.5 °C with recent
        calibration values that are traceable to NIST to determine air
        temperature.

    5.  Calibrated barometer accurate to ±135 Pa (1 mm Hg) with recent
        calibration values that are traceable to NIST to determine the
        air pressure.

    6.  Calibrated hygrometer accurate to ± 10 % with recent calibration
        values that are traceable to NIST to determine relative
        humidity.

    7.  Distilled or deionized water (See GLP 10).

    8.  Stopwatch or other suitable timing device (does not need to be
        calibrated.)

    9.  Cap to place over neck of the vessel.

2.  Procedure

    1.  Preliminary Operations

        1.  Clean the interior of the vessel with biodegradable
            low‑sudsing detergent (see GMP 6) with gentle scrubbing as
            necessary. Rinse several times with clean water to remove
            all detergent, followed by pure water. Check for leaks and
            for uniform drainage.

        2.  Clean and dry outside of container to remove any material
            which might subsequently dislodge and cause an erroneous
            weighing.

        3.  Dry inside by rinsing with small amounts of alcohol or by
            drawing clean, filtered air through the vessel (several
            hours required). For large vessels the heat from a low
            wattage light bulb suspended inside the vessel overnight
            will aid in drying by slightly heating the vessel and
            creating convection currents through the interior. Allow the
            vessel to come to thermal equilibrium with the room before
            proceeding.

    2.  Empty Weight

        1.  Weigh the empty vessel and cap using the double substitution
            procedure (SOP 4) with air buoyancy correction.

        2.  Record air temperature, humidity, and barometric pressure as
            needed for calculating air density (SOP 2) and performing
            buoyancy corrections.

        3.  The empty weight is determined as shown in the calculations
            (Section 3.1, Eqn 2).

    3.  Filled Weight

        1.  Fill the vessel with pure water to the zero point on the
            neck scale. Be sure the vessel is level. Bounce the liquid
            to disturb the meniscus to assure it has reached equilibrium
            level. Record the water tempera­ture and readjust level if
            necessary. Be sure that no water remains on the outside of
            the vessel when it is weighed. (See note 2.) The filled
            weight is determined as shown in the calculations (Section
            3.1, Eqn 2).

        2.  Weigh filled vessel and cap as in 2.3.2.

    4.  Drained Weight

        1.  Drain vessel using appropriate discharge/pour and drain
            times (see note 1). Replace cap. The empty weight is
            determined as shown in the calculations (Section 3.1, Eqn
            2).

        2.  Weigh drained vessel and cap as in 2.3.2.

    5.  Make a duplicate determination of steps 2.3.2 through 2.3.4 (Run
        2).

    6.  Neck scale plate verification

        1.  Fill vessel with water to a scale division near the bottom
            of the scale range. Record reading (*s~r~*~1~).

        2.  Make appropriate successive additions of water from a
            calibrated buret or other suitable volumetric measuring
            device. Record scale readings after each addition .

        3.  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.

        4.  Calculate the neck scale calibration value, *NSCV*, using
            the expression

            $\text{NSCV}\text{  } = \text{  }\frac{V_{W}}{(\text{sr}_{f}\text{  } - \text{  }\text{sr}_{i})}$

Table 1. Variables for neck scale calibration value equation

  ----------- -----------------------------------------------------------
  Variable    Description

  *NSCV*      Neck scale calibration value

  *V~W~*      Total volume of water added to neck

  *sr~i~*     Scale reading, initial

  *sr~f~*     Scale reading, final
  ----------- -----------------------------------------------------------

3 Calculations

3.1 To calculate the filled, empty, or drained mass, use the following
equation from SOP 4 using Option A.

$M_{(\text{filled},\text{empty},\text{drained})}\text{  } = \text{  }M_{S}\left( 1\text{  } - \text{  }\frac{\rho_{a}}{\rho_{S}} \right)\text{  } + \text{  }\frac{\left( O_{2}\text{  } - \text{  }O_{1}\text{  } + \text{  }O_{3}\text{  } - \text{  }O_{4} \right)}{2}\left\lbrack \frac{M_{\text{sw}}\left( 1\text{  } - \text{  }\frac{\rho_{a}}{\rho_{\text{sw}}} \right)}{(O_{3}\text{  } - \text{  }O_{2})} \right\rbrack$

**Table 2. Variables for Equation 2**

  -----------------------------------------------------------------------
  Symbol        Description
  ------------- ---------------------------------------------------------
  *S*           standard reference weight

  *sw*          small calibrated weight used to evaluate the sensitivity
                of the balance

  *M*           the mass (true mass) of a specific weight. Subscripts
                *s*, *sw, filled, empty, drained* are used to identify
                the weight (equals Nominal plus Correction in the case of
                mass standards)

  *ρ~a~*        density of air at time of calibration

  *ρ*           density of masses; subscripts *s*, *x*, *t~s~*, *t~x~*,
                *sw* are used to identify the weight.

  *O*           Balance observations, designated with subscripts 1, 2,
                3..., for the observation number
  -----------------------------------------------------------------------

3.2 To calculate containment volume, *V~C~*, at temperature of
measurement, *t*,

$V_{Ct}\text{  } = \text{  }(M_{\text{filled}}\text{  } - \text{  }M_{\text{empty}})\text{  }\left\lbrack \frac{1}{\left( \rho_{w}\text{  } - \text{  }\rho_{a} \right)} \right\rbrack$

$V_{Dt}\text{  } = \text{  }(M_{\text{filled}}\text{  } - \text{  }M_{\text{drained}})\text{  }\left\lbrack \frac{1}{\left( \rho_{w}\text{  } - \text{  }\rho_{a} \right)} \right\rbrack$

$$`<!-- -->`{=html}3.3 To calculate delivered volume, *V~D~*, at
temperature of measurement, *t*,

3.4 To correct volumes to reference temperature, *t~ref~*, (be sure to
match units for cubical coefficient of expansion, *α,* with temperature
units (e.g., degrees C with °C^-1^).

