There are many variables to consider to maximize the performance of your flow meter.  Flow profile quality and flow conditioners are only one small piece of the puzzle, but there are some other critical variables that must be looked at as well!

Here we outline ways in which you can help improve the performance of your liquid turbine and liquid ultrasonic meters.

Density & Viscosity: Liquid Turbine Meter Run

In the case of the turbine meter run, one equation of two unknowns exists. Density and viscosity are unknown unless both are sampled, or one is sampled and the other determined by the approach shown below. 

The orifice flow calculation is completely utilized in its entirety using the actual volumetric flow rate from the turbine meter and the differential pressure from the flow conditioner. In this case, density must be sampled.  

Alternatively, the orifice flow equation can be replaced with the Euler equation to produce exactly the same effect only in a more convoluted arrival at the same result.

Equation 1 – Orifice Flow Conditioner Flow Equation:

 

 

Term Description
V Actual Volumetric Flow Rate from turbine meter (m3/s)
Cd Coefficient of discharge (unitless)
Ev Velocity of approach factor (unitless)
Y Expansion factor (unitless)
d Orifice bore diameter (m)
D Pipe inside diameter (m)
ρ Actual density (kg/m3)
ΔP Differential Pressure (kPa)
β Beta ratio d/D (unitless)
m Mass flow rate (kg/s)

 

In equating the terms together, one is left with density and Cd unknown. Density is obtained by on-site analysis or by lab sample analysis. In this case you are left with:

 

 

This equation, when rearranged, becomes Coefficient of discharge (Cd). 

Equation 2 – Coefficient of discharge (Cd)

 

 

Canada Pipeline Accessories Flow Conditioner Orifice Equation Constants

Model Type Porosity Effective Beta Ratio 1-4
50E 0.489 0.6993 0.8723
55E 0.489 0.6993 0.8723
65E 0.582 0.7630 0.8131

 

1.1 Calculation Methodology

Hydrocarbon liquid phase flow measurement is a batch-based approach. The type of hydrocarbon fluid is expected to not change in each batch of fluid transfer. Therefore, the molecular composition does not change, but the flowing fluid – pressure, temperature, actual density, actual viscosity and flow rate – does change.

The current industry procedure paradigm is dictated by API chapter 5.3, ISO 2715, etc. These standards dictate that the flow meter acts as an actual fluid repeatability device only. Once a fluid batch session is initiated, an actual volumetric proof is carried out at that particular flowing Reynolds Number (Re). The meter proof provides a “k” factor for the meter which is an adjustment factor to convert the meter indicated volumetric flow rate to actual volumetric flow rate. If the fluid Re changes (i.e. pressure, temperature, viscosity, density, or flow rate) a new proof must be carried out to provide a new k factor since k factor is a function of Re.

The calculation process presented here allows the measurement device to “follow” the fluid Re. It should be completed as many times as possible based on the variability of the batch fluid flow Re change and the computing power available.

  1. Using a flow metering calibration lab, establish a k factor vs. Re curve for the turbine meter. Note, that this is not a k factor vs. actual volumetric flow rate curve. The abscissa of the curve must be Re now. This is a fairly detailed and lengthy requirement. This process needs to only be done once and then periodically as per government or company standard practices (often yearly, every 3 years, every 6 years, etc.). 
  2. Install the meter at site.
  3. Once the fluid transfer batch has started, collect turbine meter actual volume flow rate via data acquisition equipment (like a flow computer or SCADA equipment), along with flow conditioner data – Dp, Temperature, Pressure Real Time – once per second, per minute, or another timeframe based on Re variability of the fluid flow. Re variability of the fluid flow is determined statistically by analysis of the fluid Re change with respect to time.
  4. Collect a batch flowing fluid sample as normal. This is used to calculate standard density via lab analysis, and is typically done once after the new batch is in steady state with respect to composition. 
  5. Convert this standard density to actual density utilizing American Petroleum Institute, Manual of Petroleum Measurement Standard 11.1 (API MPMS 11.1) for the current flowing pressure and temperature of the fluid.
  6. Calculate the flow conditioner Coefficient of discharge (Cd) with this density, the flow conditioner dp, and turbine volumetric flow rate via Equation 2 as depicted above.
  7. Recall the standard American Gas Association Flow Measurement Report #3 Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids, (AGA-3) section 1.7.2 Empirical Coefficient of Discharge Equation for Flange Tapped Orifice Meters, Part 1. Using the Cd provided in step #6 back-calculate the pipe Re via reverse Cd calculation iteration.
  8. Using this Re you can now use the calibrated Re based k factor provided in step #1 above. Repeat steps 6 and 7 until the Re calculated does not change (this is an iterative process).
  9. Utilizing the Re equation below, you can now obtain the fluid viscosity:

