C133 – Density Computation – Micro Motion (Solartron)
Description
This calculation returns a corrected density value and a corrected time period based on options set by the user.
References
Solartron 7812 Manual
Solartron 7835, 7845/46/47 liquid density transducer technical manual
Schlumberger Type 7915 Flow Computer Operating Manual Part 79155001 Issue A 1991
Kelton calculation reference C133
KIMS calculation reference K149
The FLOCALC.net version of this calculation reference F012 has been replaced by the following calculations:
F081: Gas Densitometer Computation – Micro Motion
F082: Liquid Densitometer Computation – Micro Motion
Options
Fluid
Select whether a liquid or gas densitometer is being used
- Gas
- Liquid
Correct for
Select the corrections to apply
For a gas
- Temperature
- Velocity of Sound
- Upstream Conditions
For a liquid
- Temperature
- Pressure
Revised Pressure Constants
Select to use the new pressure calibration equation for liquid densitometers
- Use K20C and K21C
Temperature-pressure coupling
Select this to apply the temperature-pressure coupling correction for liquid densitometers
- Apply
Calibration certificate units
Select the unit that is used for pressure in the densitometer calibration certificate. This option is available for liquid densitometers. Note that the pressure inputs for this calculation can be entered in any units but the calibration certificate units are important as although the K coefficients are unitless on the certificate they are not dimensionless and do have effective units e.g K19 has dimensions density/temperature, K21A has dimensions density/pressure, K21B has units density/pressure2 etc.
- bar and °C
- psi and °F
- kPa and °C
VoS Method
Select velocity of sound method
- P/D Method
- User Gas Method
Calibration Gas
This option allows the user to specify which calibration gas is being used.
If ‘User Gas Method’ is selected
- Nitrogen
- Argon
- Other
If ‘P/D Method’ is selected
- Nitrogen (0-100kg/m3)
- Nitrogen (0-400kg/m3)
- Methane (0-250kg/m3)
- Argon (0-400kg/m3)
If ‘User Gas Method’ is selected the following options apply
Calbration Gas Constant
If ‘Other’ is selected from ‘Calibration Gas’ specify which way the calibration gas constant is being entered.
- User Entered
- Calculated from ratio (G)
- Calculated from Specific Gravity (SG)
Measured Gas Ratio
- User entered
- Calculated
If ‘P/D Method’ is selected the following options apply
Transducer Type
If the velocity of sound option ‘P/D method’ is selected you are given the option to either select a transducer model or select ‘other’ in which case you will be able to enter the velocity of sound constant as an input.
VOS of Measured Gas
- User entered
- Calculated
If ‘Calculated’ is selected a gas composition needs to be input to calculate the velocity of sound.
VOS of Calibration Gas
- User entered
- Calculated
If ‘Calculated’ is selected then velocity of sound is determined form the calibration gas option.
Calculations
Density Calculation
The uncorrected density ρ is calculated by
| Where | ||
|---|---|---|
| K0 | = | Densitometer constant obtained from the calibration certificate |
| K1 | = | Densitometer constant obtained from the calibration certificate |
| K2 | = | Densitometer constant obtained from the calibration certificate |
| τ | = | Time period in µs |
Temperature Correction
The temperature corrected density ρt is calculated by
| Where | ||
|---|---|---|
| ρ | = | Uncorrected density |
| K18 | = | Densitometer constant obtained from the calibration certificate |
| K19 | = | Densitometer constant obtained from the calibration certificate |
| t | = | Transducer temperature |
| tr | = | Reference temperature |
Pressure Correction
If the pressure corrected density ρc is to be calculated
| Where | ||
|---|---|---|
| ρt | = | Temperature corrected density |
| K20A | = | Densitometer constant obtained from the calibration certificate |
| K20B | = | Densitometer constant obtained from the calibration certificate |
| K20C | = | Densitometer constant obtained from the calibration certificate |
| K21A | = | Densitometer constant obtained from the calibration certificate |
| K21B | = | Densitometer constant obtained from the calibration certificate |
| K21C | = | Densitometer constant obtained from the calibration certificate |
| p | = | Transducer pressure |
| pr | = | Reference pressure |
Note that the K20C and K21C terms are only applied for newer densitometers, for older models these additional terms are not included in the pressure correction calculation.
Temperature Pressure Coupling Correction
The temperature pressure coupling correction is used to correct the density according to the formula:
| Where | ||
|---|---|---|
| ρc | = | Pressure corrected density |
| K22 | = | Densitometer constant obtained from the calibration certificate |
| K23 | = | Densitometer constant obtained from the calibration certificate |
| t | = | Transducer temperature |
| tr | = | Reference temperature |
| p | = | Transducer pressure |
| pr | = | Reference pressure |
VoS – P/D Method
The pressure/density method of determining the velocity of sound correction is calculated by
| Where | ||
|---|---|---|
| Cvos | = | Velocity of sound correction factor |
| K | = | Velocity of sound constant for the density sensor |
| τ | = | Time period in µs |
| Cc | = | Velocity of sound of calibration gas |
| Cg | = | Velocity of sound of measured gas |
Velocity of sound of measured and calibration gas
For the measured gas this is calculated in the Solartron 7915 Flow Computer by
| Where | ||
|---|---|---|
| γo | = | The ratio of specific heat for the composition |
| K5 | = | Constant for the composition calculated from table 51 |
| K6 | = | Constant for the composition calculated from table 51 |
For the calibration gas this is calculated in the Solartron 7915 Flow Computer by
| Where | ||
|---|---|---|
| Kn | = | Constants for the calibration gas |
VoS – User Gas Method
The user method for determining the velocity of sound correction is calculated by
| Where | ||
|---|---|---|
| Cug | = | The user gas correction factor |
| K3 | = | A constant for the density sensor |
| K4 | = | A constant for the density sensor |
| Tc | = | The temperature of the calibration gas |
| Tg | = | The temperature of the measured gas |
| Gc | = | The Specific Gravity / Ratio of specific heats of calibration gas assumed to be 0.6908264 for Nitrogen and 0.8224192 for Argon |
| Gg | = | The Specific Gravity / Ratio of specific heats of measured gas |
Time period calculation
The corrected time period τc can be calculated by
| Where | ||
|---|---|---|
| K0 | = | Densitometer constant obtained from the calibration certificate |
| K1 | = | Densitometer constant obtained from the calibration certificate |
| K2 | = | Densitometer constant obtained from the calibration certificate |
| ρc | = | The corrected density |