Temperature and Pressure Compensation in Instruments

3. Methods of Temperature and Pressure Compensation

3.1 General Gas Compensation

Based on the ideal gas law:

$PV = nRT$

This leads to the density compensation formula:

$$\rho_1 = \rho_0 \times \frac{P_1}{P_0} \times \frac{T_0}{T_1}$$

Where:

• $\rho_1$

  = Gas density at working conditions (

  $kg/m^3$

  )

• $\rho_0$

   = Standard gas density (

  $kg/m^3$

  )

• $P_0$

   = Standard atmospheric pressure (0.1013 MPa)

• $P_1$

  = Working pressure (absolute pressure, MPa)

• $T_0$

  = Standard temperature (293K or 20°C)

• $T_1$

  = Working temperature (absolute temperature, K)

Flow Compensation Formula for Differential Pressure Flow Meters:

$$Q = k \times \sqrt{\frac{\Delta P}{\rho}}$$

After compensation:

$$Q_c = Q \times \sqrt{\frac{\rho}{\rho_0}}$$

Where:

• $Q_c$

  = Compensated flow

• $Q$

   = Measured flow

• $\Delta P$

   = Differential pressure

• $k$

   = Instrument coefficient

3.2 Steam Compensation

For steam (both superheated and saturated), compensation is based on tabular data and linear interpolation methods:

• Compensation Principle: Based on the “Water and Steam Property Handbook” for steam properties.

• Compensation Range:

  • Superheated steam: Pressure (0.1–16) MPa (gauge), Temperature (140–560)°C

  • Saturated steam: Pressure (0–16) MPa (gauge)

Linear compensation formulas:

• Temperature compensation:

  $\rho = A \times t + B$

• Pressure compensation:

  $\rho = C \times P + D$

Where

$A$

,

$B$

,

$C$

, and

$D$

 are linear coefficients calculated from actual working conditions at two data points.

3.3 Intelligent Compensation Methods

Modern instruments use multi-point linearization compensation techniques:

• Principle: Internal programming is used to perform multi-point linearization compensation of flow signals.

• Advantages: Ensures measurement accuracy at every point within the flow range, with a range ratio of up to 1:15 (compared to the typical 1:5 for regular vortex flow meters).