# C166 – Meter Factor Computation – Master Meter (Mass)

## Description

This calculates the K-factor and the meter factor of a mass based meter using a master meter for proving.

## References

IP Petroleum Measurement Manual: Part X – Meter Proving

Kelton calculation reference C166

KIMS calculation reference K175

## Options

### Factor Type

- K-Factor
- Meter Factor

This option is chosen to…

### Ctsp

- None
- User entered
- Calculated – linear expansion coefficient
- Calculated – cubic expansion coefficient

### Cpsp

- None
- User entered
- Calculated

### Ctsm

- None
- User entered
- Calculated – linear expansion coefficient
- Calculated – cubic expansion coefficient

### Cpsm

- None
- User entered
- Calculated

## Calculation

### Uncorrected K-factor

The uncorrected K-factor is calculated by:

Where | ||
---|---|---|

K_{p} |
= | Master meter K-factor |

n_{p} |
= | Number of pulses counted by master meter |

n_{m} |
= | Number of pulses counted by duty meter |

### Temperature Correction

The correction factor due to thermal expansion of the steel (Ctsp and Ctsm) is calculated by:

Where | ||
---|---|---|

α_{c} |
= | Cubic temperature coefficient |

α_{l} |
= | Linear temperature coefficient |

T | = | Temperature |

T_{rf} |
= | Reference temperature |

### Pressure Correction

The correction factor due to pressure on the steel (Cpsp and Cpsm) is calculated by:

λ | = | Pressure coefficient |

P | = | Pressure |

P_{rf} |
= | Reference pressure |

### K-factor

The K-factor is calculated by:

Where | ||
---|---|---|

K_{u} |
= | Uncorrected K-factor |

C_{tsp} |
= | Correction factor for the thermal expansion of the steel of the master meter |

C_{psp} |
= | Correction factor for the expansion of the steel of the master meter due to pressure |

C_{tsm} |
= | Correction factor for the thermal expansion of the steel of the meter |

C_{psm} |
= | Correction factor for the expansion of the steel of the meter due to pressure |

### Meter Factor

The meter factor is calculated by:

Where | ||
---|---|---|

K_{f} |
= | Meter K-factor |

K_{b} |
= | Base K-factor |