# C108 – Meter K-factor Computation

## Description

This calculates the meter k-factor for a meter proved using either a pipe prover, compact prover or a master meter.

## References

Institute of Petroleum – Petroleum Measurement Manual: Part X – Meter Proving

Kelton calculation reference C108

FLOCALC calculation reference F066

KIMS calculation reference K119

Kelton calculation C219 – Table 54 Calculation of Ctl

Kelton calculation C220 – API Calculation of Compressibility Factor and Cpl

Kelton calculation C222 – API Calculation of Ctl (Product Groups)

Kelton calculation C223 IP Paper 2 – Compressibility & Cpl

Kelton calculation C251 – API Density Referral 2004

Kelton calculation C254 – API MPMS/GPA TP-27:2007 Ctl Calculation

## Options

### Calculate

- Meter K-factor
- Meter Factor

This option gives the choice to calculate K-factor and/or meter factor as the output.

### Prover Type

- Pipe prover
- Master meter
- Compact prover

This option allow the user to choose what type of prover is being used.

### Meter Type

- Mass
- Volume

This option is used to set whether the k-factor will be calculated in pulses/volume or pulses/mass.

### Master Meter K-factor

- Fixed
- Varies with Reynold’s number
- Varies with flow rate

This option is used to determine what the master meter k-factor will be calculated against.

### Ctlp

- None
- User entered
- Calculated

This option gives the user the option of applying a correction due to the temperature of the liquid at the prover.

### Cplp

- None
- User entered
- Calculated

This option gives the user the option of applying a correction due to the pressure of the liquid at the prover.

### Ctlm

- None
- User entered
- Calculated

This option gives the user the option of applying a correction due to the temperature of the liquid at the meter.

### Cplm

- None
- User entered
- Calculated

This option gives the user the option of applying a correction due to the pressure of the liquid at the meter.

### Ctsp

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

This option gives the user the option of applying a correction due to the temperature on the steel of the prover.

### Cpsp

- None
- User entered
- Calculated

This option gives the user the option of applying a correction due to the pressure on the steel of the prover.

### Cpsp Calculation Method

- IP Manual Part X (D/Et)
- User entered coefficient
- Alternative calculation (2r/Et)

This option is used to select how to carry out the C

_{psp}calculation. It will be done according to IP Manual Part X. The pressure coefficient can be calculated as shown in the option either using pipe diameter, radius or a user enter coefficient.

### Ctl Calculation Method

- ASTM-IP Table 54
- API Ch11.1 (1980)
- API Ch11.1 (2004)
- GPA TP-27 (2007)

If a temperature correction is required this option group will allow the user to select from one of these standards to implement a C

_{tl}calculation .

### Cpl Calculation Method

- IP Paper 2 (1984)
- API Ch11.2.1 (1984)
- API Ch11.2.2 (1986)
- API Ch11.1 (2004)

If a pressure correction is required this option group will allow the user to select from one of these standards to implement C

_{pl}calculation.

## Calculation

### Correction for temperature on steel of prover

The C_{tsp} is calculated by:

For a compact prover an additional correction is made on top of the calculation above to gain the C_{tsp}

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

α_{c} |
= | Cubic temperature coefficient |

α_{l} |
= | Linear temperature coefficient |

α_{d} |
= | Detector temperature coefficient |

T_{p} |
= | Prover temperature |

T_{d} |
= | Compact prover detector temperature |

T_{rf} |
= | Prover reference temperature |

### Correction for pressure on steel of meter

The C_{psp} is calculated by:

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

λ | = | Pressure coefficient |

P_{p} |
= | Prover pressure |

P_{rf} |
= | Prover reference pressure |

### Master meter K-factor

The master meter K-factor can be calculated against flow rate or Reynold’s number. This uses known test data and sets K-factor values against their corresponding Reynold’s number or flow rate. The flow rate/Reynold’s number is estimated from line conditions and prover geometry, linear interpolation is then employed to find the value of the K-factor. This process is done iteratively until a solution for K-factor has converged to necessary precision.

### Uncorrected K-factor

The uncorrected K-factor is calculated by:

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

n | = | Number of pulses generated by the meter during a proving run |

V_{b} |
= | Base volume of prover |

ρ | = | Observed density of liquid |

n_{mm} |
= | Number of pulses generated by the master meter during proving run |

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

### K-factor

The K-factor is calculated by:

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

K_{f0} |
= | Uncorrected K-factor |

C_{tlm} |
= | Correction for temperature of the liquid at the meter |

C_{plm} |
= | Correction for pressure of the liquid at the meter |

C_{tlp} |
= | Correction for temperature of the liquid at the prover |

C_{plp} |
= | Correction for pressure of the liquid at the prover |

C_{tsp} |
= | Correction for temperature on steel of the prover |

C_{psp} |
= | Correction for pressure on steel of the prover |

IntF | = | Interpolation factor |

### Meter Factor

The meter factor is calculated by:

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

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

K_{f} |
= | K-factor |