Find the residence time needed for 100% conversion of solids.

A solid feed consisting of
20 wt% of 1-mm particles and smaller
30 wt% of 2-mm particles
50 wt% of 4-mm particles
passes through a rotating tubular reactor somewhat like a cement kiln where it reacts with gas to give a hard nonfriable solid product (SCMI reaction control, τ = 4 h for 4-mm particles).