SOP SVP[^1]

**Standard Operating Procedure**

**For**

**Gravimetric Calibration of Dynamic Small Volume Provers**[^2]

### Introduction

1.1 Purpose of Test

This procedure describes the calibration of the \"to deliver\" volume of
dynamic small volume provers (SVP) that may be used as volumetric
measuring standards. The procedure uses gravimetric calibration
principles to minimize calibration uncertainties. Accordingly, the
procedure is especially useful for high accuracy calibrations. The
procedure does not incorporate measurement control steps to ensure the
validity of the standards and the measurement process; additional
precautions must be taken. The procedure makes use of an electronic
balance and is suitable for all sizes of gravimetric calibrations only
limited by the capacity and resolution of the balance. The procedure can
be used for both upstream and downstream calibrations. Each direction
will be treated as a separate calibration.

2.  Prerequisites

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

    2.  Verify that the standards and instruments (e.g., thermometer,
        barometer, and hygrometer) to be used have sufficiently small
        standard uncertainties for the 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, GMP 10, and gravimetric calibrations such as those used in
        SOP 14.

    5.  Verify that an adequate supply of distilled or de-ion­ized water
        (see GLP 10) is available.

    6.  Verify that the laboratory facility is free of air currents
        and/or temperature fluctuations where the SVP will be set up for
        testing.

    7.  Verify that the laboratory facilities meet the following minimum
        conditions to meet the expected uncertainty possible with this
        procedure:

# Table 1. Laboratory environmental conditions

+------------------+--------------------------+------------------------+
| Procedure        | Temperature              | Relative               |
|                  |                          |                        |
|                  |                          | Humidity               |
+------------------+--------------------------+------------------------+
| ## SVP/ Large Vo | 20 C to 23 C, a set      | 40 % to 60 %           |
| lume Gravimetric | point ± 2 C, maximum     |                        |
|                  | change 1.0 C/h           | ± 10 % maximum change  |
|                  |                          | / 4 h                  |
+------------------+--------------------------+------------------------+

8.  All necessary maintenance to the test artifact must be completed by
    the device owner prior to starting the gravimetric calibration. It
    is advisable to perform a static leak test prior to performing the
    test. Replace the seals on the prover if there is any doubt as to
    their integrity. If "as found" data is required, that data should be
    obtained before any seal replacements.

9.  The prover inlet and outlet must be blocked by the device owner
    before calibration by using a blind flange or double-block and bleed
    valve.

10. The device owner must provide all necessary manufacturers' manuals
    as well as trained personnel to operate the device.

    2 Methodology

    2.1 Scope, Precision, Accuracy

> The procedure is applicable for the calibration of any size of
> measuring container SVP that, when filled with water, will not
> overload the electronic balance used. Typical containers SVPs range in
> capacity from 15 gal to 120 gal. The precision of calibration will
> depend on strict adherence to the various steps of the procedure. The
> accuracy attainable will depend on the uncertainties of the standard
> weights, the air buoyancy, density of water, thermal expansion
> corrections that are made, and the repeatability of the SVP.

2.2 Summary

> The mass of the water delivered by the SVP is determined by weighing
> the water on an electronic balance and comparing it to mass standards.
> Volume is derived from mass using the equations provided.

3.  Equipment and Standards

    1.  Electronic balance having sufficient capacity to weigh the
        loaded vessel. The sensitivity of the balance will be a limiting
        factor in the accuracy of the measurement. The resolution and
        repeatability should be smaller than the accepted uncertainty of
        the calibration.

    2.  Calibrated mass standards with adequate accuracy and NIST
        traceable mass values. Ordinarily, weights of ASTM Class 2 or 3
        specifications, or equivalents are required.

    3.  Thermometer, calibrated to ± 0.1 C for measuring the temperature
        of the water, prover, and detector bar; ± 0.5 C for measuring
        the temperature of the air and calculating the air density,
        traceable to NIST.

