It is a new revolutionary experiment to finally measure the rest mass of the electron neutrino (and thus, combined by other data, may also answer other open questions (is it a majorana particle, masses of the other neutrinos)).
The measurement is done by measuring the energy distribution of the highest energetic electrons of the beta decay of tritium.
How much tritium is there in it?
From glancing over several papers, they don't make it quite so easy to find out a precise value of the amount tritium in the system at a given time. Instead, they flow a precise amount, $1.8\ cm^{3}/sec$, or about $40\ g$ of $T_{2}$ per day.
See: Commissioning and detailed results of KATRIN inner loop tritium processing system at Tritium Laboratory Karlsruhe, Florian Priester, Michael Sturm, and Beate Bornschein, Vacuum 116 42-47 (2015).
