NOVELTY - Processing biomass feedstock involves either method (M1): saccharifying a biomass feedstock in a vessel by mixing the biomass feedstock with a fluid medium and a saccharifying agent using a jet mixer; or method (M2): saccharifying a biomass feedstock by operation of a mixer that produces generally toroidal flow within a vessel in which the biomass feedstock has been placed with a fluid medium and a saccharifying agent.    USE - For processing biomass feedstock including a cellulosic or lignocellulosic material, and paper to produce useful products (claimed) such as fuels preferably ethanol.    ADVANTAGE - The jet mixing techniques including jet aeration and jet flow agitation provides good wetting, dispersion and mechanical disruption. By increasing the solids level of the mixture, the process can proceed more rapidly, more efficiently and more cost-effectively, and the resulting concentration of the final product can be increased.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) a feedstock saccharification apparatus comprising a tank, a biomass feedstock delivery device configured to deliver a biomass feedstock to the tank, and a saccharifying agent delivery device configured to deliver a metered amount of a saccharifying agent to the tank, and a jet mixer having a nozzle disposed within the tank and configured to mix the delivered biomass feedstock and saccharifying agent;    (2) a fermentation system comprising a vessel having a vent, a source of oxygen in communication with the vessel, an oxygen monitor configured to monitor the oxygen content of a liquid in the vessel, and a controller configured to adjust the oxygen content of the liquid, using the vent and oxygen source, in response to input from the oxygen monitor;    (3) producing (M3) product involving converting a low molecular weight sugar to a product by mixing the low molecular weight sugar with a microorganism in a fluid medium, using a jet mixer; and    (4) converting (M4) biomass feedstock to product involving saccharifying a biomass feedstock in a vessel to form a saccharified mixture, inoculating the saccharified mixture in the vessel with a microorganism, and allowing the inoculated saccharified mixture to ferment in the vessel.