    4.  Barometer, calibrated to ± 1 mm Hg and a hygrometer, calibrated
        to ± 5 % for calculating the air density, traceable to NIST.

    5.  Pressure gauge for determining the prover pressure, with
        calibration traceable to NIST. (Include the uncertainty of the
        pressure gauge in the uncertainty calculations.)

    6.  Distilled or de-ionized water and methods to verify its purity
        (See GLP No. 10).

4.  Procedure

    1.  Install SVP volumetric test kit per manufacturer's instructions.
        (Provided by device owner.)

    2.  Connect water supply to prover.

        1.  In general, ensure that all air is bled from the system,
            suitable water supply is provided and the device temperature
            is in equilibrium with that of the water supply. Set device
            valves as appropriate for the test to be conducted.

        2.  For Calibron (brand) SVPs, turn water supply on, and open
            appropriate valves to eliminate entrapped air according to
            manufacturer's instructions. After all air is bled off,
            close associated valves. Then open the appropriate valves
            and allow water to circulate until the temperature has
            stabilized.

        3.  For Daniels (brand) SVPs, establish valve position for
            control of upstream or downstream flow.

    3.  Install certified thermometers to record air temperature, water
        temperature, detector bar temperature (*T~d~*), and prover
        temperature (*T~p~*).

    4.  Install calibrated pressure gauge to record prover pressure
        (*P~p~*).

    5.  Connect prover control cable to controller (from the volumetric
        test kit.)

    6.  Apply power to the prover and the water draw circuit. One of the
        valves will switch on immediately. Note which valve switches on,
        and mark it as the overboard or bypass valve. The other valve is
        the draw valve and will only be on while the flag is between the
        two volume switches.

    7.  Record all of the prover-specific variables on the data entry
        form.

Note: All references in the following weighing options to the empty
receiving vessel assume that the empty receiving vessel has been placed
in a "wet-down" condition. This wet down condition is achieved when the
vessel has been filled with water and then drained using the same
process that will be used throughout this calibration.

8.  Weighings (Option A)

    1.  Zero the balance and record the balance indication as *O*~1~.
        Place a standard mass, *M~s~*~1~, on the balance platform
        (*M~s~*~1~ should be slightly larger than the mass of the empty
        receiving vessel.) Record the balance indication as *O*~2~.

    2.  Place the empty receiving vessel on balance platform and record
        the balance indication as *O*~3~. Caution: the receiving vessel
        must be dry on the outside for all weighings.

    3.  Record air temperature, barometric pressure and humidity at the
        time of these measurements.

    4.  Zero the balance and record the balance indication as *O*~4~.

    5.  Manipulate the system to cause the prover piston to move to the
        starting position and begin the water draw sequence. Record all
        pertinent test artifact temperatures and pressures during the
        water draw sequence. Immediately upon completion of the water
        draw sequence, place the filled receiving vessel on the balance
        and record the balance indication as *O*~6~. Read and record the
        temperature of the water in the container immediately after
        weighing.

    6.  Remove the filled receiving vessel and place a standard mass,
        *M*~s2~, on the balance platform (*M~s~*~2~ should be slightly
        larger than the mass of the filled vessel.) Record the balance
        indication as *O*~5~.

    7.  Record the air temperature, barometric pressure and humidity at
        the time of these measurements.

    8.  Make five duplicate runs with two runs at a flow rate differing
        from the others by at least 25 %. The measured result (*V*~60~)
        of each of these calibration runs must repeat within 0.02 %.

9.  Weighings (Option B)

    1.  Place mass standards that approximate the mass of the empty
        transfer vessel (with a lid) and adequate filter paper or other
        clean, lint-free padding material (to protect the standards
        being used) on the electronic balance. With these items on the
        balance, zero the balance. Note: the padding materials must be
        included on all measurements or their mass treated as tare.

    2.  Place additional mass standards approximating the nominal mass
        of the water volume to be measured on the balance. Take care to
        place the weights on filter paper or other appropriate
        protective padding. Record this balance indication as *O*~1~.

