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 :

  • Temperature
  • Pressure
  • Density
  • Viscosity

Producing a resultant value for flow compensation that is more accurate. It is compensated for the error effects of the other variables.

Formula for pressure

This post is related with how to compesate flow with pressure and temperature. If you are looking for the Pressure Formula click here!!

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.

DP Orifice Plate Diagram with Pressure and Temperature Transmitters for Flow Compensation
DP Orifice Plate Diagram with Pressure and Temperature Transmitters for Flow Compensation

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.

Differential Pressure Flowmeter based on Orifice Plate Technology installed on process plant
Differential Pressure Flowmeter based on Orifice Plate Technology installed on process plant

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.

Density Formula based on Ideal Gas Law
Density Formula based on Ideal Gas Law

Where :

  • 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….

Real Density vs Design Density Formulas
Real Density vs Design Density Formulas

Operating with the formulas for real density formula and design density we can obtain the formula to define the real density taking in account the pressure and temperature compensation.

Real Density Formula based on Design Density
Real Density Formula based on Design Density

2.Deriving the Differential Pressure Flow Equation

To obtain the Differential Pressure Flow equation we will use two basic fluid mechanics equations : Euler’s equation of continuity and Bernoulli’s principle,

The Euler's Equation for relate velocity and area for a fluid
The Euler’s Equation for relate velocity and area for a fluid
Bernoulli's principle - relates Dynamic Pressure, Static Pressure and Height
Bernoulli’s principle – relates Dynamic Pressure, Static Pressure and Height

Where :

  • V = linear velocity of fluid
  • T = Temperature
  • V = Volume

…rearranging the previous equation and assuming constant density and h1=h2 we have ….

Simplifying...
Simplifying…

Now it’s time to express fluid’s velocity in function of pipe and orifice plate restriction diameter ….

Velocity expressed as function of Areas
Velocity expressed as function of Areas

and after that, we can substitute V1 inside the previous, the resulting equation gives us the velocity at the restriction :

Velocity at the Restriction
Velocity at the Restriction

To calculate the volumetric flow we have to multiply both sides by the area of the restriction …

Volumetric Flow - Depends on Differential Pressure, Density of Gas and Ratio of diameters
Volumetric Flow – Depends on Differential Pressure, Density of Gas and Ratio of diameters

If we concentrate all the constants in just constant called K we have the following expressions refering to QV and QM :

Volumetric Flow in function of Differential Pressure and Density
Volumetric Flow in function of Differential Pressure and Density
Mass Flow in function of Differential Pressure and Density
Mass Flow in function of Differential Pressure and Density

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.

Flowmeter's manifold
Flowmeter’s manifold

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).

Volumetric Flow Compensated in Pressure and Temperature
Volumetric Flow Compensated in Pressure and Temperature
Mass Flow Compensated in Pressure and Temperature
Mass Flow Compensated in Pressure and Temperature

Remeber that you must use the flow square root extraction formula in your DCS !!!

4. References :

  1. EMERSON (2015) Theory of dP Flow
  2. MOORE Products (1994) Pressure and temperature compensation of an orifice meter using the model 352 single loop controller
  3. Wikipedia.org
  4. EMERSON –  Rosemount Differentil Pressure Flow Gas Flow Measurement
Pressure Temperature Compensation Formula
%d bloggers like this: