Uncertainty
Analysis for
Hydrocarbon Measurement
This
article has been prepared to give some guidance on how uncertainty estimation
can be carried out, how to overcome some of the statistical anomalies
found in oil industry practice, and how to prepare for a consistent
expression of uncertainty, that is compatible with international metrology
practice, says R Paton.
Introduction
Within
the oil industry, measurement has always been of prime importance in
the transfer of product both onshore and offshore. When calculating
duty payable or allocation, the accuracy in measuring the quantity of
oil is vital. It can be argued that when trading oil, consistency and
agreement in measurement between buyer and seller is more important
than accuracy (or even the correct value of the quantity!). However,
to achieve consistency, you have to measure accurately, and to judge
if you have consistency you have to know the uncertainty.
Throughout
the production and distribution chain the accuracy of the measurements
has always been important. The term accuracy is easily understood and
comes into all specifications of measurements across all fields of metrology.
It is, by definition, a qualitative term. Accuracy will usually have
a number attached but will not define the level of confidence of the
measurement. In recent years the oil industry has followed the general
trend in metrology and recognised that ‘accuracy’ is inadequate to provide
the information needed for transactions.
An
estimate of uncertainty of measurement must include (explicitly or implicitly)
the confidence in the estimate. Increasingly this is demanded as a measure
to accompany any result. As the need to express uncertainty increases,
it has become clear that the methods and traceability chains used in
the oil industry do not easily adapt to the methods of estimating uncertainty
provided by the statistically based standards in the scientific and
pure metrology fields. To retain consistency it is vital that estimation
of uncertainty must be carried out in a statistically sound and auditable
manner, but in a way that the engineers in the industry can relate to.
In many cases, uncertainty estimation is an art rather than a science
and it would be rare that two independent engineers would derive the
same value. This is an untenable situation in the oil industry where,
on transactions, agreement can be more important than accuracy. Unfortunately,
until many more uncertainty calculations are carried out and input figures
agreed, no standardisation would be possible.
This
article has been prepared to give some guidance on how uncertainty estimation
can be carried out, how to overcome some of the statistical anomalies
found in oil industry practice, and how to prepare for a consistent
expression of uncertainty, that is compatible with international metrology
practice. By following the principles set out in this article, it will
also be possible to set the expected uncertainty for transactions where
all the input measurements are within specified limits. The actual uncertainty
may be better but only individual analysis would determine that.
Historically,
the oil industry has had to meet the practical needs of measurement
in arduous conditions. As a result, uncertainty calculations using a
common methodology had not been of high priority. Traditionally, measurement
of ‘accuracy’ was defined for secondary measurements such as temperature
and much emphasis had been placed on the repeatability of measurements
based on a very small sample of results. From this an overall view of
the resultant accuracy was assumed.
Uncertainty
estimation has rarely been carried out thoroughly and, using a pragmatic
examination of results and agreement between parties, accuracy has been
defined by agreement. Similarly many of the methods used to collect
data during calibrations, appear, at first sight, to make rigorous uncertainty
estimation very difficult. Commercial and operational requirements generally
prevent the collection of data in the quantity expected from any scientific
based measurement.
The
need to estimate uncertainty has become more important in recent years
to improve the confidence in mass balance across systems and reliably
fine tune ever faster contract specifications and regulatory requirements.
It is vital that these uncertainty estimates are carried out in a consistent
manner and are understood by all parties. All estimates of uncertainty
must carry a confidence limit, but more importantly they must have the
confidence of operators, contract staff, partners and regulators.
To
comply with measurement standards from ISO etc, uncertainty should be
included in the standard and this will carry over into regulation and
contracts. Acceptance limits (criteria), accuracy expectations and
repeatability criteria will continue to feature strongly in practical
standards and procedures. Such criteria are compliant with good practical
metrology and can be used as an input to the definition of an uncertainty.
The
international standards bodies recognised that a statistically sound
methodology was required to service the need for uncertainty estimation
in metrology and hence produced the Guide to Uncertainty of Measurement
(GUM). The introduction of the guide was met with some resistance from
the industry but overwhelming enthusiasm by scientific based metrologists
and adopted by the standards bodies. Within ISO and IEC all new standards
are encouraged to include uncertainty criteria and it is now up to industry
to make these follow the guide.
What
is obvious is that the GUM does not relate easily to the history and
realities of practical industries. The GUM expresses uncertainty in
statistical terms different to the established methods familiar to most
measurement engineers. It is heavily scientifically and statistically
based. The GUM is however a guide, not a standard! It is now up to individual
industries to follow the methods and apply them to their own needs.
Gum:
The Principles
Traditionally,
uncertainty was derived by combining all estimates of the magnitude
of individual errors in a measurement. This provides an estimate of
systematic error in the final quantity. To this systematic error, the
estimate of random uncertainty is added by taking a statistical result
from multiple measurements to estimate the probability distribution
of the result, hence providing a confidence band.
The
principles outlined in the GUM are the same but the approach and terminology
is different.
The
fundamental concept of the GUM is to assume all uncertainties are equivalent
to the standard deviation of the results from many repeated tests. By
assuming this, all uncertainties can be assigned a probability function
and hence the final uncertainty fully recognises the potential distribution
of results and gives a much better confidence expression through a coverage
factor or confidence limit. This concept is sound, but the application
to industry where most uncertainties are not derived from (apparent)
knowledge of large numbers of tests requires some consideration.
A
number of terms are used in this approach:
- Standard
Uncertainty: Standard uncertainty is the uncertainty of the result
of measurements expressed as a standard deviation. All uncertainties
are initially estimated as standard uncertainties. In deriving standard
uncertainty, two types of uncertainty (type A and type B) are recognised.
- Type
A Uncertainties: Type A evaluations of uncertainty are those using
statistical methods, specifically, those that use the spread of a
number of measurements.Any measurement can be repeated a number of
times and the statistical distribution found, analysed and the standard
deviation and probability limits defined. This is equivalent to the
traditional random uncertainty but has been renamed in the GUM as
a type A uncertainty.
- Type
B Uncertainties: Type B evaluation of uncertainty is one carried
out by means other than the statistical analysis of a series of observations.It
is recognised that in many cases it is impractical or impossible to
gather enough data in the experiment to derive a representative statistical
estimate from repeated measurements. This situation leads to the derivation
of a type B uncertainty. Type B uncertainties are in some ways equivalent
to the traditional systematic error. To achieve an estimate of standard
uncertainty, type B uncertainties must be assessed not only on their
magnitude, but also on the estimated probability distribution encompassed
within the estimate. Within the GUM type B uncertainties are first
estimated in magnitude, and then reduced to an equivalent standard
uncertainty based on an assumed probability distribution. This is
achieved by the application of a divisor to reduce the spread of uncertainty
to standard uncertainty.
- Expanded
Uncertainty and
Coverage Factor: Expanded uncertainty is computed by combining all
standard uncertainties, both type A and type B, and multiplying by
a coverage factor chosen to express the results encompassed by a large
fraction of the probable values reasonably attributed to the measurement.
Generally, these confidence limits are accepted as being at 95% confidence
levels. As is explained in the GUM, a coverage factor is a better
parameter to be used. This is the factor by which the standard uncertainty
is multiplied to give the expanded uncertainty.
If a normal distribution is assumed and a large number of results
are assumed, k=2 approximates to a confidence of 95% (actually 95.45%)
and k=3 is applied to approximate to a 99% confidence.
Expanded uncertainty is therefore the final expression of an uncertainty
analysis. This is expressed formally as the measurement value with
an expanded uncertainty and a coverage factor..
...contd.
