Tank Tolerance Based on Uncertainties
Sigmafine provides two methods for determining the tolerance of a tank volume. The first, Measurement Tolerance Calculation, is described in Measurement Tolerance. The second, the calculation for "Tank Tolerance based on Uncertainties," allows you to determine the weighting value (tolerance) used in the reconciliation balances with a statistical method. This statistical method looks at the relative uncertainties of the following factors to determine an overall volume uncertainty:
- Liquid Temperature
- Gauge Reading
- Strapping Table Readings
- Volume Correction Factor (VCF) Table
This calculation uses the method listed below. The overall error is then calculated by adding systematic errors and adding the square root of the sum of the squares of the random errors as shown by the following equation.
Where:
Where:
eC = Strapping table uncertainty (%)
eI = Gauge reading uncertainty (%)
ef = Volume correction factor uncertainty (%)
et =Temperature measurement uncertainty (%)
VCF = Volume correction factor
α =Linear expansion coefficient
T = Liquid temperature
Tr = Reference temperature of liquid
h = Gauge measurement
EXAMPLE: Tank Tolerance Based on Uncertainties
The tolerance of a tank reading a gauge of 32 feet and a gross volume of 64320 bbl and 75°F, volume correction factor is 0.9911 and the corresponding liquid thermal expansion factor is 0.0005937 °F-1. The gross volume is adjusted to remove any other effects, such as floating roof corrections, and so the net volume is 64320 x 0.9911 = 63747.6 bbl.
VGross = 64320 bbl
VCF = 0.9911
VNet = 63747.6 bbl
α = 0.0005937 °F-1
Gauge = 32 ft
T = 75 F
The lowest uncertainty in the tank volume is calculated as follows.
Strapping
The uncertainty in volume bbl units is.
ec = .04
Gauge
The uncertainty in volume bbl units is calculated as follows.
el = .0512
Volume Correction Factor
The uncertainty in volume bbl units is calculated as follows.
ef = .05
Temperature
The uncertainty in volume bbl units is calculated as follows.
et = 9395
Total Volume
The total uncertainty in volume bbl units is calculated as follows.
The net volume of 63747.6 bbl has a minimum uncertainty of 68.4 bbl or 0.11%. This is based on the best methods applied to all aspects of tank calibration, temperature measurement, gauge measurement, and density determination. In actual situations, errors in these measurements are typically worse than those used in this example.
Typical values for these errors are the following:
ec = 0.1%
el = 0.125 inch
ef = 0.1%
et = 1.5°F
In this Case the total volume uncertainty is 152 bbl or 0.24%.
See Configuring - Tank Tolerance Based on Uncertainties Calculation for details on how to configure this calculation.