Zero-offset drift of an integrated flow measurement

Zero-offset drift of an integrated flow measurement is a false accumulated volume caused by an additive error in the measured volumetric flow rate. If $\hat{Q}(t)=Q(t)+b(t)$, thenA constant bias gives error $bT$; a linearly changing bias $b(t)=b_0+kt$ gives $b_{0}T+\frac{1}{2}k{T}^2$. A small flow offset can therefore produce a conspicuous trend after integration.

For a constructed offset 0.004 L/s, the error after 60 s is 0.24 L. If the true flow alternates symmetrically between forward and reverse directions, its net integral can be zero while that false trend remains. The drift is an error in the integrated signal, not evidence that the apparatus necessarily accumulated that amount of gas.

A pneumotachograph signal chain can be modeled as $e=e_0+KQ$. An error in the estimated zero $e_0$ becomes an additive flow error, while an error in $K$ changes the scale. The manufacturer's primary manual treats no-flow zeroing and known-volume calibration separately, explicitly connecting zero-flow error with steady integrated-volume drift.^[ref]

A bidirectional bench example separates those effects. Let the inferred integral be $J=aV+bT$, where $a$ is a gain factor. Equal-time strokes transporting true volumes $+V_s$ and $-V_s$ givesoWith $V_s=1$ L, $T=2$ s, $J_{+}=1.05$ L and $J_{-}=-0.95$ L, the inferred gain is 1 and the offset is 0.025 L/s. This is a constructed linear calibration model, not a measured specification of a particular instrument.

Instrumental drift, gain error, leakage and a real net flow can create different records. Subtracting an arbitrary fitted trend may hide genuine accumulation as well as measurement bias. A physical no-flow reference and a known displaced volume test the relevant assumptions more directly than forcing every integrated trace to return to its initial value.