A process for the enzymatic hydrolysis of cellulose to produce a hydrolysis product from a pre-treated cellulosic feedstock is provided. The process comprises introducing an aqueous slurry of the pre-treated cellulosic feedstock at the bottom of a hydrolysis reactor. Axial dispersion in the reactor is limited by avoiding mixing and maintaining an average slurry flow velocity of about 0.1 to about 20 feet per hour, such that the undissolved solids flow upward at a rate slower than that of the liquid. Cellulase enzymes are added to the aqueous slurry before or during the step of introducing. An aqueous stream comprising hydrolysis product and unhydrolyzed solids is removed from the hydrolysis reactor. Also provided are enzyme compositions which comprise cellulase enzymes and flocculents for use in the process. In addition, a kit comprising cellulase enzymes and flocculent is provided.