Equation 3 – Reynolds Number Using Dynamic Viscosity Centipoise (cp)

 

 

Term Description
ρ Density (kg/m3)
Ū Mean Velocity m/s
Ø Pipe Inside Diameter m
µ dynamic viscosity 0.001 kg/mS, PaS, cp

* Using Kinematic Viscosity Centistokes (cSt)

 

 

Term Description
γ kinematic viscosity 1×10-6 m2/s = 1 cSt

 

1cp 0.001 kg/ms 0.01 p 0.001 Pas
1cSt 1×10-6 m2/s 0.01 stokes  

 

  1. Additionally, if an onsite real-time densitometer is utilized rather than lab sampling, a simple real-time Reynolds Number compensated flow measurement system is available by following steps #1 through #9. Real-time Re and viscosity is subsequently provided. No onsite meter proofs are required.
  2. Over time, the data for each product batch or product type the shipper transports can be carefully recorded against that product. If enough statistically significant data is recorded, sampling of density would not be required. If temperature, pressure and product type are known, the density can be interpolated off of a mixture of temperature and pressure data. This is a perfect application of Artificial Intelligence or Machine Learning algorithms. 

Density & Viscosity: Liquid Ultrasonic Meter Run

In the special case of the liquid ultrasonic meter (LUSM) run, one equation and one additional associated relationship exists for two unknowns. Similar to the liquid turbine meter application in terms of having an actual volumetric flow rate and an orifice flow conditioner calculation available, a strong relationship between the LUSM speed of sound (SOS) and actual fluid density at pressure and temperature exists. This effectively leaves no need to sample density after the initial seeding is completed for each product batch. Density and viscosity are unknown again but, in this application, an uncorrelated 2nd relation exists between the fluid SOS and density, solving that problem.

This is, again, based on the liquid fluid transportation and measurement batching process. For each batch or product type, sample the product for onsite or lab calculation, then let that seed an SOS–density relationship against pressure and temperature for that specific product. Eventually enough data will be collected for each product type that it will no longer be necessary to sample the fluid to determine density. Continuous fluid sampling could be used to act as a quality assurance check for density accuracy only, which can be automated.

 

2.1 Calculation Methodology

Hydrocarbon liquid phase flow measurement is a batch-based approach. The type of hydrocarbon fluid is expected to not change in each batch of fluid transfer. Therefore, the molecular composition does not change, but the flowing fluid – pressure, temperature, actual density, actual viscosity and flow rates – does change. For this reason we are uninterested in the exact fluid composition – it does not matter.

The current industry procedure paradigm is dictated by API chapter 5.8, ISO 12242, etc. These standards dictate that the flow meter acts as an actual fluid repeatability device only. Once a fluid batch session is initiated, an actual volumetric proof is carried out at that particular flowing Reynolds Number (Re). The meter proof provides a “k” factor for the meter which is an adjustment factor to convert the meter indicated volumetric flow rate to actual volumetric flow rate. If the fluid Re changes (i.e. pressure, temperature, viscosity, density, or flow rate) a new proof must be carried out to provide a new k factor since k factor is a function of Re.

The calculation process presented here allows the measurement device to “follow” the fluid Re. It should be completed as many times as possible based on the variability of the batch fluid flow Re change and the computing power available.

  1. Using a flow metering calibration lab, establish a k factor vs. Re curve for the liquid ultrasonic flow meter (LUSM). Note, that this is not a k factor vs. actual volumetric flow rate curve. The abscissa of the curve must be Re now. This is a fairly detailed and lengthy requirement. This process needs to only be done once and then periodically as per government or company standard practices (often yearly, every 3 years, every 6 years, etc.). 
  2. Install the meter at site.
  3. Once the fluid transfer batch has started, collect LUSM actual volume flow rate via data acquisition equipment, like a flow computer or SCADA equipment, along with flow conditioner Dp, Temperature, Pressure and now also LUSM SOS Real Time. once per second, minute, or another timeframe based on Re variability of the fluid flow. Re variability of the fluid flow is determined statistically by analysis of the fluid Re change with respect to time.
  4. Collect a batch flowing fluid sample as normal – this is used to calculate standard density via lab analysis. This is normally done once after the new batch is in steady state with respect to composition. 
  5. Convert this standard density to actual density utilizing American Petroleum Institute, Manual of Petroleum Measurement Standard 11.1 (API MPMS 11.1) for the current flowing pressure and temperature of the fluid.
  6. A repeatable and characteristic relationship exists between a non-changing fluids SOS and density at various temperatures and pressures for each product type. In order to capture this relationship, a 4 dimensional surface must be employed via database design utilizing Artificial Intelligence or Machine Learning. 

