API 2540 – Volume Correction Factors

Introduction

This procedure calculates the Volume Correction Factor (VCF) for correcting from the density at base conditions (60°F and 0 psig) to alternate temperature and pressure conditions.

Step 1:

Unless otherwise directed, check the input values to determine if they are in the range of this standard. The following are the valid limits.

-58.0^\circ F \leq t \leq 302.0^\circ F\~\ 0 \leq P \leq 1500 \text{ psig}\~\\rho_{60,\text{min}} \leq \rho_{60} \leq \rho_{60,\text{max}}

-58.0^\circ F \leq t \leq 302.0^\circ F\\~\\ 0 \leq P \leq 1500 \text{ psig}\\~\\\rho_{60,\text{min}} \leq \rho_{60} \leq \rho_{60,\text{max}}

If commodity type is specified

The following table give 𝜌₆₀ limits for the various commodity groups.

If P<0 psig then P=0 and continue with procedure.

Step 2:

Shift the input 𝜌₆₀ value to the density basis 𝜌^∗. If the commodity group has been specified, then compute using the following formulas.

\rho^* = \rho_{60}\big{1 + \exp\left[-0.8A^2 – A^2\right] \big}

\rho^* = \rho_{60}\big\{1 + \exp\left[-0.8A^2 - A^2\right] \big\}

Where:

A = \left[ \left(\frac{K_0}{\rho_{60}} + K_1 \right) \frac{1}{\rho_{60}}\right]

A = \left[ \left(\frac{K_0}{\rho_{60}} + K_1 \right) \frac{1}{\rho_{60}}\right]

𝐾₀ − Coefficient in correlation for 𝛼₆₀(kg²/m⁶℉)
𝐾₁ − Coefficient in correlation for 𝛼₆₀(kg/m³℉)
𝜌₆₀ − Density at base conditions (60℉ and 0psig)(kg/m³)

Step 3:

In preparation of calculating the correction factor due to temperature, 𝐶_𝑇𝐿, determine the coefficient of thermal expansion at the base temperature of 60°F, 𝛼₆₀. The coefficients used in this equation depend upon the commodity group. Use the same coefficients that were used in Step 3.

\alpha_{60}=\left(\frac{K_0}{\rho^*}+K_1 \right)\frac{1}{\rho^*}

\alpha_{60}=\left(\frac{K_0}{\rho^*}+K_1   \right)\frac{1}{\rho^*}

Where:
𝐾₀ − Coefficient in correlation for 𝛼₆₀(kg²/m⁶℉)
𝐾₁ − Coefficient in correlation for 𝛼₆₀(kg/m³℉)
𝜌^∗ − Density at shifted base conditions(kg/m³)

Step 4:

Calculate the difference in the Reference Temperature and the Liquid Temperature.

\Delta t=t-T_1

\Delta t=t-T_1

Where:
Δ𝑡 − Reference Temperature minus the Liquid Temperature(℉)

Use this value to calculate the volume correction factor due to temperature, 𝐶𝑇𝐿:

C_{TL}=esp\big{-\alpha_{60}\Delta t \left[1+0.8\alpha_{60}(\Delta t)\right]\big}

C_{TL}=esp\big\{-\alpha_{60}\Delta t \left[1+0.8\alpha_{60}(\Delta t)\right]\big\}

Step 5:

Correct a volume measured at alternate conditions to base conditions and/or correct base density to alternate conditions.

\rho = C_{TL} \cdot \rho_{60} \~\ V_{60} = V_t \cdot C_{TL}

\rho = C_{TL} \cdot \rho_{60} \\~\\ V_{60} = V_t \cdot C_{TL}

Where:
𝜌 − Density at alternate conditions(kg/m³)
𝐶_𝑇𝐿 − Volume Correction Factor due to Temperature
𝑉₆₀ − Volume at base conditions (60℉ and 0psig)
𝑉_𝑡 − Volume at alternate temperature
𝜌₆₀ − Density at base conditions (60℉ and 0psig)(kg/m³)

Case Guide

Part 1: Create Case

Input Parameters

• Liquid Type
• Specific Gravity Range
• Ko – API Correlation Parameter
• K1 – API Correlation Parameter
• Reference Temperature (°F)
• Specific Gravity
• Liquid Temperature (°F)

Part 2: Outputs/Reports

Results

• Coefficient of Thermal Expansion
• Volume Correction Factor for Thermal Expansion
• Corrected Specific Gravity

References

• Hydraulics for Pipeliners – C.B. Lester
• API standard 2540 Manual of Petroleum Measurement Standards, Chapter 11.1-Volume Correction Factors, Volume X – Background, Development, and Program Documentation.
• API RP 1117 Movement of In-Service Pipeline