online uncertainty calculation

Application of online uncertainty calculation in a fiscal gas metering station

A method to improve maintenance and avoid measurement error

The measurement uncertainty indicates the uncertainty of a measured value of a physical quantity. The measurement uncertainty is a quantity that characterizes the spread of values that can reasonably be assigned to the measurement quantity. Measurement uncertainty represents the quality of the measurement.

The following flow measurement types can be distinguished with AML-Metering:

  1. Custody transfer (ca 0.5-1%)
  2. Sales Allocation (ca 2-5%)
  3. Product allocation (ca 5-10%)
  4. Environmental (ca 2-5%)

Every measurement classification has its maximum uncertainty limit depending on the measurement principle. The measurement uncertainties are described and should be under the agreement between buyer and seller, partners, and government.

Particular uncertainties will be determined first for every part of the measurement installation. These uncertainties are used to calculate the delay in actual and standard volume flow, mass flow, and energy flow.

In the Oil & Gas industry, everyone is interested in low measurement uncertainty in the (standard) gas volume and energy determined by a (fiscal) oil and gas measuring station. Uncertainty calculations can be performed on many measurement configurations and measurement principles (Orifice plate, Coriolis meter, Turbine, US, orifice, venture, etc.) systems. During the operation of a (fiscal) gas measuring station, the aim should be to achieve the lowest possible measurement uncertainty throughout the entire life cycle. Sections about measurement uncertainty are often included in gas contracts; a maximum limit is set for measurement uncertainty in standard volume and energy; for example, the value of this limit is 1%.

The measurement uncertainty in volume, mass and energy as a function of time indicates the quality/status of the gas measuring station at any desired moment. Uncertainty calculations are regularly performed by Measurement Engineers and Consultants(SME), etc. The result of such a single offline calculation is often a snapshot and gives an impression of the status of the gas measuring station at that time. Suppose the measurement uncertainty is unacceptably high (exceeding the maximum limit). In that case, one can find the cause and take possible actions to reduce further this measurement uncertainty (“preventive maintenance”). In this way, steps can be taken quickly, and high costs are saved.

Recipe measurement uncertainty

The general concept for uncertainty analysis consists of four steps. This concept is based on the international standard Guide to the Expression of Uncertainty in Measurement (ISO / IEC Guide 98-3: 2008). It is the current globally accepted standard for the calculation of measurement uncertainty. An alternative method is according to the written standard ISO 5168: 2005.

The four steps are described below:

  1. Describe the measurement setup.
  2. Determine the mathematical model. The model indicates the relationship between all input quantities and the measurement result (output quantity)
  3. Determine for each input quantity:
    a. The value and uncertainty. Each input quantity has its measurement uncertainty, and various sources of uncertainty can be assigned to the measurement of an input quantity.
    b. The distribution function (e.g., normal distribution) and the standard uncertainty.
    The analytical method determines the partial derivative and is often used with relatively simple mathematical models. c. Determination of sensitivity factor, i.e., how sensitive is the measurement result for a variation in this input quantity. In complex physical/mathematical models, numerical methods calculate the sensitivity factors. A further approach is the application of Monte Carlo simulations.
    d. The uncertainty contribution of each input quantity to the measurement result.
    e. Enter this data in an Excel spreadsheet.
  4. Determine and present the result.

Another ISO standard that was applied to calculate the uncertainty of the flow measurement is ISO 5158: 2005 “Measurement of fluid flow – Procedures for the evaluation of uncertainties.” However, this standard has expired.

We can distinguish two types of measurement uncertainty according to the ISO/IEC Guide 98:

  1. Type A measurement uncertainty: Determination of the value and measurement uncertainty of a quantity through statistical methods. Standard uncertainty is the experimental standard deviation of the mean.
  2.  Type B measurement uncertainty: Other parameters influence the measurement result. Determination of the value and uncertainty of a quantity through non-statistical methods. In this context, insight must be gained into factors that impact measurement uncertainty. For example, correction for drift, correction for temperature, resolution, data from a certificate or specification, etc.

The standard uncertainty is equivalent to “one standard deviation,” we then speak of a coverage factor k equal to one. The wish is to express the uncertainty with a coverage factor k that is equal to two. If the measured values are typically distributed, also called “Gaussian distribution,” then the coverage factor is two, and one speaks of a confidence interval of 95%. Calibration certificates often display uncertainty with a coverage factor equal to two.

3. Application of uncertainty analysis on a gas measuring station

The following fiscal measuring instruments are installed in a modern gas measuring station: flow meter, pressure transmitter, temperature transmitter/element, online gas chromatograph. Other tools include water dew point meter, hydrocarbon dew point meter, relative density meter, but these are not fiscal measuring instruments.

In a (fiscal) gas measuring station, several quantities are continuously measured with various fiscal measuring instruments installed there.

  1. Volume flow / mass flow at operational conditions, or the gas volume measured during a specific time interval. A distinction can be made between the various types of flow instrumentation, such as a Coriolis meter, turbine meter, ultrasonic meter, and measuring flange (orifice plate).
  2. Gas pressure: absolute, atmospheric, and gauge
  3. Gas temperature
  4. Gas composition using an online gas chromatograph or based on sampling and laboratory analysis
  5. Flow computer uncertainty
  6. A/D conversion
  7. Pipe temperature and pressure correction due to actual temperatures different from calibration temperature

This is the description of the measurement setup or measurement system. The below figure shows a schematic overview of a typical gas measuring station.


online uncertainty calculation


Said quantities are measured continuously, and the values of these measured quantities are therefore known at a specific desired time. Signals from the various measuring instruments are read into a Flow Computer and online gas chromatograph.

Many calculations are carried out in a (fiscal) gas measuring station with the signals from the installed measuring instruments as input. Estimates are made in the Flow Computer and the online gas chromatograph.

