B016 – Calculated Density
Description
This block can be used to calculate the uncertainty in oil line density, standard density and VCF.
Options
Reference
- API MPMS Ch11.1 (2004)
- API MPMS Ch11.1 (1980)
- Table 24:1952/API MPMS 11.2.1
- Table 54:1952/API MPMS 11.2.1
- Table 54:1952/IP Paper 2
- IP Paper 2
- GPA TP-25
- GPA TP-27
- Manual
This option is used to select which reference the densities will be calculated according to. If user entered is selected thermal expansion coefficient and compressibility of the fluid needs to be entered.
Density Referral Uncertainty
- API MPMS Ch11.1
- Manual
This option is used to select whether the uncertainty in the temperature and pressure corrections is entered manually or calculated according to the uncertainty guidelines in API MPMS Ch11.1. This option is available to the user so long as Manual is NOT selected from the Reference option.
Note: if density referral is selected to be entered manually then Cpl and Ctl model uncertainty needs to be entered.
Input
U_Ctl
Uncertainty in temperature correction on fluid volume.
Note this input is only required if Manual is selected from the Density referral Uncertainty.
U_Cpl
Uncertainty in pressure correction on fluid volume.
Note this input is only required if Manual is selected from the Density referral Uncertainty.
API MPMS Ch11.1 (2004)
Commodity Group
- Crude Oil
- Fuel Oils
- Jet Fuels
- Transition Zone
- Gasolines
- Lubricating Oil
- User Entered
This option is used to select the appropriate commodity group for API MPMS Ch 11.1 (2004). Consult the standard to choose representative commodity. If user entered is selected then a thermal expansion coefficient will need to be entered.
Standard Temperature
- 15°C
- 20°C
- 60°F
Note: only when the API MPMS Ch11.1 (2004) and GPA TP-27 standards are selected from the reference option is 20°C a selectable option.
Input
Vapour pressure
Equilibrium pressure of fluid.
Thermal expansion coefficient
Thermal expansion coefficient of fluid.
API MPMS Ch11.1 (1980)
Product Group
- Crude Oil
- Gasolines and Naphthenes
- Jets and Naphthenes
- Jet Fuels, Kerosenes and Solvents
- Diesel and Heating Oil
- Lubricating Oil
- Other
Note: Consult the standard to choose representative product. If other is selected then K0, K1 and K2 values will have to be entered for the product.
Standard Temperature
- 15°C
- 60°F
Note: only the more recent standards have 20°C as a selectable option.
Vapour Pressure
- Include
OR
- Don’t include
If include is selected this will allow the user to enter the value for the vapour pressure; otherwise, it will be set equal to standard atmospheric pressure (1.01325 bar).
Precision
- Full
- Rounding
This option is used to select whether calculations will be carried out with full precision or whether intermediate values are rounded or truncated according to the algorithms laid out in the standard.
Inputs
Vapour pressure
Equilibrium pressure of fluid.
K0
Correlation coefficient for thermal expansion factor. Note this input is only required if Other is selected from the Product Group option.
K1
Correlation coefficient for thermal expansion factor. Note this input is only required if Other is selected from the Product Group option.
K2
Correlation coefficient for thermal expansion factor. Note this input is only required if Other is selected from the Product Group option.
Table 24:1952/API MPMS 11.2.1
Vapour Pressure
- Include
OR
- Don’t include
If include is selected this will allow the user to enter the value for the vapour pressure; otherwise, it will be set equal to standard atmospheric pressure (1.01325 bar).
Precision
- Full
- Rounding
This option is used to select whether calculations will be carried out with full precision or whether intermediate values are rounded or truncated according to the algorithms laid out in the standard.
Inputs
Vapour pressure
Equilibrium pressure of fluid.
Table 54:1952/API MPMS 11.2.1
Vapour Pressure
- Include
OR
- Don’t include
If include is selected this will allow the user to enter the value for the vapour pressure; otherwise, it will be set equal to standard atmospheric pressure (1.01325 bar).
Precision
- Full
- Rounding
This option is used to select whether calculations will be carried out with full precision or whether intermediate values are rounded or truncated according to the algorithms laid out in the standard.
Inputs
Vapour pressure
Equilibrium pressure of fluid.
Table 54:1952/IP Paper 2
Vapour Pressure
- Include
OR
- Don’t include
If include is selected this will allow the user to enter the value for the vapour pressure; otherwise, it will be set equal to standard atmospheric pressure (1.01325 bar).
Precision
- Full
- Rounding
This option is used to select whether calculations will be carried out with full precision or whether intermediate values are rounded or truncated according to the algorithms laid out in the standard.
Inputs
Vapour pressure
Equilibrium pressure of fluid.
IP Paper 2
Product Group
-
- Crude Oil
- Gasolines and Naphthenes
- Jets and Naphthenes
- Jet Fuels, Kerosenes and Solvents
- Diesel and Heating Oil
- Lubricating Oil
- Other
Note: Consult the standard to choose representative product. If other is selected then K0, K1 and K2 values will have to be entered for the product.
Standard Temperature
- 15°C
- 60°F
Select the standard temperature to be used.
Vapour Pressure
- Include
OR
- Don’t include
If include is selected this will allow the user to enter the value for the vapour pressure; otherwise, it will be set equal to standard atmospheric pressure (1.01325 bar).
Precision
- Full
- Rounding
This option is used to select whether calculations will be carried out with full precision or whether intermediate values are rounded or truncated according to the algorithms laid out in the standard.
Inputs
Vapour pressure
Equilibrium pressure of fluid.
K0
Correlation coefficient for thermal expansion factor. Note this input is only required if Other is selected from the Product Group option.
K1
Correlation coefficient for thermal expansion factor. Note this input is only required if Other is selected from the Product Group option.
