Custody Transfer Uncertainty Fundamentals

1. Uncertainty Concepts

Measurement uncertainty is not the same as error. Error is the difference between a measured value and the true value (which is unknowable). Uncertainty is a quantitative expression of the range within which the true value is expected to lie, with a stated confidence level. This distinction is fundamental to the ISO GUM framework.

Key Terminology

Term	Definition	Example
Standard Uncertainty (u)	Uncertainty expressed as one standard deviation (1-sigma, ~68% confidence)	DP transmitter: u = 0.25%
Combined Uncertainty (u_c)	RSS combination of all standard uncertainties weighted by sensitivity	u_c = 0.35%
Expanded Uncertainty (U)	Combined uncertainty multiplied by coverage factor k	U = 2 × 0.35 = 0.70%
Coverage Factor (k)	Multiplier for desired confidence level	k=2 (95%), k=3 (99.7%)
Sensitivity Coefficient (c_i)	How much the output changes per unit change in input	c_DP = 0.5 for orifice meter
Type A	Uncertainty evaluated by statistical analysis of repeated measurements	Proving run repeatability
Type B	Uncertainty evaluated from manufacturer specs, calibration data, or judgment	Transmitter accuracy spec

Why uncertainty matters: A custody transfer station flowing 100 MMSCF/d of gas at $3.50/MMBTU has daily revenue of approximately $357,000. A 0.5% uncertainty means the true volume could differ from the measured volume by up to $1,785/day or $651,000/year. This exposure is split between buyer and seller, creating strong economic incentive to minimize uncertainty.

2. ISO GUM Methodology

The ISO Guide to the Expression of Uncertainty in Measurement (GUM), published as ISO/IEC Guide 98-3, provides the internationally accepted framework for evaluating and expressing measurement uncertainty. ISO 5168 applies this framework specifically to fluid flow measurement.

GUM Procedure

Step-by-Step GUM Process: 1. Define the measurand (what you are measuring) Example: Standard volumetric flow rate Q_s (MSCF/d) 2. Identify all input quantities that affect Q_s For orifice: C_d, d, D, hw, P_f, T_f, Z_f, G_r 3. Determine standard uncertainty for each input u(hw) = 0.25% (from manufacturer spec, Type B) u(P_f) = 0.10% (from calibration certificate) 4. Determine sensitivity coefficients c_i = partial(Q) / partial(x_i) (partial derivative) 5. Combine using RSS: u_c = sqrt( sum( (c_i * u_i)^2 ) ) 6. Apply coverage factor: U = k * u_c (k=2 for 95% confidence) 7. Report: Q = Q_measured +/- U (at 95% confidence)

Type A vs. Type B Evaluation

Type A evaluation uses statistical analysis of a series of observations. For example, the standard deviation of 10 proving runs provides a Type A uncertainty for meter factor. Type B evaluation uses any other available information: manufacturer specifications, calibration certificates, published data, or engineering judgment. Both types are equally valid and are combined using the same RSS method. The distinction is about how the uncertainty was determined, not about its quality.

Common mistake: Many engineers confuse instrument accuracy with uncertainty. A transmitter with 0.04% accuracy specification has a standard uncertainty of approximately 0.04/sqrt(3) = 0.023% if the specification represents a rectangular distribution (uniform probability within the limits), or 0.04/2 = 0.02% if it represents 2-sigma limits. Always clarify the statistical basis of manufacturer specifications.

3. Sensitivity Coefficients

Sensitivity coefficients determine how each measurement error propagates to the overall flow rate uncertainty. They are derived from the partial derivatives of the flow equation with respect to each input variable. Different meter types have different flow equations and therefore different sensitivity coefficients.