    3.  Remove all mass standards. Record the air temperature,
        barometric pressure, and relative humidity readings.

    4.  Place the empty receiving vessel on the balance, with the
        padding material and zero the balance indication. Remove the
        transfer vessel, lid, and padding material and record the base
        empty vessel reading (B).

    5.  Manipulate the system to cause the prover piston to move to the
        starting position and begin the water draw sequence filling the
        receiving vessel. Read and record all pertinent test artifact
        temperatures and pressures during the water draw sequence. Place
        the lid on the receiving vessel to limit evaporation.

    6.  Immediately prior to weighing full vessel record balance reading
        as (*d*~1~). This reading will be used to calculate drift while
        filling the vessel.

    7.  Place the filled vessel and all padding material on the balance.
        If needed, add known mass standards as tare weights to bring the
        water mass up to the mass of the standards used for *O*~1~. This
        balance reading is recorded as *O*~2~. Record the mass of all
        tare weights.

    8.  Remove the filled receiving vessel and record the balance
        indication as (*d*~2~). This reading will be used to calculate
        drift over the entire process.

    9.  Immediately after removing the filled receiving vessel from the
        balance, record the temperature of water in the vessel.

    10. Make five duplicate runs with two runs at a flow rate differing
        from the others by at least 25 %. The measured result (*V*~60~)
        of each of these calibration runs must repeat within 0.02 %.

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2.  Calculations

    1.  Compute the volume at the temperature of the measurement,
        *V~t~*, for each determination using the equation:

        (Option A)

$V_{T}\left\lbrack O_{6(\text{filled})}\frac{M_{s2}\left( \text{1 - }\frac{\rho_{a}}{\rho_{s2}} \right)}{\left( O_{5} - O_{4} \right)}_{3(\text{drained})}\frac{M_{s1}\left( \text{1 - }\frac{\rho_{a}}{\rho_{s1}} \right)}{\left( O_{2} - O_{1} \right)} \right\rbrack\left( \frac{1}{\rho_{w}\text{ - }\rho_{a}} \right)$
Eqn. 1

> Table 2. Variables for volume equation

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

  *M~s~,         mass of standards
  M~s~*~1~*,     
  M~s~*~2~       

  *~s~*          density of *M~S~*

  *~w~*          density of water at the temperature of measurement

  *~a~*          density of air at the conditions of calibration

  *V~t~*         Volume at the temperature of the test
  -------------- --------------------------------------------------------

(Option B)

$V_{T}\left\{ \left\lbrack O_{\text{2c}}\left( \frac{M_{s}}{O_{1}} \right)\left( \text{1 - }\frac{\rho_{a}}{\rho_{s}} \right) \right\rbrack\text{ - }M_{t}\left( \text{1 - }\frac{\rho_{a}}{\rho_{t}} \right) \right\}\left( \frac{1}{\rho_{w}\text{ - }\rho_{a}} \right)$
Eqn. 1

$O_{2c}\  = \ O_{2}\  + \ \left\{ \left\lbrack \frac{\left( d_{1} + d_{2} \right)}{2} \right\rbrack - B \right\}$
Eqn. 3

> Table 3. Variables for volume equations

+---------+------------------------------------------------------------+
| V       | Description                                                |
| ariable |                                                            |
+---------+------------------------------------------------------------+
| *O*~1~  | Observation #1, balance reading for mass standard          |
+---------+------------------------------------------------------------+
| *O*~2~  | Observation #2, balance reading for water delivered from   |
|         | prover                                                     |
+---------+------------------------------------------------------------+
| *O      | Drift compensated *O*~2~ reading                           |
| *~2*c*~ |                                                            |
+---------+------------------------------------------------------------+
| *d*~1~  | ## Drift while filling the vessel                          |
+---------+------------------------------------------------------------+
| *d*~2~  | ## Drift over entire process                               |
+---------+------------------------------------------------------------+
| *B*     | ## Base balance reading drift is based on                  |
+---------+------------------------------------------------------------+
| *M~S~*  | ## Mass of mass standards (true mass, vacuum mass)         |
+---------+------------------------------------------------------------+
| *M~t~*  | Mass of tare weights                                       |
+---------+------------------------------------------------------------+
| *~a~*   | Air density                                                |
+---------+------------------------------------------------------------+
| *~s~*   | Density of M~S~                                            |
+---------+------------------------------------------------------------+
| *~t~*   | Density of M~t~                                            |
+---------+------------------------------------------------------------+
| *~w~*   | Water density                                              |
+---------+------------------------------------------------------------+

