Wet-Leg Density Compensation Calculator (Boiler Drum)

This industrial-grade calculator accurately determines level measurement errors in Boiler Drums and pressurized vessels where significant density differences exist between the process liquid (Hot) and the wet leg reference (Cold). It uses built-in Steam Tables to calculate saturation densities and corrects for the vapor phase density effect at high pressures.

1. Calibration Data (Design Conditions)

Transmitter Config
Reference Leg

2. Operating Conditions (Actual)

Process State
Reading

Engineering Insights: Boiler Drum Level Measurement

1. The Necessity of the Wet Leg

Boiler drums contain saturated steam and boiling water. We measure level by measuring the hydrostatic head (weight) of the water column. However, we need a reference pressure from the top of the drum to cancel out the huge static steam pressure (e.g., 60 bar).

If we simply ran a tube from the top tap to the transmitter, steam would enter it, cool down, and condense. This would form erratic slugs of water, causing the level reading to jump wildly. To prevent this, we intentionally fill the reference leg with water (condensate) up to a "Condensate Pot" at the top tap level. This creates a constant, known head of water called a Wet Leg.

2. The Density Discrepancy

This is the root cause of all errors.

  • Inside the Drum: The water is at saturation temperature (e.g., 275°C at 60 bar). At this temp, water expands significantly. Its density drops to ~750 kg/m³.
  • Inside the Wet Leg: The water is outside the boiler insulation. It cools down to ambient temperature (e.g., 35°C). Its density is ~994 kg/m³.
The transmitter measures Differential Pressure ($DP = P_{high} - P_{low}$). The wet leg ($P_{low}$) is much heavier than the process leg ($P_{high}$). This creates a Negative DP.

Transmitters are calibrated assuming a specific density (usually the normal operating pressure). If the boiler pressure changes (e.g., during startup), the density inside the drum changes dramatically, but the wet leg density stays mostly constant. This density mismatch causes the indicated level to be wrong.

3. The Weight of Steam

At low pressures, steam (vapor) has negligible weight. But at 100 bar, saturated steam has a density of ~55 kg/m³ (5% of water!). This is no longer negligible.

The vapor pushing down on the water surface adds to the High Side pressure, but the vapor column in the drum above the liquid level subtracts from the differential (buoyancy effect). The rigorous formula for level calculation accounts for this:

$$ H_{level} = \frac{DP + (\rho_{ref} \cdot H)}{(\rho_{water} - \rho_{steam})} $$

Ignoring $\rho_{steam}$ at high pressures causes the level to read lower than actual, which is dangerous (risk of carryover).

4. Startup Dynamics (Shrink & Swell)

When a boiler starts up cold (0 bar), the water density in the drum is 1000 kg/m³. The wet leg is also 1000 kg/m³. The level indication is accurate.

As pressure builds to 60 bar, the drum water expands (density drops to 750 kg/m³), but the wet leg stays cold (994 kg/m³). The level Swells physically, but the DP transmitter sees less pressure difference per inch of level. Without compensation, the transmitter would read Lower than actual. Modern DCS systems use "Drum Level Pressure Compensation" blocks to dynamically adjust the SG based on real-time drum pressure measurements.

5. Zero Elevation Calculation

Because the wet leg is always full and colder (heavier) than the drum water, the Low Side pressure is always higher than the High Side pressure (at zero level). This results in a negative DP.

0% Level (Empty Drum): $DP = P_{process\_0} - P_{wet\_leg}$. Since $P_{process\_0} \approx 0$ head, $DP = - \rho_{ref} \cdot H$. This huge negative value (e.g., -1000 mmH2O) is the LRV (Lower Range Value). This is called Zero Elevation.