A method comprises introducing biomass solids to a digester comprising a reactor, a circulation system including a first injector; providing a catalyst-containing digestion medium and an organic solvent layer floating thereon; circulating the medium through the circulation system; flowing gas through the medium; keeping the medium hot enough to digest the solids; and operating the digester such a headspace exists above the solvent. The digester includes a first eductor having an inlet in the headspace, a second eductor having an inlet in the organic layer, and a downdraft tube having an inlet in the digestion medium. A motive fluid flowing from the first injector draws gas from the headspace into the first eductor, a motive fluid flowing from the first eductor draws fluid from the organic layer into the second eductor, and a motive fluid flowing from the second eductor draws fluid from the digestion medium into the downdraft tube.