It is
important to accurately measure hydrocarbon commodities transferred through
pipelines or marine terminals at the point where ownership of the commodity is
transferred. To ensure accurate measurement, it is essential to quantify and
adjust for the performance of flowmeters (e.g., turbine meters, ultrasonic
meters, Coriolis meters) for the variations in the characteristics of fluid,
operating process conditions, etc.
In the oil
and gas industry, it is well-established to use a prover that provides a meter
factor (MF) to facilitate defensible and traceable measurement. Bidirectional
provers are one of the common types used in the industry. A typical
bidirectional prover has a length of pipe through which a sphere travels,
displacing liquid between two points known as a calibration section. The
totalized flowmeter volume reading during the time required for the sphere to
travel between the detecting points is compared with the known volume of the
calibration section—also known as the base prover volume (BPV)—to provide
accurate meter calibration data or establish a meter factor.
The accuracy
of the meter factor, and therefore the measurement accuracy, by the flowmeter
directly depends on the accuracy of the BPV. It is common industry practice to
routinely recalibrate the prover to ensure measurement defensibility or
calibrate and generate a revised prover base volume if one or more detectors
are repaired or replaced.
Multiple prover volumes. The BPV is the established actual
volume between the pair of detectors at standard or base condition. The actual
volume between two detectors located on each side of the calibrated section is
derived during the prover calibration process. A single pair of detector
switches is required in a bidirectional prover to calculate the meter factor of
the flowmeter. Often, a second pair of detectors is also provided to provide
BPV redundancy. With multiple detectors (usually four), four different BPVs can
be derived.
International
standards provide a method and calculation procedure to derive the BPV between
a pair of detectors.1–3 No industry practice is known to
identify inconsistencies among multiple volumes derived using multiple
detectors on the same prover (and mostly at the same time). Inconsistency among
four BPVs implies that the value of at least one BPV is beyond estimated
uncertainty (i.e., it has a larger-than-acceptable error).
The general
objective of this article is to provide an analytical method to identify
anomalies among these BPVs. The BPV could have been derived using a water draw
or master meter method. The description of a commonly used water draw method is
provided in the next section.
Water draw method of prover calibration. FIG. 1 illustrates the typical setup
and components required for bidirectional prover water draw calibration. The
water draw method is generally preferred, where feasible, to calibrate the
prover and establish the BPV, as it provides the least uncertainty compared to
other methods of calibration. Water draw is normally used during the initial
calibration of the prover to ensure and establish the BPV footprint with the
least uncertainty.
In the water
draw method of prover calibration, the volume of water between two detectors is
displaced and directly drawn into calibration standard measures. A calibration
controller diverts displaced water to the reservoir when the sphere is not in
the calibration section and in standard measures when the sphere is displacing
water in the calibration section.
During
calibration operation, when the sphere is outside the calibration section, the
displaced water from the prover is directly returned to the water reservoir
without filling standard measures. Due to the push of the water pumped from the
reservoir, when the sphere approaches and activates the detector at one end of
the prover, the calibration controller operates the solenoid valve to divert
water to the standard measures. The bypass manual valve, located in parallel to
the solenoid valve, can now be manually opened to achieve the desired
calibration flowrate.
Once the
sphere is about to reach a detector on the other end of the prover, the bypass
manual valve is closed. As the sphere activates the detector switch, the water
flow is now diverted directly to the reservoir. The water collected in the
calibration measures represents the volume of water drawn from the calibration
section of the prover at operating condition. This process is repeated in
forward and reverse directions multiple times as guided by international
standards and procedures. The repeatable prover volumes are delivered during
multiple calibration passes calculated at base conditions and averaged to
establish the BPV for that pair of detectors.
The water
draw process is repeated four times to establish four independent BPVs for the
prover with four detectors (two pairs of detectors).
FIG. 2 illustrates a bidirectional
sphere prover, which is normally constructed in a U shape. For easy
understanding of the concept, the prover is illustrated in a straight line in
other figures. TABLE 1 illustrates
the multiple BPVs that can be derived using four detectors on a typical prover
and other associated parameters.
The prover
volume between Detector 1 and Detector 2 is small and normally not calibrated
nor established. For the purpose of the discussion in this article, the volume
between these switches is depicted as X in Eqs.1 and 2.
Similarly, the prover volume between Detector 3 and Detector 4 is small and
normally not established.
Measurement and uncertainty. Practically, it is impossible to
derive the true value of the parameters, as all measurement processes present
inherent uncertainties. Uncertainty is a parameter associated with the result
of measurement that characterizes the dispersion of the values that could
reasonably be attributed to the measurement. Uncertainty of a measured value is
an interval around that value, such that any repetition of the measurement will
produce a new result that lies within this interval. Uncertainty defines a
statistical interval around the measured value within which true value is
expected to lie.
FIG. 3 illustrates the typical values
of BPVs that could be derived with four detector switches. The derived BPV will
be smaller or larger than the true value. The true value of the BPV is expected
to lie within uncertainty intervals of the established BPV, as shown by the
interval in the red line for each BPV.
Potential inconsistencies. International standards and industry
best practices provide guidelines and methodologies on calibrating provers and
criterion to validate the established BPV. One well-established criteria is
repeatability within intermediate prover volumes in forward, reverse and
round-trip during prover calibration for each pair of detectors. Industry
practices or standards do not provide guidelines on the verification of
consistencies among these four BPVs. Since detectors are common within multiple
volumes, the methods described in subsequent sections will provide indications
on inconsistencies.
