## 1 Introduction
Moreover, the supercritical state of carbon dioxide is easily obtained (pressure up to 30 MPa and temperature up to 373 K). [PERSON] et al. [25] described two mechanisms involved during the supercritical debinding of organic polymers in a solid state: the solubilization of the polymer molecules, and the diffusion of the solubilized species. Various models have been developed to predict the debinding time and the degradation kinetics of the binders, adapted to available extraction methods [9; 25; 26; 27]. [PERSON] et al. [25] developed a model using the diffusion principle to determine the accurate extraction kinetic of a soluble solid organic binder during supercritical debinding. Their model was in good agreement with the experimental results for paraffin extraction. Unfortunately, their model was not adapted to liquid binders and had to be completed with capillary migration. Moreover, the diffusion coefficient was identified at each debinding time and pressure. There were many variables for parameter identification and the model was evaluated on bar specimens. Modelling condensed-solvent debinding, using the diffusion principle to predict the removal of organic binders contained in components produced by MIM, was also previously studied by [PERSON] et al. [28]. They considered that the soluble binder dissolved into the solvent and then diffused to the compact surface, where it was removed. Their model was based on [PERSON]'s diffusion law. They considered that the main step of the debinding process is the interdiffusion of the solvent and binder within the compact. Using linear regression on the experimental results and considering diffusion along one direction, the coefficient was identified as the temperature function. Their method made it possible to easily identify the main parameter of the diffusion model: the diffusion or interdiffusion coefficient. It was used in our current study to predict the binder extraction with a supercritical fluid. There is a lack of simulations of PEG extraction of a feedstock composed of a super-alloy powder during supercritical debinding, and existing models are insufficient for clearly identifying the main parameters affecting the component shapes. Thus, one of the major objectives and the highlight of this investigation is to identify the diffusion coefficient from the solvent-debinding model investigated by [PERSON] et al. [28] and to use it to predict binder extraction through numerical simulations. This is because the two debinding techniques, solvent and supercritical fluid debinding, use the same extraction mechanism: Diffusion of the solution binder/solvent from the interior to the external surfaces of the component [16; 25]. The method applied [PERSON]'s second law, which expresses a linear relation between the mass flow and the concentration gradient. The effective length scale presented by [PERSON] et al. [29] to consider the component shape is given by the volume to surface area ratio of a component. It was used in this current study to consider all directions during the diffusion in a cylindrical component. The numerical simulation of the debinding step using supercritical CO\({}_{2}\) with the Comsol Multiphysics(r) finite-element software platform was performed to predict the PEG binder distribution and the degradation or removal from the component, and to optimize the component design before the debinding stage. The model's main parameter is the diffusion coefficient, which was identified with experimental data obtained from supercritical CO\({}_{2}\) debinding at three different temperatures. The simulation of the process is used to validate the model that describes the binder extraction. Moreover, various experimental tests of supercritical debinding at different debinding times were carried out on injected components. The numerical and experimental results were compared.