A method for producing a first intermediate product, comprising the steps of a. providing a feedstock that comprises a first polyester; b. contacting the feedstock with a first amount of a first organic compound in a volume section V 1 to obtain a first initial mixture, wherein the first amount is in the form of a liquid and wherein the intrinsic viscosity of the first polyester in the volume section V 1 varies by less than 15 %; c. transporting the first polyester to a volume section V 2 from the volume section V 1; d. contacting the first polyester with a further amount of the first organic compound in the volume section V 2; e. reducing an intrinsic viscosity of the first polyester in the volume section V 2, wherein after the reduction step has been completed in the volume section V 2, the first polyester has an intrinsic viscosity in the range of 0.10 dL/g to 0.45 dL/g; f. transporting the first polyester to a volume section V 3; g. contacting the first polyester with a further organic compound in the volume section V 3 to obtain a further initial mixture; h. reducing a weight average molar mass of the first polyester in the volume section V 3 to obtain a first intermediate mixture, wherein the first intermediate mixture comprises i. a first intermediate product that has an intrinsic viscosity in the range of 0.010 dL/g to 0.090 dL/g, ii. the further organic compound; wherein the first polyester is transported I./ in a first direction that is at least partially opposite the direction of gravity when the first polyester has an intrinsic viscosity that is larger than or equal to Y IV,1, where Y IV,1 is 0.10 dL/g; II./ in further direction that is at least partially along the direction of gravity when the first polyester has an intrinsic viscosity that is less than or equal to Y IV,2, where Y IV,2 is 0.09 dL/g; and III./ the transport of the first polyester along the first direction comprises transport from the volume section V 1 to the volume section V 2 and transport through the volume section V 2, with the intrinsic viscosity determined according to the method described herein. a. providing a feedstock that comprises a first polyester; b. contacting the feedstock with a first amount of a first organic compound in a volume section V 1 to obtain a first initial mixture, wherein the first amount is in the form of a liquid and wherein the intrinsic viscosity of the first polyester in the volume section V 1 varies by less than 15 %; c. transporting the first polyester to a volume section V 2 from the volume section V 1; d. contacting the first polyester with a further amount of the first organic compound in the volume section V 2; e. reducing an intrinsic viscosity of the first polyester in the volume section V 2, wherein after the reduction step has been completed in the volume section V 2, the first polyester has an intrinsic viscosity in the range of 0.10 dL/g to 0.45 dL/g; f. transporting the first polyester to a volume section V 3; g. contacting the first polyester with a further organic compound in the volume section V 3 to obtain a further initial mixture; h. reducing a weight average molar mass of the first polyester in the volume section V 3 to obtain a first intermediate mixture, wherein the first intermediate mixture comprises i. a first intermediate product that has an intrinsic viscosity in the range of 0.010 dL/g to 0.090 dL/g, ii. the further organic compound; I./ in a first direction that is at least partially opposite the direction of gravity when the first polyester has an intrinsic viscosity that is larger than or equal to Y IV,1, where Y IV,1 is 0.10 dL/g; II./ in further direction that is at least partially along the direction of gravity when the first polyester has an intrinsic viscosity that is less than or equal to Y IV,2, where Y IV,2 is 0.09 dL/g; and III./ the transport of the first polyester along the first direction comprises transport from the volume section V 1 to the volume section V 2 and transport through the volume section V 2,