Orifice Meter (AGA 3)

AGA 3 Flow Equation (simplified): Q = K * C_d * E * d^2 * sqrt(hw * P_f / (T_f * Z_f * G_r)) Sensitivity coefficients (from partial derivatives): c_dp = partial(Q)/partial(hw) * (hw/Q) = 0.5 (square root) c_P = partial(Q)/partial(P_f) * (P_f/Q) = 0.5 c_T = partial(Q)/partial(T_f) * (T_f/Q) = 0.5 (inverse) c_Cd = partial(Q)/partial(C_d) * (C_d/Q) = 1.0 (linear) c_d = partial(Q)/partial(d) * (d/Q) = 2.0 (squared) Implication: Orifice bore diameter (d) has the highest sensitivity coefficient (2.0), meaning a 0.1% error in bore measurement causes a 0.2% error in flow rate. This is why AGA 3 requires precise bore measurement to 0.001 inches.

Sensitivity Comparison by Meter Type

Parameter	Orifice (AGA 3)	Turbine (AGA 7)	Ultrasonic (AGA 9)
Differential Pressure	0.50	N/A	N/A
Static Pressure	0.50	1.00	1.00
Temperature	0.50	1.00	1.00
Gas Composition	0.25	0.25	0.25
Calibration/Meter Factor	1.00	1.00	1.00
Installation Effects	0.50	0.30	0.20

4. Meter Type Comparison

The choice of meter technology fundamentally affects achievable uncertainty. Each meter type has inherent advantages and limitations that determine the uncertainty floor even with perfect instrumentation and calibration.

Feature	Orifice (AGA 3)	Turbine (AGA 7)	Ultrasonic (AGA 9)
Typical Expanded Uncertainty	0.5 – 1.0%	0.25 – 0.5%	0.1 – 0.3%
Rangeability	3:1 to 5:1	10:1 to 20:1	50:1 to 100:1
Permanent Pressure Loss	High (40-60%)	Low (3-5%)	Negligible
Maintenance	Plate inspection	Bearing replacement	Transducer check
Capital Cost	Low	Medium	High
Flow Profile Sensitivity	High	Moderate	Low (multipath)

Technology trend: Ultrasonic meters (AGA 9) are increasingly preferred for custody transfer due to their superior rangeability, low pressure loss, no moving parts, and diagnostic capabilities. Multipath designs (4+ paths) provide built-in flow profile verification that reduces installation uncertainty to 0.1-0.2%.

5. Uncertainty Budgets

An uncertainty budget is a systematic accounting of all sources of uncertainty, their magnitudes, sensitivity coefficients, and relative contributions. It is the primary tool for identifying which component dominates the overall uncertainty and where improvement effort should be focused.

Example Uncertainty Budget: Orifice Meter Station Source u_i(%) c_i (c_i*u_i)^2 Contribution ----------------------------------------------------------------- DP Transmitter 0.25 0.50 0.015625 25.5% Static Pressure 0.10 0.50 0.002500 4.1% Temperature 0.10 0.50 0.002500 4.1% Gas Composition 0.10 0.25 0.000625 1.0% Discharge Coeff. 0.20 1.00 0.040000 65.2% Installation 0.01 0.50 0.000025 0.0% ----------------------------------------------------------------- Sum of variances: 0.061275 Combined (u_c): sqrt(0.061275) = 0.2475% Expanded (U, k=2): 0.495% Conclusion: Discharge coefficient (calibration) dominates at 65.2% of total variance. Improving DP transmitter would have limited impact compared to better C_d determination.

The uncertainty budget reveals that the discharge coefficient uncertainty is the dominant contributor. This means investing in better plate edge sharpness, more precise bore measurement, and lower Reynolds number uncertainty will reduce overall station uncertainty more effectively than upgrading the DP transmitter.

6. Financial Impact Analysis

The financial impact of measurement uncertainty is straightforward to calculate but often surprisingly large. It represents the range within which the true monetary value of the transferred gas may differ from the measured value.

