Data-driven models for the operation of a dynamic primary standard based on permeation

¹ VSL, Data Science & Modelling Department, Thijsseweg 11, 2629 JA Delft, The Netherlands
² VSL, Chemistry Department, Thijsseweg 11, 2629 JA Delft, The Netherlands

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 17 February 2026

Abstract

For the preparation of calibration gas mixtures with low levels of reactive compounds, the permeation method as described in ISO 6145-10 is excellently suited. In the past years, it has proved to be useful for developing primary standards for key impurities in hydrogen, such as ammonia, hydrogen fluoride and hydrogen chloride. Using an automated balance to measure the mass loss of the permeation tube, large volumes of data are gathered, from which the permeation mass flow rate is calculated. The residuals of traditional simple straight-line regression show patterns which deserve further attention. They suggest that the current approach may underrate the uncertainty associated with the permeation rate. The permeation system is operated with a dilution system using thermal mass flow controllers. These produce large volumes of data as well, which are processed to obtain a mass flow rate and associated uncertainty. It is shown how time series models enable assessing correlations in the data from the magnetic suspension balance and the thermal mass flow controllers. These data-driven models provide a better description of the features of the data and thereby provide more realistic estimates of the mass flow rates and associated uncertainties. The time series analysis reveals that the permeation data are quite heavily autocorrelated, whereas the data from the thermal mass flow controllers are uncorrelated.