Identifying inconsistencies. In FIG. 4, it can
be stated that the value of X can be calculated by Eqs. 1 or
2:
X = BPVA –
BPVC (1)
X = BPVD –
BPVB (2)
For the true
value of BPVs (i.e., using BPVA, BPVB, BPVC and BPVD), the value of X obtained
by Eqs. 1 or 2 will be the same (Eq. 3):
BPVA – BPVC =
BPVD – BPVB
or, in other
words:
BPVA + BPVB –
BPVC – BPVD = 0 (3)
Practically,
it is impossible to derive the true value of the BPV during calibration; as
such, the established BPV would not satisfy Eq. 3 but would have the value
of Etotal (Eq. 4):
BPVA + BPVB –
BPVC – BPVD = Etotal (4)
Based on the
relation of between the true value of the BPV and the established value of the
BPV (as provided in TABLE
1), Eq. 4 can be rewritten as:
(BPVA + Ea) + (BPVB + Eb) – (BPVC + Ec) – (BPVD + Ed) = Etotal
BPVA + BPVB – BPVC – BPVD + Ea + Eb – Ec – Ed = Etotal
or, in other
words (Eq. 5):
Ea + Eb – Ec
– Ed = Etotal (5)
(as BPVA +
BPVB – BPVC – BPVD = 0 per Eq. 3).
As the true
values of the BPVs are not known, Ea, Eb, Ec and Ed could assume a “+” or “–“
sign. The maximum value of Etotal will happen when
errors in BPVA and BPVB are of the opposite sign as the errors in BPVC and
BPVD.
Per the
characteristics of the term uncertainty, the maximum error in each of the
established BPVs should be less than the estimated uncertainty in the
established BPVs. So, the equation can be written as (Eq. 6):
Ua + Ub + Uc
+ Ud = Utotal ≥ Etotal (6)
When errors
in the established BPVs are within the estimated uncertainty, Etotal ≤ Utotal will
hold true. In other words, it can be stated that if Utotal is
less than the totals of errors (i.e, Etotal > Utotal),
at least one of the BPVs has an error more than the estimated uncertainty.
Probable cases of anomalies. The totals errors in the calibration
result (Eq. 4) can be positive or negative. In the event of a positive error
(i.e., BPVa + BPVb – BPVc – BPVd > 0, if Etotal > Utotal (i.e.,
BPVa + BPVb – BPVc – BPVd > Utotal ), this can be an
instance of inconsistency where BPVa and/or BPVb have an error/offset beyond
the estimated uncertainty on the positive “+” (i.e., Ea > Ua, Eb > Ub), or BPVc
and/or BPVd have an error/offset beyond the estimated uncertainty on the negative
“–“ (i.e., –Ec < –Uc, –Ed < –Ud).
Similarly,
for a negative error (i.e., BPVa + BPVb – BPVc – BPVd < 0) if Etotal > Utotal (i.e.,
BPVa + BPVb – BPVc – BPVd ˃ Utotal), this is an instance
of inconsistency where BPVa and/or BPVb have an error/offset beyond the
estimated uncertainty on the negative “–“ (i.e., –Ea ˂ –Ua, –Eb < –Ub) or BPVc
and/or BPVd have an error/offset beyond the estimated uncertainty on the
positive “+” (i.e., Uc ˂ Ec, Ud ˂ Ed).
An
illustration of one probable instance of positive error is provided in FIG. 5 for BPVA.
As shown in the figure, the true value of BPVA is beyond the estimated
uncertainty in BPVa (i.e., Ea ˃ Ua), but the error in the other BPV is within
estimated uncertainty.
Analysis of typical calibration results. The recalibration results of a 30-in.
bidirectional prover of a nominal base prover with an 84-bbl volume (13.35 m3)
using the water draw method is provided in TABLE 2. The prover had four
detectors and four independent BPVs were derived.
The
uncertainty in the BPVs was estimated to be 0.03% after considering all factors
that would impact and result in the spread of the derived volume in
consideration. The Etotal of all BPVs in the forward direction
was 57.64 in.3, which is within the Utotal of
494.7688 in.3. The Etotal of all BPVs in the
reverse direction was 546.9823 in.3, which is more than the Utotal of
494.9015 in.3. This is an incidence of inconsistency where either
BPVa and/or BPVb have an error/offset beyond the estimated uncertainty on the
positive “+” or BPVc and/or BPVd have an error/offset beyond the estimated
uncertainty on the negative “–“. The comparation of derived BPVs with previous
calibration data indicated that BPVb had error larger than estimated and
required recalibration.
Caution. The method described here helps
identify that at least one BPV has an error beyond the acceptable limit. It
should be noted that errors in BPVA or BPVB are nullified by an error of the
same sign in BPVC or BPVD. Therefore, there can be instances when even the
total errors are less than the totals of estimated uncertainty—two or more BPVs
have errors beyond acceptable uncertainty. The method described here does not
replace the requirement of scrutinizing results in all aspects, including
comparing results with past calibration records.
Takeaways. This paper details an approach to
identify the existence of inconsistencies, if any, in four BPVs derived during
the calibration operation of a prover using water draw or any other method
where the calibration of the prover is performed independently for each pair of
detectors. The method described is for a prover with four detectors, but the
concept can be extended if the prover has more than four detectors. HP
NOTE
The
suggestions and guidelines provided in this article should be considered
general in nature. Readers are encouraged to refer to relevant codes and
standards by legal metrology and other institutes.
LITERATURE
CITED
Chandulal N. Bhatasana is the Chairman of the Custody Measurement Standards Committee at Saudi Aramco and has more than 30 yr of experience in custody/fiscal metering and instrumentation. Bhatasana has authored several papers and received patents on innovative techniques related to proving systems in custody metering. He holds a BS degree in engineering.