## 3 Results of Literature Review and Economic Assessment
### A Novel Long-Duration Storage, Hybrid of Hydro-Pneumatic UPHES with PTES
#### Moving the Storage Capacity outside of UPHES, toward Thermal Stores  
In response to the medium-high Capex for pure UPHES, a further innovative leap in technology and cost structure is needed as the third improvement of UPHES to achieve a Capex compatible with long-duration storage (5-500 h), one order of magnitude lower than the previously computed value of 200 USD/kWh for storages of short and medium duration. Since the required volume of such pressurized UPHES would prove too large and therefore too costly for long duration storage, the storage of energy must be diverted elsewhere. We opt for large, low-cost, insulated, atmospheric, thermal pits or thermal tanks as described in Figure 5. One pit, called Hot Store contains hot water at 95 \({}^{\circ}\)C, similar to the 40,000-200,000 m\({}^{3}\) pits used in Denmark for seasonal thermal storage, losing only 0.1 K per day [23]. A second pit, called Cold Store contains a salted ice slurry at -20 \({}^{\circ}\)C.  
The exergy from a thermal energy source is defined by the amount of mechanical work recoverable by a Carnot machine. Very interestingly, one shall realize that exergy of hot water is very high, much higher than energy of water subject to the sole earth gravity. For instance, exergy of water at 100 \({}^{\circ}\)C related to ambient temperature is equal to 12 kWh/m\({}^{3}\). This is one order of magnitude higher than the mechanical energy of the same water in pumped-hydro, equal to 1.2 kWh/ m\({}^{3}\) for a hydro plant of 360 m head. Figure 6 illustrates the principles of energy storage for a PTES using a UPHES for electricity conversion, while Figure 7 describes its main components. The radical innovation is that those two stores are thermally charged and recharged by the heat supplied and extracted during the time hydroelectricity is charging the UPHES, the slow moving CO\({}_{2}\)-water interface acting as a novel type of heat-pump. Figure 5: Insulated, atmospheric, thermal pits and thermal tanks, designed for thermocline layers. An alternative configuration is shown in Figure 8 below, devoid of the CO\({}_{2}\) smaller pressurized cavern and where the necessary heat exchanges for CO\({}_{2}\) happen instead by using an ancillary multiphasic CO\({}_{2}\) blower/pump and external CO\({}_{2}\) tubing leading to external heat exchanger(s). A bypass circulation pipe, fitted with a valve, is allowing the CO\({}_{2}\) heat exchanges during ied times when the flexible membrane gets fully collapsed. Figure 9 describes the system operation on the Pressure-Enthalpy diagram related to CO\({}_{2}\). It is specified that placements of cycles vary with the level of completion/depletion of thermal stores, in particular with temperatures available from the Hot Store, and that optimal cycles for campaign of energy charge can be significantly different from optimal cycles for campaign of energy discharge. For the Hot Store to work in the domain of 95 \({}^{\circ}\)C temperature, it is pointed-out that the pressure and temperature of pure CO\({}_{2}\) in the cavern needs to exceed pressure and temperature of CO\({}_{2}\) at the critical point (7.39 MPa, 31.1 \({}^{\circ}\)C). Such charging and discharging operations in trans-critical phases do not create specific irreversibilities of their own, except for the added complexity that overall heat exchanges for the expansion and contraction of supercritical CO\({}_{2}\) at the upper constant-pressure ceiling needs to be performed by a glide of several heat exchanges at increasing and decreasing temperatures. It is specified than despite incursions of the working fluid in supercritical phase, the hydro-pump and the hydro-turbine remain the only two machineries needed by the novel storage. Figure 6: Principles for a PTES (Pumped Thermal Electricity Storage) using a UPHES (Underground Pumped-Hydro Energy Storage) as the locus of energy conversion. Figure 7: Main components of the hybrid UPHES-PTES for long-duration storage (here in stand-alone configuration and with a smaller pressurized cavern dedicated to CO\({}_{2}\)).