###### Abstract  
The decarbonization of the industrial sector is imperative to achieve a sustainable future. Carbon capture and storage technologies are the leading options, but lately the use of CO\({}_{2}\) is also being considered as a very attractive alternative that approaches a circular economy. In this regard, power to gas is a promising option to take advantage of renewable H\({}_{2}\) by converting it, together with the captured CO\({}_{2}\), into renewable gases, in particular renewable methane. As renewable energy production, or the mismatch between renewable production and consumption, is not constant, it is essential to store renewable H\({}_{2}\) or CO\({}_{2}\) to properly run a methanation installation and produce renewable gas. This work analyses and optimizes the system layout and storage pressure and presents an annual cost (including CAPEX and OPEX) minimization. Results show the proper compression stages need to achieve the storage pressure that minimizes the system cost. This pressure is just below the supercritical pressure for CO\({}_{2}\) and at lower pressures for H\({}_{2}\), around 67 bar. This last quantity is in agreement with the usual pressures to store and distribute natural gas. Moreover, the H\({}_{2}\) storage costs are higher than that of CO\({}_{2}\), even with lower mass quantities; this is due to the lower H\  
In this technology, excess energy is used to produce a synthetic fuel. The most common fuel is hydrogen, but it also could be synthetic natural gas (SNG), methanol, and others. In particular, when methane is produced, power-to-gas (PtG) is one of the most versatile energy storage technologies and it converts surplus renewable electricity into synthetic natural gas by combining H\({}_{2}\) from water electrolysis with CO\({}_{2}\) through methanation reaction. This technology has also been proposed for carbon utilization using captured CO\({}_{2}\) to produce a \"CO\({}_{2}\) neutral' natural gas [7]. Under certain design configurations, where synthetic fuels are used in the same installation where the CO\({}_{2}\) is captured (industry or power plant), the CO\({}_{2}\) could be effectively recycled [8]. It allows the temporal displacement (storage) in the use of renewable energy. The CO\({}_{2}\) source could also be through direct air capture (DAC) [9], and in this case environmental impacts are clearly minimized. In a PtG process renewable electrical energy is converted into CH\({}_{4}\) through two processes: (i) electrolysis of water, which produces H\({}_{2}\) and O\({}_{2}\) (Reaction 1); and (ii) conversion of H\({}_{2}\) into CH\({}_{4}\) with an external source of CO\({}_{2}\) through methanation, according to the Sabatier reaction (Reaction 2). \[\mathrm{H_{2}O}\ \leftrightarrow\mathrm{H_{2}}+\frac{1}{2}\mathrm{O_{2}} \qquad\Delta\mathrm{H_{298K}}=+285.8\ \mathrm{kJ/mol} \tag{1}\]  
\[\mathrm{CO_{2}}+4\mathrm{H_{2}}\ \leftrightarrow\mathrm{CH_{4}}+2\mathrm{H_{2}O} \qquad\Delta\mathrm{H_{298K}}=-164.9\ \mathrm{kJ/mol} \tag{2}\]  
The methanation implies an enrichment in energy density, while H\({}_{2}\) has an energetic density of 12.7 \(\mathrm{MJ/m^{3}N}\); in turn, the energetic density of CH\({}_{4}\) is 40 \(\mathrm{MJ/m^{3}N}\)[10]. Furthermore, the CH\({}_{4}\) produced can be injected directly into the natural gas grid as a storage structure or used as a substitute for fossil fuels. In the case of H\({}_{2}\) and CO\({}_{2}\), which are the inputs for the reaction, it would be necessary to have storage vessels to manage the renewable production (H\({}_{2}\)) and the utilization of carbon emissions (CO\({}_{2}\)). The necessity of these storage vessels opens a new research line about the feasible operational variables that minimize the energy requirements and system costs, to help carry out multi-criteria optimization of this energy storage design. This work is an attempt to address this problem.