One needs to determine the density of the wet steam. For wet steam one parameter, either the pressure or the temperature, would suffice to fix the other.
Assuming the steam is used in petroleum production sites,
1 Bbl = 42 gal = 0.159 m3.
Steam tables would give us specific volumes of the steam and of the water (moisture) at the given conditions. The relative masses of steam and water are given by the steam quality.
An example taken from the internet:
Wet steam quality: 95%. Pressure: 10 barg. Specific volumes from tables are:
dry steam, 0.1773 m3/kg; water, 0.0011 m3/kg.
The estimated volumes in m3 per kg of wet steam:
Dry steam: 0.95 [×] 0.1773 = 0.1684; in the same way,
Water: 0.05 [×] 0.0011 = 0.000055
Total volume: 0.1684 + 0.000055 = 0.168455
Since 1 Bbl = 0.159 m3, its mass would be:
0.159 m3 [÷] 0.168455 m3/kg = 0.944 kg.
The time factor remains unchanged.