$V_{t\text{ref}}\text{  } = \text{  }V_{t}\lbrack 1\text{  } - \text{  }\alpha(t\text{  } - \text{  }t_{\text{ref}})\rbrack$

3.5 To convert the volume measured in mL (cm^3^) to gal:

*V*~gal~ = (0.000 264 172) *V~mL~* (There are 3 785.411 784 mL per gal.)

Table 2. Variables for volume equation

  ----------------- -----------------------------------------------------
  Symbol            Description

  *ρ~w~*            density of water at temperature of filling

  *ρ~a~*            density of air

  *t*               temperature at time of test

  *t~ref~*          reference temperature, usually 60 °F (or 20 °C)

  *α*               cubical coefficient of expansion of the vessel (must
                    match temperature units in °C^-1^or °F^-1^)
  ----------------- -----------------------------------------------------

6.  Calculate the average volume at reference temperature (*V~t\ ref~* )

7.  Physical Constants

    1.  Density of Air

> Value at environmental conditions at time of weighings calculated from
> the equation given in the Appendix to SOP 2.

2.  Density of Water

> Calculate the density of water using the formula given in GLP 10 or
> look up the value from appropriate tables.

3.7.3 Cubical Coefficient of Expansion

> Values for the cubical coefficient of expansion of various materials
> are given in NISTIR 6969, Table 9.10 and are normally printed on the
> vessel identification plate (for test measures and provers).

3.  Measurement Assurance

> 4.1 Duplicate the process with a suitable check standard (See GLP 1,
> SOP 30, and NISTIR 6969, Sec. 7.4)
>
> 4.2 Plot the check standard value and verify that it is within
> established limits OR a *t*‑test may be incorporated to check the
> observed values against an accepted value.

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

4.  Check standard observations are used to calculate the standard
    deviation of the measurement process, *s~p~*.

    5 Assignment of Uncertainties

> The limits of expanded uncertainty, *U*, include estimates of the
> standard uncertainty of the mass standards used, *u~s~*, plus the
> uncertainty of measurement, s~p~, at the 95 percent level of
> confidence. See SOP 29 for the complete standard operating procedure
> for calculating the uncertainty.

5.1 The standard uncertainty for the mass 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*. See SOP 29 for proper handling of uncertainties
when multiple standards are used.

5.2 Standard deviation of the measurement process from control chart
performance (See SOP 17 or 20.) The value for *s~p~* is obtained from
the control chart data for check standards or estimated based on the
range of duplicate measurements over time. This value will incorporate a
repeatability factor related to the precision of the weighings and the
setting of the meniscus, but not related to errors in reading the
meniscus.

5.3 Other standard uncertainties usually included at this calibration
level include uncertainties associated with water temperature
measurements, thermometer accuracy, the coefficient of expansion,
viscosity, reading the meniscus, calculation of air density, standard
uncertainties associated with the density of the standards used,
improper observance of drainage times, viscosity or the surface effects
on the volume of liquid clinging to vessel walls after draining and lack
of internal cleanliness.

**Additional References:**

Bean, V. E., Espina, P. I., Wright, J. D., Houser, J. F., Sheckels, S.
D., and Johnson, A. N., NIST Calibration Services for Liquid Volume,
NIST Special Publication 250-72, National Institute of Standards and
Technology, Gaithersburg, MD, (2006).

> **Appendix**
>
> Test Notes

1.  Pour and drain times.

> It is impractical to completely drain a filled container, because some
> of the contents will remain as a film. By strict adherence to a
> specified procedure, the residual contents can be held essentially
> constant so that, reproducible calibration constants can be obtained.
> The conditions conventionally selected are as follows:
>
> a For bottom‑drain containers: open drain valve fully and allow
> contents to discharge at maximum rate. When flow ceases, wait 30 s,
> close valve, and touch off any drops adhering to spout.

b For pour‑type containers: pour contents by gradually tilting container
to an 85 º angle, so that virtually all is delivered in 30 s. Allow to
drain for an additional 10 s, then touch off any drops adhering to the
lip.

> The instructions described above must be precisely followed during
> calibration and use of the calibrated vessels.

2.  Evaporation losses.

> A suitable cap (an empty glass beaker, for example) should be placed
> on the top of open vessels to minimize evaporation losses. If used,
> the cap must be included in all weighings.

3 Slicker-plate.

When a slicker‑plate standard is calibrated, the plate should be used to
fix the water level in it. This plate must be weighed with the standard
during each such operation.

[^1]: Based on the work of J. Houser \"Procedure for the Calibration of
    Volumetric Test Measures\" NISTIR 73‑287.

[^2]: 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 reference temperature for petroleum
    products is 60 ºF and volume values are typically in gallons.

[^3]: Values from the thermometer, barometer and hygrometer are used to
    calculate the air density at the time of the measurement. The air
    density is used to make an air buoyancy correction. The accuracies
    specified are recommended for high precision calibration. Less
    accurate equipment can be used with only a small degradation in the
    overall accuracy of the measurement.