A method for producing a first intermediate product, comprising the steps of a. providing a feedstock that comprises a first polyester; b. contacting the first polyester with a further amount of a first organic compound in a volume section V 2; c. 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; d. transporting the first polyester to a volume section V 3; e. contacting the first polyester with a further organic compound in a volume section V 3 to obtain a further initial mixture; f. 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 a first fraction of the further amount of the first organic compound contacted with the first polyester is in the form of a gas and a further fraction of the further amount of the first organic compound contacted with the first polyester is in the form of a liquid, wherein the first fraction makes up in the range of 50 wt-% to 90 wt-% of the further amount of the first organic compound, with the wt-% is based on the total weight of the further amount of the first organic compound, the first polyester enters the volume section V 2 via at least one inlet of a first kind, and the first fraction enters the volume section V 2 via at least one inlet of a further kind, wherein the at least one inlet of the further kind is adapted and arranged such that a flow direction of the first fraction, which enters through the at least one inlet of the further kind, through the volume section V 2 is at least partially along a transport direction of the first polyester through the volume section V 2, the further fraction of the further amount of the first organic compound enters the volume section V 2 via at least one inlet of an even-further kind, wherein the at least one inlet of the even-further kind is adapted and arranged such that a flow direction of the further amount of first organic compound, which enters through the at least one inlet of the even-further kind, through the volume section V 2 is at least partially opposite the transport direction of the first polyester through the volume section V 2, and the volume section V 2 comprises a first zone and a further zone, wherein a temperature in the first zone is in the range of 50 °C to 190 °C, with the intrinsic viscosity and the temperature determined according to the methods described herein. a. providing a feedstock that comprises a first polyester; b. contacting the first polyester with a further amount of a first organic compound in a volume section V 2; c. 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; d. transporting the first polyester to a volume section V 3; e. contacting the first polyester with a further organic compound in a volume section V 3 to obtain a further initial mixture; f. 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; a first fraction of the further amount of the first organic compound contacted with the first polyester is in the form of a gas and a further fraction of the further amount of the first organic compound contacted with the first polyester is in the form of a liquid, wherein the first fraction makes up in the range of 50 wt-% to 90 wt-% of the further amount of the first organic compound, with the wt-% is based on the total weight of the further amount of the first organic compound, the first polyester enters the volume section V 2 via at least one inlet of a first kind, and the first fraction enters the volume section V 2 via at least one inlet of a further kind, wherein the at least one inlet of the further kind is adapted and arranged such that a flow direction of the first fraction, which enters through the at least one inlet of the further kind, through the volume section V 2 is at least partially along a transport direction of the first polyester through the volume section V 2, the further fraction of the further amount of the first organic compound enters the volume section V 2 via at least one inlet of an even-further kind, wherein the at least one inlet of the even-further kind is adapted and arranged such that a flow direction of the further amount of first organic compound, which enters through the at least one inlet of the even-further kind, through the volume section V 2 is at least partially opposite the transport direction of the first polyester through the volume section V 2, and the volume section V 2 comprises a first zone and a further zone, wherein a temperature in the first zone is in the range of 50 °C to 190 °C, with the intrinsic viscosity and the temperature determined according to the methods described herein.