2.  Compute *V~60~*, the volume at 60 F, for each run, using the
    equation:

    $\begin{array}{r}
    V_{\text{60}} = \frac{\text{Vw}}{\text{CCF}} \\
    \text{where} \\
    \text{CPL}_{p} = \frac{1}{\left\lbrack 1 - \left( (0\text{.}\text{0000032} \ast P_{p} \right) \right\rbrack} \\
    \text{CTS}_{p} = \left\{ \left( 1 + \left\lbrack \left( T_{p} - T_{b} \right) \ast G_{a} \right\rbrack \right) \ast \left( 1 + \left\lbrack \left( T_{d} - T_{b} \right) \ast G_{l} \right\rbrack \right) \right\} \\
    \text{CPS}_{p} = 1 + \left( \frac{\left( P_{p} \ast \text{ID} \right)}{E \ast \text{WT}} \right) \\
    \text{CCF} = \text{CPL}_{p} \ast \text{CTS}_{p} \ast \text{CPS}_{p}
    \end{array}$

> **Table 4. Additional Variables for Volume E**quations

+----------+-----------------------------------------------------------+
| Variable | Description                                               |
+----------+-----------------------------------------------------------+
| *T~b~*   | Reference (Base) temperature                              |
+----------+-----------------------------------------------------------+
| *T~d~*   | Detector bar temperature (Temperature, detector)          |
+----------+-----------------------------------------------------------+
| *T~p~*   | Prover temperature (Temperature, prover)                  |
+----------+-----------------------------------------------------------+
| *P~p~*   | ## Prover pressure (Pressure, prover) in psig             |
+----------+-----------------------------------------------------------+
| *E*      | ## Modulus of elasticity (flow tube)                      |
+----------+-----------------------------------------------------------+
| *WT*     | Wall Thickness of flow tube                               |
+----------+-----------------------------------------------------------+
| *ID*     | Inside Diameter of flow tube                              |
+----------+-----------------------------------------------------------+
| *G~l~*   | Coefficient of linear expansion (switchbar)               |
+----------+-----------------------------------------------------------+
| *G~a~*   | Coefficient of flow tube area thermal expansion           |
+----------+-----------------------------------------------------------+
| *CPL*    | Correction for the pressure on the liquid                 |
+----------+-----------------------------------------------------------+
| *CTS*    | Correction for the temperature on the standard prover     |
+----------+-----------------------------------------------------------+
| *CPS*    | Correction for the pressure on the standard prover        |
+----------+-----------------------------------------------------------+
| *CCF*    | Combined correction factor                                |
+----------+-----------------------------------------------------------+

3.  Calculate water density using the equation provided in GLP 10.

4.  Calculate the air density per SOP 2.

5.  Calculate the uncertainty for the calibration using Appendix B:

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3.  Measurement Assurance

    1.  Record and plot standard deviations of each five run calibration
        to determine short-term variations of the measurement process.

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 % level of confidence.
> See SOP 29 for the complete standard operating procedure for
> calculating the uncertainty.

1.  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*.

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 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.

5.3 Other standard uncertainties usually included for this type of
calibration level include uncertainties associated with water
temperature measurements, thermometer accuracy, calculation of air
density, and standard uncertainties associated with the density of the
standards used or the lack of internal cleanliness.

