What is Flow Compensation?
Why do you do process temperature and pressure flow compensation?
In gas flow measurement, the density of the gas changes as pressure and temperature change. This change in density can affect the accuracy of the measured flow rate if it is uncompensated. Temperature, pressure compensated flow control is a flow modified mathematically by one or more additional variables, like :
Producing a resultant value for flow compensation that is more accurate. It is compensated for the error effects of the other variables.
Pressure Temperature Compensation Flow Measurement Formula
Orifice meters require Pressure Temperature Compensation Formula when we use them to measure gas flow in pipes with variable operating pressure and temperature. Normally we do not have an online density measurement. In this case we will consider the density constant to simplify the calculations. If you want to perform a density compensation in the flow measurement you must take into account the density variation.
The variations in pressure and temperature have a significant effect on gas density, this is why without this pressure and temperature compensation the flow measurement can have large errors.
This post will help you to understand the basics concepts around this formulas (flow compensation formula) and will aslo let you implement them on your process control system.
1.Obtaining the Real Density Formula
Staring with the ideal gas law, we can extract density from the formula and calculate de density for two different situations (design and real). We need to apply a density compensation in flow measurement.
- P = Pressure
- T = Temperature
- V = Volume
- Mw = Molecular Weight
- n = Number of mols
- R = Gas Constant
- rho = gas density
After simplify the previous equation we can have different results depending on the different situations, so we can have a set of design conditions and also a set of real situation conditions….
2.Deriving the Differential Pressure Flow Equation
- V = linear velocity of fluid
- T = Temperature
- V = Volume
…rearranging the previous equation and assuming constant density and h1=h2 we have ….
Now it’s time to express fluid’s velocity in function of pipe and orifice plate restriction diameter ….
and after that, we can substitute V1 inside the previous, the resulting equation gives us the velocity at the restriction :
To calculate the volumetric flow we have to multiply both sides by the area of the restriction …
If we concentrate all the constants in just constant called K we have the following expressions refering to QV and QM :
How does pressure compensated flow control work?
3. Pressure Temperature Compensation Formula (gas flow compensation formula)
Now it’s time to substitute the real density by the density calculated in point 1.
After the substitution we will have the following formulas which are used to calculate the compensated flow for every orifice plate flowmeter (depending if you need volumen or mass flow).
Remeber that you must use the flow square root extraction formula in your DCS !!!
4. References :
- EMERSON (2015) Theory of dP Flow
- MOORE Products (1994) Pressure and temperature compensation of an orifice meter using the model 352 single loop controller
- EMERSON – Rosemount Differentil Pressure Flow Gas Flow Measurement