Per the suggestion of @Frazbro
At 0 psi there are 0.85 volumes (1.68g/l) of CO2 in the beer at room temp and 1.47 volumes (2.91g/l) at cold crash temperature.
So the difference is 1.23g/l. For 23l 28.29g CO2 are required, which will translate to 15.56 liters CO2 at room temperature.
This number seems more reasonable.