## 1 Introduction
In Cuba, the use of power plants is considered as Distributed Generation (DG) of electricity because it is an alternative method to centralize energy generation [22; 23; 24; 25]. The main purpose of DG is to support the National Electro-energetic System (NES) during peak hours, where the consumption of electrical energy reaches a maximum value, and also to improve its transmission, especially in isolated regions. During combustion in the engines, the energy obtained from fuel produces electricity and translates into useful work; the rest dissipates into heat and exhaust gases. The heat produced during the combustion reaction in the engine has to be dissipated and generally, water is used as a cooling medium [26]. Untreated water contains several compounds such as CaCO\({}_{3}\), Ca(HCO\({}_{3}\))\({}_{2}\), MgSO\({}_{3}\), Mg(HCO\({}_{3}\))\({}_{2}\), sulphates, nitrates and phosphates which can produce corrosion and incrustation and thereby affect the efficiency of the engines [27; 28]. Therefore, power plants have a Water Treatment Unit (WTU) that improves the quality of the water (to guarantee the physical and chemical characteristics of the water feed) used in the cooling system (see Figure S1 in Supplementary information). In the chemical regeneration of AC, certain specific chemical reagents are used to desorb or decompose the adsorbates [21; 29; 30; 31]. Acidic and alkaline reagents, when used,dissolve the adsorbed inorganic substances based on their affinity for the reagents. Treatment with these chemicals may also affect the structure of the AC [21; 30]. Although the efficiency of chemical regeneration depends on the type of contaminant in the spent AC, it also depends on the reactivity of the adsorbates and the AC with the chemical reagents [30]. Chemical regeneration is also applied to AC used in water treatment and is depending on the type of adsorbate. Acid washing is the chemical regeneration option, offering the most potential for remediation of accumulated metal ions and some of its carbonates on AC (being the main inorganic component in this research) [21; 26; 32; 33; 34]. Acid-leached samples attest to the fact that much of the calcium is removed via acid washing and therefore result in a lower Ca and ash content [35; 36]. The rapid small-scale column test (RSSCT) is an alternative to time-consuming and expensive plant studies [37]. RSSCTs use continuous-flow packed beds of adsorbent material that, through dimensionless analysis, can predict full-scale system performance in time [38]. The basic idea is to study the breakthrough behaviour in small columns that are specifically designed in a manner that guarantees that the operational conditions in the small-scale column reflect exactly the situation in the large-scale fixed-bed adsorber [37]. A major aspect of the RSSCT concept is then to transfer results produced with filters containing small-sized GAC to filters with larger sized GAC, for performance prediction [39]. One of the main units in the WTU is the GAC adsorbent, which adsorbs undesired compounds present in the water (organics, chlorine, Ca and Mg carbonates and metal ions). It has been demonstrated that the GAC filter removes ions of Ca, Al, Fe, Mn and Mg in significant amounts during exploitation; however, CaCO\({}_{3}\) is the calcium species present in the highest concentration in the GAC while organics are only present in trace amounts [40]. Recent publications demonstrate that the use of HCl can efficiently regenerate AC exhausted with the mentioned compounds [41]. In this work, two different scenarios in the power plant are compared using an economic tool which demonstrates the advantage of a correct GAC management strategy. In scenario one, regeneration of the exhausted GAC is applied instead of replacing it, leading, as will be proved, to a reduction in exploitation cost. In scenario two, after exhaustion, GAC is completely removed from the filter (causing a solid waste problem for the plant) and replaced by expensive virgin material.