Digestion units for processing cellulosic biomass can comprise a chamber having a height that is greater than its width, the chamber having an opening suitable for solids introduction located within the upper 20% of its height; one or more first fluid conduits connected to the chamber within the lower 20% of its height, at least one of the first fluid conduits extending into the chamber and being elevated above the bottom of the chamber; one or more second fluid conduits connected to the chamber within the upper 20% of its height, at least one of the first fluid conduits being fluidly coupled to at least one of the second fluid conduits; a porous medium located in the chamber within the lower 20% of its height; and a movable pressure isolation device covering the opening; wherein the digestion unit is operable to maintain a pressure of at least about 30 bar.