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, and preferably at least a fraction of the first amount of the first organic compound, from the volume section V 1 to a volume section V 2, wherein the volume section V 2 is at least partially filled with the first organic compound, and wherein i. a level of the first organic compound in the volume section V 1 is at a height H 1 from a floor, and ii. a level of the first organic compound in the volume section V 2 is at a height H 2 from the floor; d. reducing an intrinsic viscosity of the first polyester in the volume section V 2, wherein, after the reductions step has been completed, the first polyester has an intrinsic viscosity in the range of 0.10 dL/g to 0.45 dL/g; e. transporting the first polyester to a volume section V 3; f. contacting the first polyester with a further organic compound in the volume section V 3 to obtain a further initial mixture; g. 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 0.120 dL/g, ii. the further organic compound; wherein H 1 < H 2, and at least a fraction of the first organic compound in the volume section V 2 is transported from the volume section V 2 to the volume section V 1, with the intrinsic viscosity, H 1, and H 2 determined according to the methods 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, and preferably at least a fraction of the first amount of the first organic compound, from the volume section V 1 to a volume section V 2, wherein the volume section V 2 is at least partially filled with the first organic compound, and wherein i. a level of the first organic compound in the volume section V 1 is at a height H 1 from a floor, and ii. a level of the first organic compound in the volume section V 2 is at a height H 2 from the floor; i. a level of the first organic compound in the volume section V 1 is at a height H 1 from a floor, and ii. a level of the first organic compound in the volume section V 2 is at a height H 2 from the floor; d. reducing an intrinsic viscosity of the first polyester in the volume section V 2, wherein, after the reductions step has been completed, the first polyester has an intrinsic viscosity in the range of 0.10 dL/g to 0.45 dL/g; e. transporting the first polyester to a volume section V 3; f. contacting the first polyester with a further organic compound in the volume section V 3 to obtain a further initial mixture; g. 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 0.120 dL/g, ii. the further organic compound; i. a first intermediate product that has an intrinsic viscosity in the range of 0.010 dL/g to 0.120 dL/g, ii. the further organic compound; H 1 < H 2, and at least a fraction of the first organic compound in the volume section V 2 is transported from the volume section V 2 to the volume section V 1, with the intrinsic viscosity, H 1, and H 2 determined according to the methods described herein.