the Fudge Factor approach
Without industrial apparatus, unfeasible for costs, size and complexity of use, pressure is still the most practical method for measuring the quantity of gases.
We all know that the Ideal Gas calculations to prepare helium-based mixtures - especially high fractions of helium - lead to considerable deviations.
This issue has become even more critical by the trends in recent years:
• the switchover from Heliair in favor of best mix
• high fractions of Helium
• reuse of residual gas
This issue has not been fully resolved, and so many technical diving teaching agencies include instructions in their blending manuals on how to adopt empirical corrections known as "Fudge Factor" to make up for these errors; some programmers have even included these empirical adjustment approaches in their software.
Some technical diving teaching agencies even suggest proceeding with "trials & errors".
Of course, professional blenders of the sector have developed their own personal experience to get excellent results. Some of them have successfully mixed hundreds of thousands of cubic meters of trimix (or, if you prefer, some million cubic feet); it should be stressed, however, that this is due to their experience and not by relying on advanced applications.
To confirm this, what came out after having spoken to some of them, was that the ability to produce accurate high helium-based mixtures is restricted to certain tested conditions and not reproducible in different conditions.
In other words, if you change the scenario, for example the gas sequence or the mix composition, the “fudge factor” that works in one case does not work in others.
I am not against "Fudge Factors" in itself, I respect everything that works, “what works, works”, regardless of the reason. Of course I would like to understand why it works.
However, I believe that using empirical corrections is the explicit admission of failure in managing the matter with a scientific approach.
When the equations are refined in the laboratory by finding the factors of interaction and compressibility that are used to align the mathematical model to the experimental data, the steps of the properties (pressure, temperature and molar composition) must be as small as possible, so as to coincide the calculations as close as possible to the actual results, limiting the interpolations as much as possible.
This gives us a measure of how a single empirical adjustment does not give any guarantee of work beyond the condition in which it was tested, and the more we move away from these, the greater the uncertainty.