## 2 Methodology
### Case Study Results  
Since the process is made up of different stages in series, the calculation process is iterative for the different scenarios. The main variables that influence power consumption and thermal energy that can be utilized are the inlet gas compressor temperature, number of intercooling-compression stages, isentropic efficiency, inlet gas pressure, and working gas. To evaluate the influence of gas temperature at the compressor inlet, this parameter was modified from 50 \({}^{\circ}\)C to 100 \({}^{\circ}\)C using a single compression stage. The results of this single scenario show a reduction of 13.85% in the specific work required by the compressor using lower inlet temperatures. Therefore, the lower the temperature at the compressor inlet, the lower the power consumption. Hence, this idea justifies the necessity of placing intermediate heat exchangers between compressors to minimize specific power consumption. Another parameter that has direct influence on global consumption is the number of intercooling compression stages used to reach a certain storage pressure. In this research different scenarios were studied--ranging from one to five intercooling compression stages keeping a constant pressure of 20 bar to see the differences in consumption between scenarios. Then, if the two scenarios that differ in the number of compression stages are compared (3 and 4 stages), the results show a decrease in consumption of 2.98% using 4 compression stages (base case). Therefore, scenarios with a higher number of stages in series offer lower consumptions. This is a key result to be considered in the optimization procedure due to the higher number of stages implying an increase in equipment costs. Thus, the optimal scenario will have to consider low consumption without compromising the global costs. Table 3 illustrates the net power requirements, heat to be used, and heat to be discarded due to a low temperature level with different compressor-intercooling stages for CO\({}_{2}\) and H\({}_{2}\) as the operating gas. For scenarios with a higher number of compressors, the power required by each compressor is lower than the case with few compressors. Working with less compressor stages leads to higher temperatures in the compressor outlet and, therefore, the specific power requirements are higher than in the case of more stages. In designs that include a lower number of stages, more heat is transferred in the heat exchangers and could be used elsewhere. In contrast, when increasing the number of compression stages, the heat not reused is getting higher due to the increasing number of stages. These effects are well-described in the literature [16; 20; 21]. In reference to the whole system, the inlet gas pressure has a considerable effect on the target variable. Several inlet gas pressures (1-3 bar) were tested given a different number of compression stages (k = 1-5), and the results indicate that for a fixed storage pressure, the higher the gas pressure at the inlet, the lower the consumption as has been validated elsewhere [28]. This is justified because the difference between the inlet pressure and storage pressure is reduced and, as a consequence, the work required by the compressor drops, too. Finally, the working gas is the variable that has a larger influence on global consumption due to the intrinsic properties of each gas (Table 3). For compressing low-density gases, there is work required by the compressors; therefore, the consumption is higher than for high-density gases. A comparison was set between the two working gases in this paper and it has shown a huge difference in consumption due to H\({}_{2}\) having a much lower density than CO\({}_{2}\). To summarize, the two variables that facilitates minimum power consumption are: low gas temperatures at compressor inlet and using multiple compression stages. However, this statement implies a direct increase in the CAPEX needed for the whole installation since more equipment is needed.