Alternatively, arrangement of SOS, Density, Pressure and Temperature in self-made thermodynamic tables can be employed. Flowing density must be sampled and provided to populate the database so that, eventually, each product type at any given pressure and temperature a flowing density can be “looked up”.

Typically the thermodynamic database tables for this would theoretically appear as shown below (although the database size will be much larger):

Product ABC – The Example Oil Company
  T1     T2     T3   Etc.
SOS ρ P SOS ρ P SOS ρ P
1 a P1 1 a P1 1 a P1
2 b P2 2 b P2 2 b P2
2 c P3 2 c P3 2 c P3
. . P. . . P. . . P.
. . P. . . P. . . P.
. . P. . . P. . . P.
SOSi ρj Pk SOSi ρj Pk SOSi ρj Pk
  T4     T5     T6  
SOS ρ P SOS ρ P SOS ρ P
1 a P1 1 a P1 1 a P1
2 b P2 2 b P2 2 b P2
2 c P3 2 c P3 2 c P3
. . P. . . P. . . P.
. . P. . . P. . . P.
. . P. . . P. . . P.
SOSi ρj Pk SOSi ρj Pk SOSi ρj Pk
  T7     T8     T9  
SOS ρ P SOS ρ P SOS ρ P
1 a P1 1 a P1 1 a P1
2 b P2 2 b P2 2 b P2
2 c P3 2 c P3 2 c P3
. . P. . . P. . . P.
. . P. . . P. . . P.
. . P. . . P. . . P.
SOSi ρj Pk SOSi ρj Pk SOSi ρj Pk
  T10     T11     T12  
SOS ρ P SOS ρ P SOS ρ P
1 a P1 1 a P1 1 a P1
2 b P2 2 b P2 2 b P2
2 c P3 2 c P3 2 c P3
. . P. . . P. . . P.
. . P. . . P. . . P.
. . P. . . P. . . P.
SOSi ρj Pk SOSi ρj Pk SOSi ρj Pk
  T13     T14     T15  
SOS ρ P SOS ρ P SOS ρ P
1 a P1 1 a P1 1 a P1
2 b P2 2 b P2 2 b P2
2 c P3 2 c P3 2 c P3
Etc.

Once populated with a sufficient and statistically significant level of data, you will be able to ascertain the temperature, pressure and the appropriate density corresponding to the LUSM SOS. Use this density for the following steps.

  1. Calculate the flow conditioner Coefficient of discharge (Cd) with this density, the flow conditioner dp, and turbine volumetric flow rate via Equation 2. 
  2. Recall the standard American Gas Association Flow Measurement Report #3 Orifice Metering of Natural Gas and Other Related Hydrocarbon Fluids, (AGA-3) section 1.7.2 Empirical Coefficient of Discharge Equation for Flange Tapped Orifice Meters, Part 1. Using the Cd provided in the previous step, back calculate the pipe Re via reverse iteration.
  3. Using this Re, you can now use the k factor provided in step #1 above. Repeat steps 1 through 8 until the Re calculated does not change (this is an iterative process).
  4. Utilizing the Re equation below, you can now obtain the fluid viscosity:

Equation 3 – Reynolds Number Using Dynamic Viscosity Centipoise (cp)

 

 

Term Description
ρ Density (kg/m3)
Ū Mean Velocity m/s
Ø Pipe Inside Diameter m
µ dynamic viscosity 0.001 kg/mS, PaS, cp

* Using Kinematic Viscosity Centistokes (cSt)

Term Description
γ kinematic viscosity 1×10-6 m2/s = 1 cSt

 

1cp 0.001 kg/ms 0.01 p 0.001 Pas
1cSt 1×10-6 m2/s 0.01 stokes  

 

  1. We now have the fluid flowing density, viscosity, Re and an accurate LUSM k factor resulting in the usage of the meter k factor Re curve. As a result, meter proofs with a meter prover are no longer required; instead, we know the fluid density and viscosity without densitometers or viscometers. 

Conclusion

This guide is designed to provide you with the calculations needed to improve measurement accuracy along your pipeline, specific to liquid turbine and liquid ultrasonic meters. 

To learn more about obtaining high fluid flow measurement accuracy and pipeline accessories manufactured right here in Canada, connect with us at info@cpacl.ca