Financial Exposure Calculation: Daily Revenue = Q (MSCF/d) × HV (BTU/SCF) / 1000 × Price ($/MMBTU) Daily Exposure = Daily Revenue × U / 100 Annual Exposure = Daily Exposure × 365 Example: Q = 100,000 MSCF/d, HV = 1020 BTU/SCF, Price = $3.50/MMBTU, U = 0.5% Daily Revenue = 100,000 × 1020/1000 × $3.50 = $357,000/d Daily Exposure = $357,000 × 0.005 = $1,785/d Annual Exposure = $1,785 × 365 = $651,525/yr Value of reducing uncertainty from 0.5% to 0.3%: Delta = $357,000 × (0.005 - 0.003) × 365 = $260,610/yr

Investment justification: The annual savings from reducing uncertainty often pays for instrument upgrades within months. For example, upgrading a DP transmitter from 0.25% to 0.04% uncertainty costs $3,000-$5,000 but can reduce annual exposure by $50,000-$200,000 on a high-volume station.

7. Reducing Uncertainty

Priority Hierarchy

Address the dominant source first: The uncertainty budget shows which source contributes most to total variance. Reducing the largest contributor has the most impact.
Improve calibration: Regular calibration with NIST-traceable standards reduces systematic uncertainty. Calibrate at actual operating conditions when possible.
Upgrade instruments: Modern smart transmitters achieve 0.04% accuracy versus 0.25% for legacy instruments. Pressure and temperature instruments should match meter accuracy.
Optimize installation: Ensure adequate upstream/downstream straight runs per AGA requirements. Use flow conditioners if space is limited.
Improve gas analysis: Use online gas chromatographs instead of spot samples. Reduce composition uncertainty from 0.3% to 0.05%.

8. Metering Audits

Regular metering audits verify that the actual uncertainty matches the design uncertainty budget. Audits should cover instrument calibration records, installation compliance, computational correctness, and comparison with check meters or proving results.

Audit Item	Frequency	Standard
Instrument calibration verification	Monthly to quarterly	AGA 3/7/9
Gas chromatograph calibration	Daily to weekly	GPA 2261
Flow computer validation	Quarterly	API MPMS Ch. 21
Orifice plate inspection	Annually	AGA 3
Complete station audit	Annually	API MPMS Ch. 13
Uncertainty analysis update	Annually or after changes	ISO 5168

9. Best Practices

Document everything: Maintain complete uncertainty budgets, calibration records, and audit trails for every custody transfer station.
Use check meters: A secondary meter (different technology) provides independent verification and helps detect gross errors.
Monitor trends: Track meter factor, calibration shifts, and proving results over time. Systematic trends indicate developing problems before they become significant.
Train operators: Measurement technicians should understand uncertainty concepts and proper measurement techniques. Errors in field procedures often exceed instrument uncertainty.
Contract alignment: Ensure that measurement contracts specify uncertainty limits, reference standards, and dispute resolution procedures clearly.

10. Industry Standards

Standard	Title	Relevance
ISO/IEC Guide 98-3	Guide to the Expression of Uncertainty in Measurement (GUM)	Foundational uncertainty framework
ISO 5168	Measurement of Fluid Flow — Estimation of Uncertainty	Fluid flow specific uncertainty
AGA Report No. 3	Orifice Metering of Natural Gas	Orifice meter uncertainty analysis
AGA Report No. 7	Measurement of Gas by Turbine Meters	Turbine meter specifications
AGA Report No. 9	Measurement of Gas by Multipath Ultrasonic Meters	USM uncertainty and diagnostics
AGA Report No. 8	Compressibility Factors of Natural Gas	Z-factor uncertainty contribution
API MPMS Ch. 4	Proving Systems	Meter proving procedures
API MPMS Ch. 13	Statistical Aspects of Measuring and Sampling	Statistical methods for measurement
API MPMS Ch. 21	Flow Measurement Using Electronic Metering Systems	Flow computer requirements

u_c = √(∑(c_i × u_i)²)

U = k × u_c

ISO 5168 · AGA 3/7/9

Contents

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