5.  References

    1.  Manual of Petroleum Measurement Standards; Chapter 11.2.3 -
        Water Calibration of Volumetric Provers; First Edition, August
        1984.

Gravimetric Calibration Data Sheet

  ----------------- ---------------------------------------------------------------------------------- -------------- --------------------------------------
  Company Name:     \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_   Test No:       \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

  Address:          \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_   Purchase Order \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
                                                                                                       No:            

  City, State, Zip: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_   Date           \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
                                                                                                       Scheduled:     

  Representative:   \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_   Date Received: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

  Phone:            \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Fax: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_         Date Tested:   \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

  Email:            \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_   Date Returned: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_

  Company URL:      \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_   Next           \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
                                                                                                       Appointment:   

  General           \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_                  
  Description                                                                                                         

  Manufacturer:     \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_                  

  Model Number:     \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Serial Number: \_\_\_\_\_\_\_\_\_\_\_                              

  Condition:        \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_                  
  ----------------- ---------------------------------------------------------------------------------- -------------- --------------------------------------

  -------------------- ------------- --------------------------- ------------
  Compressibility      3.2000E-06    Area Thermal Expansion      
  factor for water                   Coefficient (Ga)            

  Reference            60            Detector Thermal Expansion  
  Temperature(Tb)                    Coefficient (GI)            
  (^o^F)                                                         

  Reference            15.55555556   Modulus of Elasticity (flow 
  Temperature (^o^C)                 tube) (E)                   

  Reference Pressure   0             Flow Tube Inside Diameter   
  (psig)                             (inches) (ID)               

                                     Flow Tube Wall Thickness    
                                     (inches) (WT)               
  -------------------- ------------- --------------------------- ------------

  ----------------------------------- -----------------------------------
  Standards Used                      

  Full Vessel                         Empty Vessel

                                      

                                      

                                      

                                      

                                      

                                      

                                      

                                      
  ----------------------------------- -----------------------------------

Observations

  ------------------------ --------- --------- --------- --------- ---------
  Fill Number              Fill \# 1 Fill \# 2 Fill \# 3 Fill \# 4 Fill \# 5

  Flow Rate                Fast      Fast      Fast      Slow      Slow

  Run Time (sec)                                                   

  Zero Balance, *O*~1~                                             

  Balance Reading *O*~2~                                           
  (Standards Empty)                                                

  Balance Reading *O*~3~                                           
  (Empty Vessel)                                                   

  Zero Balance, *O*~4~                                             

  Balance Reading *O*~5~                                           
  (Standards Full)                                                 

  Balance Reading *O*~6~                                           
  (Full Vessel)                                                    

  Air Temperature (^o^C)                                           

  Barometric Pressure                                              
  (mmHg)                                                           

  Relative Humidity (% RH)                                         

  Water Temperature (^o^C)                                         

  Detector Bar Temperature                                         
  (*T~d~*) (^o^C)                                                  

  Prover Temperature                                               
  (*T~p~*) (^o^C)                                                  

  Prover pressure (*P~p~*)                                         
  (psig)                                                           
  ------------------------ --------- --------- --------- --------- ---------

Example uncertainty components listed in order of effect on total
uncertainty:

-   Standard deviation of the measurement process, *s~p~*

-   Water temperature

-   Reproducibility

-   Mass calibration uncertainty

-   Water density

-   Prover temperature

-   Water compressibility

-   Detector temperature

-   Prover pressure

-   Area thermal expansion (Ga)

-   Air temperature

-   Detector thermal expansion (Gl)

-   Barometric pressure

-   Relative humidity

-   Modulus of elasticity

-   Flow tube diameter (ID)

-   Tube wall thickness (WT)

[^1]: Certain commercial equipment, instruments, or materials are
    identified in this publication in order to specify the experimental
    procedure adequately. Such identification is not intended to imply
    recommendation or endorsement by the National Institute of Standards
    and Technology, nor is it intended to imply that the materials or
    equipment identified are necessarily the best available for the
    purpose.

[^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.