Gas Leak Rate Calculation Formula

Gas Leak Rate Calculator (Pressure Decay)

Liters

Min

Bar

Bar

Test Results

Pressure Drop (ΔP): –

Leak Rate (SCCM)

0

Standard Cubic Cm/Min

Leak Rate (mbar·L/s)

0

Millibar Liters/Sec

Calculating the gas leak rate is a critical procedure in industrial quality control, pipeline maintenance, and safety engineering. The most common non-destructive method for determining a leak rate is the Pressure Decay Method. This calculator assists engineers and technicians in quantifying leaks by monitoring pressure changes within a closed volume over a specific duration.

The Physics: Ideal Gas Law Application

The calculation relies on the Ideal Gas Law ($PV = nRT$). Assuming the temperature remains constant during the test (isothermal conditions), the leak rate ($Q$) can be derived from the change in pressure ($\Delta P$) over time ($t$).

The Formula

The standard formula used for the Pressure Decay method is:

Q = (V × ΔP) / t

Where:

• Q = Leak Rate (flow of gas volume per unit time)
• V = Internal Volume of the system being tested (Liters or cm³)
• ΔP = Pressure Drop ($P_{initial} – P_{final}$)
• t = Time duration of the measurement

Understanding the Units

Leak rates are often expressed in various units depending on the industry and location:

• SCCM (Standard Cubic Centimeters per Minute): Highly common in US industrial applications. It represents the flow rate normalized to standard temperature and pressure conditions (STP).
• mbar·L/s (Millibar Liters per Second): The standard unit in Europe and vacuum technology. It represents the quantity of gas (pressure × volume) flowing per second.

How to Perform a Pressure Decay Test

1. Pressurization: The component is sealed and pressurized to the target test pressure (P1).
2. Stabilization: A short period is allowed for the gas to settle thermally and mechanically.
3. Measurement: The pressure is monitored for a set time ($t$).
4. Final Reading: The final pressure (P2) is recorded.
5. Calculation: Use the formula above (or this calculator) to determine if the leak rate falls within acceptable tolerance limits.

Example Calculation

Suppose you are testing a vessel with a volume of 10 Liters. You pressurize it to 5.0 Bar. After 5 minutes, the pressure drops to 4.98 Bar.

• Volume (V) = 10 L
• Pressure Drop (ΔP) = 5.0 – 4.98 = 0.02 Bar (20 mbar)
• Time (t) = 5 minutes (300 seconds)

Result:

• Leak Rate = (10 L × 20 mbar) / 300 s = 0.66 mbar·L/s
• Converted to SCCM ≈ 39.5 sccm

function calculateLeakRate() { // Clear previous errors and results document.getElementById('errorArea').style.display = 'none'; document.getElementById('resultsArea').style.display = 'none'; // Get Input Values var vol = parseFloat(document.getElementById('sysVolume').value); var time = parseFloat(document.getElementById('testDuration').value); var pStart = parseFloat(document.getElementById('startPressure').value); var pEnd = parseFloat(document.getElementById('endPressure').value); // Validation Logic if (isNaN(vol) || isNaN(time) || isNaN(pStart) || isNaN(pEnd)) { showError("Please fill in all fields with valid numbers."); return; } if (vol <= 0) { showError("System volume must be greater than zero."); return; } if (time pStart) { showError("Final pressure cannot be higher than initial pressure (Check for thermal expansion or sensor error)."); return; } // Calculation Logic // 1. Calculate Pressure Drop (Delta P) in Bar var deltaP_Bar = pStart – pEnd; // 2. Convert Delta P to mbar for standard calculation var deltaP_mbar = deltaP_Bar * 1000; // 3. Calculate Leak Rate in mbar·L/min // Q = (V_liters * DeltaP_mbar) / Time_minutes var leakRate_mbarL_min = (vol * deltaP_mbar) / time; // 4. Convert to mbar·L/s (European Standard) var leakRate_mbarL_sec = leakRate_mbarL_min / 60; // 5. Convert to SCCM (Standard Cubic Centimeters per Minute) // 1 mbar·L/s is approximately equal to 59.2 SCCM (at standard conditions 1013.25 mbar, 20C) // Precise derivation: 1 sccm = 1 atm*cc/min (roughly). // 1 mbar*L/s = 100 Pa * 0.001 m^3 / s = 0.1 Pa*m^3/s. // SCCM standard: P_std = 1013.25 mbar. // Q_sccm = Q_mbarL_min * (1000 / 1013.25) * 1 (approx correction for standard atmosphere) // Standard industry conversion factor: 1 mbar l/s = 59.21 sccm var leakRate_sccm = leakRate_mbarL_sec * 59.21; // Display Results document.getElementById('resultsArea').style.display = 'block'; // Format numbers nicely document.getElementById('resDeltaP').innerHTML = deltaP_Bar.toFixed(4) + " Bar"; document.getElementById('resSCCM').innerHTML = leakRate_sccm.toFixed(2); document.getElementById('resMbarLs').innerHTML = leakRate_mbarL_sec.toFixed(4); // Contextual Status Message var statusElem = document.getElementById('leakStatus'); if (leakRate_sccm === 0) { statusElem.innerHTML = "Perfect seal detected (or measurement duration too short for sensor resolution)."; statusElem.style.color = "#27ae60"; } else if (leakRate_sccm < 10) { statusElem.innerHTML = "Small leak detected. Acceptable for many general industrial applications."; statusElem.style.color = "#f39c12"; } else { statusElem.innerHTML = "Significant leak detected. Maintenance likely required."; statusElem.style.color = "#c0392b"; } } function showError(msg) { var errDiv = document.getElementById('errorArea'); errDiv.style.display = 'block'; errDiv.innerHTML = msg; }