Below is an overview of the most important calculations to be performed:

  1. Volume flow at standard conditions.
  2. Gas density at operational and legal conditions.
  3. Mass flow under operating conditions.
  4. Energy flow at normal conditions.
  5. Gas compressibility under operating and standard requirements.
  6. The calorific value of the gas (superior and inferior). In practice, the Superior Calorific value is often calculated. Calorific value is also calculated per component.

Various algorithms are used to calculate the different parameters and are based on multiple international standards. These algorithms are programmed in Flow Computers and Gas Chromatographs.

Important standards that are applied include:

  1. AGA 8:2017
  2. AGA 10:2002
  3. ISO 6974:2014 or 6975:2005 for sample analysis
  4. ISO 6976:2016
  5. SGERG88 / 91
  6. Viscosity calculation

The mathematical model applied in a gas measuring station is the calculation of the standard volume ΔVn and the energy ΔE that is measured by a flow meter during a specific time interval Δt. In formula form, the standard volume that is measured by a meter that outputs several pulses ΔNm (e.g., turbine meter) is represented as follows:


online uncertainty calculation


The amount of energy ΔE is given as follows:


online uncertainty calculation


In which:

Pm = current gas pressure (bar)

Pn = gas pressure at standard conditions (bar)

Tm = current gas temperature (K)

Tn = gas temperature at common conditions (K)

Zm = compressibility of the gas under operational conditions (-)

Zn = compressibility of the gas under normal conditions (-)

ΔNm = number of pulses that the turbine meter detects during a time interval Δt (-)

I’m = pulse factor of the gas meter (pulses / m3)

Hs = Superior Calorific Value (J /mn3)

em = deviation of the gas meter according to the calibration certificate (-)

Ct = correction factor due to the current gas temperature that deviates from the calibration temperature (-)

Cp = correction factor due to the existing gas pressure that deviates from the calibration pressure (-)

The input parameters are time-dependent: Pm, Pn, Tm, Tn, Zm, Zn, ΔNm, and Hs.

The compressibility Zm at operational conditions is an input quantity that is dependent on the current pressure and temperature and gas composition;

The compressibility Zn at standard conditions is an input quantity that is dependent on the normal pressure and standard temperature (both fixed values) and current gas composition;

The Superior Calorific Value Hs depends on the current gas composition and can be calculated using an ISO 6976.

The deviation em of the gas meter is a function of the gas flow rate and is determined by comparison with a reference meter during a calibration. With a calibration, this deviation is determined at several values of the gas flow rate; in this way, the calibration curve is determined. A polynomial can be fitted through the measuring points through curve fitting.

The value and uncertainty of all input variables are determined at one given moment.

Hint has several programs with which the total measurement uncertainty in standard volume and energy of a gas measuring station can be determined online. Examples of programs are, e.g., based on a flow meter that delivers pulses such as a turbine meter. Another program has been developed to apply for an orifice plate as a flow meter in the gas installation.

An example of such a spreadsheet is given below, which is the basics of online programming.




Sensitivity factors for all input variables are calculated in these spreadsheets, uncertainty contribution of each input quantity, and the result. Several fixed elements in the program must be entered again for each gas measuring station. Fixed factors/numbers include Pn, Tn, Im, Ct, and Cp.

Measurement uncertainty as a function of time (real-time)

Several input variables are time-dependent signals that a Flow Computer reads in. By also reading in these time-dependent values (within a time interval Δt) in the available spreadsheet/algorithm, the uncertainty in common volume/mass and energy can be determined online. The time interval with which the uncertainty is determined depends on the sample time of the various measuring instruments. The measuring device with the lowest sampling frequency determines the time interval of the online uncertainty. An online gas chromatograph determines the current gas composition once every 5 minutes and is the instrument with the lowest sampling frequency.

The Hint AML 4.0 software provides the ability to program the online uncertainty tool for each type of fiscal gas and oil metering station. Customized software can be developed for any fiscal gas and oil metering station.

Data Quality

Maintaining low uncertainty is one way to optimize data quality. The uncertainty of measurement is related to process data. However, data quality is not just about the process data. The issue with data quality is looking at all data of the entire evacuation system, including all measurements, usage, value, and historical maintenance, diagnostic, calibration, and validation data.

In today’s highly competitive landscape, to keep your company financially healthy and accountable
you want to:

  • have a transparent system
    • deliver the exact numbers, with the right quality, without altering the data
  • optimize the system
  • reducing errors
    • work closer to operation limits while keeping it safe
  • have traceability of your data

However, it is easier said than done. The desire to fix the problem is often ignored due to the expectation of highly high costs, effort, and required time.

Currently, operators only use data validity as a check, e.g., is the process reading within the expected range of 50 bar but measuring 60 bar.

We have found that other parameters are missing and should be added to the current real-time data analysis to get better results:

  • Data integrity: the rate of change of the process measurement, measuring 60 bar and it is changing within 20 sec from 60 bar to 50 bar
  • Data redundancy: two process measurements for the same parameter, e.g., two pressure transmitters are measuring 60 bar.
  • Data consistency: a holistic view using different pieces of information about the system to verify the quality of the measurement, e.g., your flow is going from low to high pressure.
  • Diagnostic real-time data: telling you the current health status of the meter, do I still have flow in my analyzer?
  • Real-time uncertainty data: total and calibration uncertainty, recalibration when outside the uncertainty limits.
  • Historical data: measurement data history, uncertainty data history, diagnostic data history, validation data history, maintenance data history, operational state history, sample analysis data history
  • Maintenance data: telling you about historical maintenance data like calibration, validation, verification, sample & calibration frequencies, manufacturer requirements, and sensor failures.