Gas Transport Time Calculator
How long gas takes to travel a sample line, and the delay it adds to a reading
The reference state that the standard flow unit is defined against. Mass flow controllers are not consistent here: 0 °C is common in Europe, 20 °C and 25 °C both appear on US instruments, and the choice changes the answer by several percent. Check the controller datasheet.
The gas fills the tube and is pushed along it, so the time to traverse the line is the volume of the tube divided by the volumetric flow through it.
t = V / Q v = Q / A
D is the inner diameter and L the length, so V is the internal volume of the tube. Q is the volumetric flow at the conditions inside the line, which is the part that needs care.
Standard flow is not the flow in the tube
sccm and slm are mass flow expressed as the volume that amount of gas would occupy at a stated reference state. The gas in the sample line sits at line pressure and line temperature, and it occupies a different volume there. At ambient pressure and 20 °C against a 0 °C reference the difference is about 7 %, which is small. At elevated pressure it is not: a line at 3 bar absolute holds three times as much gas per metre, so the same standard flow takes roughly three times as long to traverse it. Reading a standard flow figure as though it were the flow inside the tube is the most common way this calculation goes wrong.
First arrival comes well before the mean
The time above is the mean residence time, which is when the average parcel of gas arrives. In laminar flow, which covers most sample lines at these diameters and flows, the velocity profile is parabolic and the gas on the centre line moves at twice the mean velocity. The leading edge of a step change therefore reaches the analyzer at around half the calculated time, and the reading then approaches its final value over a period comparable to the mean time. If you are specifying a response time, the mean is the right figure for a settled reading and the earlier arrival is what you will see first on the trace.
What this does not account for
Pressure drop along the line is ignored, so the gas is treated as having the same density everywhere. Adsorption and desorption on the tube wall delay reactive and polar species well beyond the transport time, which is why heated and passivated lines are used for those. Dead volume in fittings, filters and the analyzer cell adds to the total, and the figure here covers the tube alone.
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