## 4 Conclusions  
Two aspects relevant for a consistent thermo-hydraulic modelling of clay-based engineered barriers for deep geological repositories for radioactive waste have been studied: the saturated water vapour pressure and the specific heat capacity of liquid water and vapour. The temperature range of interest has been set between 0 and 150 \({}^{\circ}\)C.  
Several expressions for the saturated water vapour pressure have been inspected, including reference expressions and those most applied in works modelling unsaturated soils and clay-based barriers. This has led to successfully identifying an accurate (relative error not greater than \(\pm\)0.2%) and simple enough expression (ranked as the selected model using both the Akaike information criterion and the Bayesian information criterion), [PERSON]'s [6] equation, Equation (3), as the optimal option for modelling in the temperature range between 0 and 150 \({}^{\circ}\)C.  
Further, the enthalpy of vaporisation of water and the internal energy difference between liquid water and vapour as a function of temperature have been studied to derive the consistency of pairs of constant specific heat capacity values for liquid water and water vapour. Several pairs of values from the literature used for modelling unsaturated soils and clay-based barriers have been inspected. Their difference has been compared to reference values and to coefficients identified from the enthalpy of vaporisation and the difference of internal energy. It has been found that using constant specific heat capacity pairs corresponding to reference values at the same temperature can lead to underestimating the decrease in the enthalpy of vaporisation and of the internal energy difference with increasing temperature. To minimise this loss of accuracy, a model should use specific heat capacity pairs as close as possible to the fitted coefficient 2398.9 J/kg/K for isobaric values and 2841.5 J/kg/K for isochoric values. In the case of using reference specific heat capacity pairs for the same temperature, this means using pairs for a temperature as close to 0 \({}^{\circ}\)C as possible. However, the relative error associated with this loss of accuracy is limited, being below 2% for all the specific heat capacity pairs from the literature inspected, and up to a 6% for the reference specific heat capacity pairs for the same temperature between 0 and 150 \({}^{\circ}\)C.  
Figure 8: Relative error in \(\Delta h_{\text{LV}}\) and \(\Delta u_{\text{LV}}\) at 150 \({}^{\circ}\)C using specific heat capacity pairs from reference values [13] at temperatures 0–150 \({}^{\circ}\)C.  
**Author Contributions:** Conceptualisation, V.N. and L.A.; methodology, V.N. and L.A.; software, V.N. and L.A.; validation, L.A. and V.N.; formal analysis, V.N. and L.A.; investigation, V.N. and L.A.; data curation, V.N. and L.A.; writing--original draft preparation, L.A.; writing--review and editing, V.N., G.U. and L.A.; visualisation, V.N., L.A. and G.U.; supervision, V.N.; project administration, V.N. and L.A.; funding acquisition, L.A. and V.N. All authors have read and agreed to the published version of the manuscript.  
This research was funded by MCIN/AEI/10.13039/501100011033, grant number PID2020-118291 RB-I00. The APC was funded by MDPI open access publishing in Basel/Switzerland.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Data were obtained from the references cited throughout the text, and are available from those documents.  
The authors declare no conflict of interest. The funder had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.