What is the length of anaerobic biodigestion stages?
To give timescales for the different processes is very difficult because the speed (in g/d product yield) depends greatly on the number of bacteria, so first you'd have to modl the bacteria growth. I assume you don't want to go that road.

Also note that not all of the substrate is in the same state of fermentation at the same time, more so if you have bigger lumps. Like whole carrots.

One industrial batch-style fermneter I know of uses total retention times of 3-4 weeks, and they mix half the digestate into the fermenter again to provide for inocculum.