# Economic Analysis of a Zero-Water Solar Power Plant for Energy Security
## 2 Methodology
### Estimation of the Cost of the Earth-CAT System  
The costs of the project are divided into the total capital investment and the subsequent O&M costs. The investment includes all of the material and equipment costs plus the excavation and refilling labor costs. The material costs are the piping costs, calculated from the price per length unit of a PVC pipe. A price generator for architects, engineers, and construction is used to estimate the prices of the PVC pipes [34]. The cost of a 0.5 m diameter PVC-U pipe depends on the nominal pressure of the design, i.e., its thickness. A pipe with a nominal pressure of 6 atm and a thickness of 12.3 mm is estimated at EUR 120.54/m. The same kind of pipe costs EUR 185.80/m and EUR 277.93/m for nominal pressures of 10 atm (19.1 mm thickness) and 16 atm (29.7 mm thickness), respectively. For the operating pressure of 1.1 bar used in this work and applying an overpressure safety  
Figure 1: Simplified scheme of the air flow entering the air condenser from the Earth-CATs and the flow conditions of the steam existing the steam turbine. factor, the cost of a 0.5 m pipe with a nominal pressure of 1.5 atm is estimated with the following equation [35]:  
\[C_{PE,Earth-CAT}=C_{PE,Ref}\left(\frac{X_{Earth-CAT}}{X_{Ref}}\right)^{\alpha} \tag{1}\]  
where \(C_{PE,Earth-CAT}\) is the purchase unit cost of Earth-CAT tubes, \(C_{PE,Ref}\) is the purchase unit cost of the reference tubes, \(X_{Earth-CAT}\) and \(X_{Ref}\) are the nominal pressures of the Earth-CAT and the reference tubes, respectively, and \(\alpha\) is a scaling exponent that takes into account economies of scale (here, it is assumed to be equal to 0.95 for pipes with diameters between 0.05 and 0.75 m). The average unit cost estimated for the Earth-CAT system is thus calculated to be equal to EUR 30.76/m. The power required by a fan to compensate for the pressure losses of 226 Pa in the pipe and the air condenser is approximately equal to 65 W. One fan is installed for each set of 5 pipes arranged vertically, processing a flow rate of 5302.33 m\({}^{3}\)/h. A standard commercial fan for a volumetric flow of 6860 m\({}^{3}\)/h (the available one found for flow rate just above 5302 m\({}^{3}\)/h) costs EUR 319 and has a power input requirement of 760 W [36]. The power input is assumed to also compensate for the pressure losses within the filters and the inlet and outlet vertical pipes and is also used to drag accumulated dust by blowing the air at a higher velocity. A particle filter with a nominal volumetric flow of 3400 m\({}^{3}\)/h with a cost of EUR 100 is installed at the inlet of each 5-pipe set [37]. Thereby, a cost of EUR 156 is estimated for a nominal flow of 5302 m\({}^{3}\)/h. Furthermore, dryers or dehydrator filters are also necessary, as the dew point of the water content in the air must be considered. For example, at an ambient temperature of 35 \({}^{\circ}\)C and a typical relative humidity of 42% in the summer in the province of Seville, the dew point is approximately at 24 \({}^{\circ}\)C and condensation may occur, forming mildew inside the pipes [38]. In this work, the cost of a dehydrator filter is considered the same as that of the particle filter (EUR 156). In addition,  
Figure 2: Sketch of the proposed design. the buried pipes are assumed to be slightly inclined to purge condensation [39]. Costs of electronic and electrical installations are assumed to be 10% of the equipment cost [22]. Excavation and refilling costs in unleashed soil are considered to be EUR 2.4/m3 and EUR 2.0/m3, respectively, according to the lithological map of the Iberian Peninsula [27], [40]. These costs are included in the initial investment of the project. Finally, the O&M costs that ensure the correct operation of the system are calculated (costs of the electricity requirements, cleaning costs, repair costs, and overhauls). The electricity consumed by the fans is supplied directly by the plant itself, so a lower net power will be produced by the plant.