Temperature and Pressure Compensation for Orifice Flow Meters: Calculation and PLC/DCS Implementation Guide - Just Measure it

Temperature and Pressure Compensation for Orifice Flow Meters: Calculation and PLC/DCS Implementation Guide

/ Flow meter

Introduction

Orifice flow meters are widely used for measuring the flow rate of gases, steam, and liquids in industrial processes. However, when measuring compressible fluids such as gas and steam, the flow measurement accuracy can be significantly affected by changes in operating temperature and pressure.

The reason is that the density of a compressible fluid changes with temperature and pressure variations:

  • When pressure increases, gas density increases.
  • When temperature increases, gas density decreases.

Therefore, to obtain accurate flow measurement results under actual operating conditions, temperature and pressure compensation is required.

This article explains the principle of temperature and pressure compensation for differential pressure (DP) flow meters, including orifice plates and averaging pitot tube flow meters, and provides practical implementation methods in PLC/DCS systems.

1. Principle of Temperature and Pressure Compensation

The flow calculation of an orifice flow meter is usually based on a specific design condition, including:

  • Design pressure
  • Design temperature
  • Reference density

However, actual operating conditions are rarely constant. The process pressure and temperature continuously fluctuate, causing changes in fluid density.

For compressible fluids, the relationship between density, pressure, and temperature follows the ideal gas law:

 

ρ=PRT\rho=\frac{P}{RT}

 

Where:

  • ρ = Fluid density
  • P = Absolute pressure
  • T = Absolute temperature
  • R = Gas constant

Therefore, the actual flow rate must be corrected according to the real-time pressure and temperature values.

The compensation calculation normally requires:

  • Flow signal
  • Pressure signal
  • Temperature signal

These signals are sent to the DCS or PLC system, where the compensation calculation is performed and the corrected standard flow value is displayed.

2. Temperature and Pressure Compensation System Architecture

A typical compensation system consists of:

 
                 Orifice Plate
                      |
                      |
              Differential Pressure
                Transmitter
                      |
                      |
              Flow Signal (DP)
                      |
                      |
      --------------------------------
      |                              |
Pressure Transmitter        Temperature Sensor
      |                              |
      --------------------------------
                      |
                    PLC/DCS
                      |
          Temperature & Pressure
          Compensation Calculation
                      |
              Corrected Flow Output
 

The PLC/DCS calculates the compensated flow based on actual operating conditions.

3. Implementation Steps

3.1 Import Field Measurement Signals

The first step is to introduce all required signals into the PLC/DCS system:

  • Differential pressure signal
  • Pressure transmitter signal
  • Temperature transmitter signal

The analog signals are converted into engineering values through the PLC/DCS input modules.

Example:

  • 4–20 mA pressure signal → MPa
  • 4–20 mA temperature signal → ℃
  • Flow signal → Nm³/h or kg/h

4. Check the Square Root Calculation Function

For DP flow measurement, the relationship between differential pressure and flow rate is:

 

Q∝ΔPQ \propto \sqrt{\Delta P}

 

Therefore, square root calculation is required.

There are two different configurations:

Case 1: Differential Pressure Transmitter with Square Root Output

Some DP transmitters have a built-in square root function.

For example, in an EJA differential pressure transmitter:

Select:

 
Output Mode:
LINE → Linear Output

SQUARE ROOT → Flow Output
 

When the transmitter outputs a linear flow signal, the PLC/DCS receives the calculated flow value directly.

The compensation formula becomes:

 
OUT_Q :=
IN_Q × SQRT
(((Actual_P + 0.101325)
× (Design_T + 273.15))
/
((Design_P + 0.101325)
× (Actual_T + 273.15)))

Formula Explanation

OUT_Q

Temperature and pressure compensated flow value.

(Unit: Nm³/h)

IN_Q

Measured flow value from the transmitter.

(Unit: Nm³/h)

Actual_P

Actual operating pressure measured by the pressure transmitter.

(Unit: MPa)

Design_P

Design pressure from the orifice calculation sheet.

(Unit: MPa)

Actual_T

Actual operating temperature measured by the temperature transmitter.

(Unit: ℃)

Design_T

Design temperature from the orifice calculation sheet.

(Unit: ℃)

0.101325

Atmospheric pressure correction value.

(Unit: MPa)

Please note:

Atmospheric pressure is not always 0.101325 MPa. It changes depending on altitude.

For high-altitude applications, the local atmospheric pressure should be used.

273.15

Temperature conversion factor:

 

K=℃+273.15K=℃+273.15

All thermodynamic calculations must use absolute temperature (Kelvin).

5. Case 2: DP Transmitter Without Square Root Output

If the transmitter does not perform square root calculation, the PLC/DCS receives the differential pressure value directly.

In this case:

First calculate:

 

Q=ΔPQ=\sqrt{\Delta P}

 

Then apply temperature and pressure compensation.

PLC/DCS formula:

 
OUT_Q :=
SQRT(IN_P)
× SQRT
(((Actual_P + 0.101325)
× (Design_T + 273.15))
/
((Design_P + 0.101325)
× (Actual_T + 273.15)))
 

Where:

IN_P

Measured differential pressure value.

(Unit: MPa)

Actual_P

Actual operating pressure.

Actual_T

Actual operating temperature.

Design_P / Design_T

Reference conditions from the orifice calculation sheet.

6. Absolute Pressure and Absolute Temperature Conversion

Temperature and pressure compensation must use absolute values.

Pressure Conversion

The relationship is:

 

Absolute Pressure=Gauge Pressure+Atmospheric PressureAbsolute\ Pressure = Gauge\ Pressure + Atmospheric\ Pressure

 

Example:

Gauge pressure:

0.5 MPa

Atmospheric pressure:

0.101325 MPa

Absolute pressure:

0.601325 MPa

Temperature Conversion

The relationship is:

 

T(K)=T(℃)+273.15T(K)=T(℃)+273.15

 

Example:

Operating temperature:

200℃

Absolute temperature:

473.15 K

The value 273.15 is a fixed physical conversion constant and does not change with location.

7. Steam Flow Compensation Considerations

For steam measurement, temperature and pressure compensation is especially important.

Applications include:

  • Boiler steam
  • Superheated steam
  • Saturated steam
  • Process steam

For saturated steam:

Pressure is the main compensation parameter because steam temperature is related to pressure.

For superheated steam:

Both pressure and temperature must be measured and compensated.

Common equipment configuration:

  • Orifice plate
  • Differential pressure transmitter
  • Pressure transmitter
  • Temperature transmitter
  • Flow computer / PLC / DCS

8. Common Field Errors During Compensation

1. Double Square Root Calculation

A common mistake:

  • DP transmitter already outputs flow signal
  • PLC performs square root again

Result:

Incorrect low flow indication.

2. Incorrect Pressure Unit

Example:

Using gauge pressure directly instead of absolute pressure.

Wrong:

 
P = 0.5 MPa
 

Correct:

 
P = 0.5 + 0.101325 MPa
 

3. Using Celsius Instead of Kelvin

Wrong:

 
Temperature = 200
 

Correct:

 
Temperature = 200 + 273.15

Conclusion

Temperature and pressure compensation is essential for accurate measurement of gases and steam using orifice flow meters and other differential pressure flow meters.

A reliable compensation system requires:

  • Correct differential pressure measurement
  • Accurate pressure and temperature signals
  • Proper square root calculation
  • Correct conversion to absolute pressure and Kelvin temperature
  • Proper PLC/DCS programming

By implementing correct compensation logic, industrial users can significantly improve flow measurement accuracy and ensure reliable process control.

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