Line Pack Formulas - Petroleum Liquids

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Petroleum Liquids Formula

The CygNet Line Pack engine calculations for petroleum liquids comply with the API standards published in the following standards document: Manual of Petroleum Measurement Standards, Chapter 11 — Physical Properties Data, Section 1 — Temperature and Pressure Volume Correction Factors for Generalized Crude Oils, Refined Products, and Lubricating Oils. Adjunct to: ASTM D 1250-04 and IP 200/04. Measurement Coordination October 2002. May 2004. Addendum 1, September 2007.

Depending on the variables the user configures to be calculated, appropriate calculations are made and the results are written out to the various Line Pack points. As the formula used to calculate estimated line pack volume for petroleum liquids is very complex, the following describes the calculation steps in a simplified manner.

See the following subsections below for more information:

Assumptions
Calculation Flow Diagram
Calculation Steps
Formula Inputs Reference
Formula Outputs Reference

Assumptions

The following inputs must be provided to perform all calculations:

Observed density
Observed temperature at which observed density was measured
Observed pressure at which observed density was measured
Either a single pair of inlet and outlet temperatures, or multiple temperature values at different points on the pipeline segment
Either a single pair of inlet and outlet pressures, or multiple pressure values at different points on the pipeline segment
Standard temperature at which the liquids line pack volume will be calculated
Standard pressure at which the liquids line pack volume will be calculated
Liquids commodity type or thermal expansion factor at base condition (60°F and 0 psig)
Pipeline segment volume based either on the segment’s configured length and diameter or a user-configured volume
Optionally provide inlet and outlet Maximum Allowable Operating Pressure (MAOP), or provide multiple MAOP readings at different points on the pipeline segment

Also see Formula Inputs Reference below.

Calculation Flow Diagram

The following diagram shows a graphical representation of the flow of calculations for the petroleum liquids line pack formula. Click the following image to see an enlarged diagram:

Calculation Steps

Step 1

Using the API 11.1 Observed to Base formula, calculate Base Density with inputs: Observed Temperature, Observed Pressure, Observed Density, and Commodity Group (or Alpha 60).

Intermediate Output	Description
ρ60	Density at base conditions 60°F and 0 psig

Step 2

Calculate the Average Temperature, Average Pressure and Average MAOP for the pipeline segment using selected formulas on Temperature, Pressure, and MAOP readings at pipeline segment (inlet and outlet, or multiple).

Intermediate Outputs	Description
T,a	Average Pipeline Segment Temperature
P,a	Average Pipeline Segment Pressure
MAOP,a	Average Pipeline Segment MAOP

Step 3

Convert from Base to Average conditions using the API 11.1 Base to Alternate formula with inputs: Average Pipeline Segment Temperature, Average Pipeline Segment Pressure, Base Density, Pipeline Segment Volume, and Commodity Group (or Alpha 60).

Intermediate Outputs	Description
CTL,a	Volume correction factor due to temperature at pipeline segment average conditions
CPL,a	Volume correction factor due to pressure at pipeline segment average conditions
FP,a	Scaled compressibility factor at pipeline segment average conditions
CTPL,a	Combined volume correction factor due to temperature and pressure at pipeline segment average conditions
ρ,a	Density at pipeline segment average conditions
V60	Volume at base conditions (60°F and 0 psig)

Step 4

Convert from Base to Standard conditions using the API 11.1 Base to Alternate formula with inputs: Standard Temperature, Standard Pressure, Base Density, and Commodity Group (or Alpha 60).

Intermediate Outputs	Description
CTL,s	Volume correction factor due to temperature at standard conditions
CPL,s	Volume correction factor due to pressure at standard conditions
FP,s	Scaled compressibility factor at standard conditions
CTPL,s	Combined volume correction factor due to temperature and pressure at standard conditions
ρ,s	Density at standard conditions

Step 5

Calculate Line Pack Volume and Line Pack Mass.

Outputs	Description
Line Pack Volume (at standard conditions)	(Volume at base conditions) / (Combined volume correction factor due to temperature and pressure at standard conditions)
Line Pack Mass	(Line Pack Volume) * (Density at standard conditions)

Step 6

Convert from Base to MAOP conditions using the API 11.1 Base to Alternate formula with inputs: Pipeline Segment Average Temperature, Pipeline Segment Average MAOP, Base Density, Pipeline Segment Volume and Commodity Group (or Alpha 60).

Output
No persisted outputs from this step. But the calculated MAOP Volume at base conditions will be used in the next step.

Step 7

Calculate MAOP Line Pack Volume and MAOP Line Pack Mass.

Outputs	Description
MAOP Line Pack Volume (at standard conditions)	(MAOP Volume at base conditions) / (Combined volume correction factor due to temperature and pressure at standard conditions)
MAOP Line Pack Mass	(MAOP Line Pack Volume) * (Density at standard conditions)

Formula Inputs Reference

The Line Pack formula for petroleum liquids uses the following inputs to its calculation.

Inputs/Intermediate Outputs	Symbol	Description	Units
Alpha 60	a60	Pre-calculated 60°F thermal expansion factor (used if Commodity Group not given)	°F-1
Commodity Group	none	Commodity group type describing liquid (used if a 60 not input)	N/A
Density, Observed	ρo	Density at observed conditions to and Po	kg/m³
MAOP, Inlet	MAOP1	MAOP input 1 at the inlet (upstream) end of the pipeline segment	psig
MAOP, Outlet	MAOP2	MAOP input 2 at the outlet (downstream) end of the pipeline segment	psig
Pipeline Segment Volume	V_seg	Volume of the pipeline segment based either on the segment’s configured length and diameter or a user-configured volume	MCF
Pressure, Inlet	P1	Pressure input 1 at the inlet (upstream) end of the pipeline segment	psig
Pressure, Outlet	P2	Pressure input 2 at the outlet (downstream) end of the pipeline segment	psig
Pressure, Observed	Po	Pressure at which the observed density was measured	psig
Pressure, Standard	P	Standard pressure at which density is desired	psig
Temperature, Inlet	T1	Temperature input 1 at the inlet (upstream) end of the pipeline segment	°F
Temperature, Outlet	T2	Temperature input 2 at the outlet (downstream) end of the pipeline segment	°F
Temperature, Observed	to	Temperature at which the observed density was measured	°F
Temperature Standard	t	Standard temperature at which density is desired	°F

Formula Outputs Reference

The Line Pack formula for petroleum liquids calculates the following output variables as part of its calculation.

Outputs	Description	Units
CPL,a	Volume correction factor due to pressure at pipeline segment average conditions	N/A
CPL,s	Volume correction factor due to pressure at standard conditions	N/A
CTL,a	Volume correction factor due to temperature at pipeline segment average conditions	N/A
CTL,s	Volume correction factor due to temperature at standard conditions	N/A
CTPL,a	Combined volume correction factor due to temperature and pressure at pipeline segment average conditions	N/A
CTPL,s	Combined volume correction factor due to temperature and pressure at standard conditions	N/A
Density, Average	Density at pipeline segment average conditions	kg/m³
Density, Base	Density at base conditions (60°F and 0 psig)	kg/m³
Density, Standard	Density at standard conditions t and P	kg/m³
FP,a	Scaled compressibility factor at pipeline segment average conditions	Psi-1
FP,s	Scaled compressibility factor at the standard temperature	Psi-1
Line Pack Mass	Line Pack Mass	lbs
Line Pack Volume	Line Pack Volume at standard conditions	MCF
MAOP Line Pack Mass	MAOP Line Pack Mass	lbs
MAOP Line Pack Volume	MAOP Line Pack Volume at standard conditions	MCF
V60	Volume at base conditions (60°F and 0 psig)	same set of units as V_seg