A method for pulping a comminuted cellulosic fibrous organic feed material in a feed system (22, 10), a prehydrolysis reactor vessel and a Kraft cooking vessel, the method comprising the steps of: (a) steaming and adding wash filtrate to the feed material as the feed material flows continuously through the material feed system (22, 10); (b) pressurizing the feed material flowing from the material feed system (22, 10) in a high pressure transfer device; (c) moving the pressurized feed material into the prehydrolysis reactor vessel; (d) subjecting the feed material to a hydrolysis reaction in a hydrolysis zone in the prehydrolysis reactor vessel, wherein an acidic pH level is maintained throughout the hydrolysis zone, and wherein the feed material and liquor flow concurrently downward through the hydrolysis zone; (e) extracting hydrolysate formed in the hydrolysis zone and the wash filtrate through a screen located at a first elevation of the prehydrolysis reactor vessel proximate to a lower region of the hydrolysis zone in the prehydrolysis reactor vessel; (f) reintroducing a portion of the extracted hydrolysate to the prehydrolysis reactor vessel at a second elevation which is above the first elevation so as to lower the pH of the feed material in upstream portions of the prehydrolysis reactor vessel and promote a uniformly mild acidic pH level throughout the hydrolysis zone; (g) adding a wash liquid to a wash zone in the prehydrolysis reactor vessel, wherein the wash zone is below the hydrolysis zone in the prehydrolysis reactor vessel; (h) moving the feed material continually downward through the hydrolysis zone and the wash zone of the prehydrolysis reactor vessel; and moving the wash liquid continually upward through the wash zone to the screen; (i) discharging the feed material from the prehydrolysis reactor vessel; (k) moving the discharged feed material into the Kraft cooking vessel; (l) adjusting the pH of the discharged feed material to alkaline while the feed material is in the Kraft cooking vessel, and (m) cooking the feed material in the Kraft cooking vessel to produce pulp. (a) steaming and adding wash filtrate to the feed material as the feed material flows continuously through the material feed system (22, 10); (b) pressurizing the feed material flowing from the material feed system (22, 10) in a high pressure transfer device; (c) moving the pressurized feed material into the prehydrolysis reactor vessel; (d) subjecting the feed material to a hydrolysis reaction in a hydrolysis zone in the prehydrolysis reactor vessel, wherein an acidic pH level is maintained throughout the hydrolysis zone, and wherein the feed material and liquor flow concurrently downward through the hydrolysis zone; (e) extracting hydrolysate formed in the hydrolysis zone and the wash filtrate through a screen located at a first elevation of the prehydrolysis reactor vessel proximate to a lower region of the hydrolysis zone in the prehydrolysis reactor vessel; (f) reintroducing a portion of the extracted hydrolysate to the prehydrolysis reactor vessel at a second elevation which is above the first elevation so as to lower the pH of the feed material in upstream portions of the prehydrolysis reactor vessel and promote a uniformly mild acidic pH level throughout the hydrolysis zone; (g) adding a wash liquid to a wash zone in the prehydrolysis reactor vessel, wherein the wash zone is below the hydrolysis zone in the prehydrolysis reactor vessel; (h) moving the feed material continually downward through the hydrolysis zone and the wash zone of the prehydrolysis reactor vessel; and moving the wash liquid continually upward through the wash zone to the screen; (i) discharging the feed material from the prehydrolysis reactor vessel; (k) moving the discharged feed material into the Kraft cooking vessel; (l) adjusting the pH of the discharged feed material to alkaline while the feed material is in the Kraft cooking vessel, and (m) cooking the feed material in the Kraft cooking vessel to produce pulp.