K2
Correlation coefficient for thermal expansion factor. Note this input is only required if Other is selected from the Product Group option.
GPA TP-25
Vapour Pressure
- User entered
OR
- Calculated using TP-15
Select if user wants to enter the value for the vapour pressure or calculated using the Vapor Pressure Correlation for Commercial NGL’s.
Precision
- Full
- Rounding
This option is used to select whether calculations will be carried out with full precision or whether intermediate values are rounded or truncated according to the algorithms laid out in the standard.
Inputs
Vapour pressure
Equilibrium pressure of fluid.
GPA TP-27
Standard Temperature
- 15°C
- 20°C
- 60°F
Note: only when the API MPMS Ch11.1 (2004) and GPA TP-27 standards are selected from the reference option is 20°C a selectable option.
Vapour Pressure
- User entered
OR
- Calculated using TP-15
Select if user wants to enter the value for the vapour pressure or calculated using the Vapor Pressure Correlation for Commercial NGL’s.
Precision
- Full
- Rounding
This option is used to select whether calculations will be carried out with full precision or whether intermediate values are rounded or truncated according to the algorithms laid out in the standard.
Inputs
Vapour pressure
Equilibrium pressure of fluid.
Manual
Standard Temperature
- 15°C
- 20°C
- 60°F
Note: only the more recent standards have 20°C as a selectable option.
Inputs
Compressibility
Compressibility factor of fluid.
Thermal expansion coefficient
Thermal expansion coefficient of fluid.
Vapour pressure
Equilibrium pressure of fluid.
Calculations
The line and standard density are calculated according to the procedure selected from the Reference option. The VCF is equal to the line density divided by the standard density.
The line pressure and temperature will be taken from the Input/Output tab and the expanded uncertainties used will be as calculated in blocks B001 – Pressure and B003 – Temperature respectively. The densitometer pressure and temperature will be taken from the Input/Output tab the uncertainties associated with these are assumed to be the same as those for the line values.
The measured density will be taken from the Input/Output tab and its expanded uncertainty used will be as calculated in block B012 – Measured Density.
Ctl and Cpl model uncertainties are either calculated based on data set out in the relevant standard or taken from the block inputs depending on option selection.
Uncertainty Budget
The uncertainty calculation is detailed in the uncertainty budget tables for line density and/or VCF (whichever is relevant to the module) giving a break down of how the overall uncertainty is calculated for that parameter.
Uncertainties associated with these values are taken in as the Expanded Uncertainties. The Standard Uncertainty is calculated from dividing the Expanded Uncertainty by the coverage factor which is determined by the probability distribution that best suits that uncertainty component.
The Standard Uncertainty is then multiplied by the sensitivity value then squared. This is done for each parameter that contributes to the overall uncertainty in the density. The Standard Uncertainty in the density is the square root of the sum of each component variance as shown in the following equation:
The sensitivity coefficients for each of these input uncertainties are determined using the finite difference method, where each of the calculation input quantities are varied, one at a time, by magnitude of their uncertainty, and the effect on the output determined.
The Expanded Uncertainty is the Standard Uncertainty multiplied by the coverage factor (k). The coverage factor is defaulted to k = 2 (equivalent to a confidence level of approximately 95%). The Relative Uncertainty is the Expanded Uncertainty divided by the measured density.
References
Standards
ISO 5168:2005 – Measurement of fluid flow – Procedures for the evaluation of uncertainties
ISO Guide 98-3 – Uncertainty of measurement – Part 3: Guide to the expression of uncertainty in measurement (GUM:1995) (2008)
API MPMS Chapter 11.1 – Volume correction factors Volume 10 – Background, Development and Program Documentation: API Standard 2540 (1980)
API MPMS Chapter 11.2.1M – Compressibility Factors for Hydrocarbons: 638-1074 Kilograms per Cubic Metre Range (1984)
API MPMS Chapter 11.2.2M – Compressibility Factors for Hydrocarbons: 350-637 Kilograms per Cubic Metre Density (15°C) and -46°C to 60°’b0C Metering Temperature (1986)
API MPMS Chapter 11.1 – Temperature and Pressure Volume Correction Factors for Generalized Crude Oils, Refined Products, and Lubricating Oils (ASTM D 1250-04; IP 200/04) (1st edition 2004, Addendum 1 2007)
Institute of Petroleum, Petroleum Measurement Paper No. 2; Guidelines for users of the petroleum measurement tables (API Std 2540; IP 200; ANSI/ASTM D 1250) (1984)
ASTM-IP Petroleum Measurement Tables, Metric Edition, (ASTM D 1250; IP 200) (1952)
Report on the Development, Construction, Calculation and Preparation of the ASTM-IP Petroleum Measurement Tables (ASTM D 1250; IP 200) (1960)
GPA Technical Publication TP-25, API MPMS 11.2.4 – Temperature Correction for the Volume of Light Hydrocarbons Tables 23E and 24E (1998)
GPA Technical Publication TP-27, API MPMS 11.2.4 – Temperature Correction for the Volume of NGL and LPG Tables 23E, 24E, 53E, 54E 59E and 60E (2007)
API MPMS 11.2.5/GPA Technical Publication TP-15 – A Simplified Vapor Pressure Correlation for Commercial NGLs (2007)
KCCL Calculations
C012 – API/Table 54:1952 Density referral
C019 – IP Paper 2/Table 54:1952 Density referral
C022 – IP Paper 2 Density Referral
C023 – API Density Referral 1980-86
C251 – API Density Referral 2004
C295 – GPA TP-25 – NGL and LPG Density Referral Calculation
C296 – GPA TP-27 – NGL and LPG Density Referral Calculation
Uncertainty Blocks