## 1 Introduction  
The critical point marks a borderline above which the physical properties of a fluid suffer severe changes. Supercritical fluids have a density similar to the density of liquids, but their high diffusivity, and low viscosity and surface tension are characteristics of gases. Furthermore, they efficiently dissolve gases and organic compounds thanks to their low dielectric constant. CO\({}_{2}\) is the most used supercritical fluid because of its mild critical constants, P\({}_{\rm c}\) = 73 bar and T\({}_{\rm c}\) = 31 \({}^{\circ}\)C. Thanks to the previously described properties, supercritical CO\({}_{2}\) (SCCO\({}_{2}\)) is used to extract organic compounds retained in liquids or on solid matrixes [1]. The regeneration of activated carbons (ACs) is one of the applications in which SCCO\({}_{2}\) is used as extracting fluid. ACs have excellent adsorbent properties that turn them into a suitable material to purify polluted gaseous and liquid streams [2]. During this process, the pollutants accumulate on the surface of the ACs and their adsorption capacity is progressively reduced until they are completely exhausted. The economical and environmental viabilities of this purification process strongly depend on the removal of the pollutants retained on the ACs and the recovery of their adsorption capacity, that is to say, on the regeneration of the ACs. Several methods to regenerate ACs exist [3, 4], although the search for efficient, low-cost, and environmentally sustainable procedures continues because just a few methods gather all of these characteristics. As an example, thermal regeneration with inert gases at high temperatures is the most widespread method despite the damages that it causes in the structure of the ACs. Furthermore, temperatures about 700-900 \({}^{\circ}\)C are needed to remove strongly retained pollutants [5; 6]. In this context, SCCO\({}_{2}\) regeneration arises as an interesting alternative. SCCO\({}_{2}\) is able to flow through the porous net of the ACs, reach the micropores where the pollutants are retained, and extract them. The temperatures used in this method so far are lower than 100 \({}^{\circ}\)C; consequently, the energy waste is restricted regarding thermal regeneration, and the porosity of the ACs is better preserved. Furthermore, the extracted adsorbate can be easily recovered to be reused or destroyed once the SCCO\({}_{2}\) is cooled and depressurized to atmospheric pressure. SCCO\({}_{2}\) is usually employed to regenerate ACs saturated with volatile organic compounds like benzene [7], toluene [8; 9; 10; 11], m-xylene [12], cyclohexane [13], or ethyl acetate [14; 15]. The regeneration of ACs saturated with inorganic compounds is less usual and co-solvents must be used to efficiently extract these adsorbates [16]. The employment of SCCO\({}_{2}\) has also been studied to regenerate ACs saturated with low-volatile organic compounds, e.g., phenol [17; 18; 19], pesticides [20], herbicides [21], or insecticides [22]. Phenol is the most common model compound in the field of regeneration of ACs [3]: it is a pollutant frequently found in wastewater and drinking water that remains strongly retained on the carbon surface of ACs. The limited number of works that have studied the SCCO\({}_{2}\) regeneration of ACs exhausted with phenol state that, at regeneration pressures and temperatures below 200 bar and 60 \({}^{\circ}\)C, respectively, phenol is not properly extracted [19] and the ACs are not efficiently regenerated [18]. The exhausted activated carbon fibers (ACFs) can also be regenerated using other supercritical fluids as regeneration agents, namely, supercritical water (SCW).