# Computer systems: standard temperature accounting

## Introduction

It is now the norm for volumetric conversions to be performed by a computer. Volume X of the Petroleum Measurement Tables is dedicated to the computer procedures involved in the conversion of volumes to volumes at 15ºC.

The volume correction factor to be applied to a volume of product at a known temperature is:

the density of the product at the observed temperature |

the density of the product at 15ºC |

If the observed product density is supplied by an in-line densitometer and the product density at 15ºC is supplied by analysis then the STA volume correction is a simple matter.

When, as is normal with refinery production, the product density at 15ºC varies the calculation of volumes at 15ºC becomes a complex mathematical equation.

Where there is a significant number of transactions then the use of a computer system to perform the calculations can be expected.

The complexity of the calculations is brought about because the only available equation to calculate the density of a product at a specified temperature requires the density of the product at 15ºC and it cannot be mathematically “reversed” to give a density at 15ºC if the density at the observed temperature is provided.

To resolve this problem a mathematical process known as iteration is employed.

## Iteration

A “guess” is made as to the density at 15ºC (normally the measured density) and the equation calculates a density at the observed temperature which is then compared to the known density. The difference in the calculated and the known densities enables an improved estimate of density at 15ºC to be made and the calculation repeated. The process is repeated until an acceptable difference between the known and calculated densities is achieved and the last estimated density is accepted as the density at 15ºC.

## Calculation of volume correction factors

Calculation of volume correction factors can be made for all products represented in the Energy Institute’s Petroleum Measurement Tables.

For calculation purposes there are 5 types of product:

Product Group | Density Range |

(kg/m3) | |||

From | To | ||

Crudes | 610.5 | 1075.0 | |

Fuel Oil | 839.0 | 1075.0 | |

Jet group | 788.0 | 838.5 | |

Jet/Gasoline Transition | 770.5 | 787.5 | |

Gasolines | 653.0 | 770.0 | |

(N.B. Lubricating oils have been excluded) |

The conversion equations are referenced in Volumes IX and X of the Petroleum Measurement Tables. Products which fall in the Jet / Gasoline Transition block are exceptional in that they use a different equation in the conversion calculation.

Standard Temperature Accounting may be performed by programs held within flow computers or by other systems. The verification of the correctness of these programs can be validated using test data with the expected results calculated from the Energy Institute tables (formerly the Institute of Petroleum). Test data should address the specific requirements of the system.

## Requirements for standard temperature accounting systems

It is expected that within any system performing Standard Temperature Accounting (STA) calculations the relevant program will have the following:

- a density range check to ensure that only valid values are accepted. The IP equations are only valid within specific density ranges;
- arithmetic accuracy sufficient to handle the expected values generated during the calculation process;
- the capability to calculate values to the required number of decimal places and to correctly round up or down as appropriate; and
- a temperature range check to ensure only valid temperatures are accepted. The temperature ranges are specific to density ranges.