## 1 Introduction  
To accurately model a thermo-hydraulic problem in clay-based engineered barriers, especially at temperatures significantly higher than standard temperature (20 \({}^{\circ}\)C), it is crucial to include accurate water vaporisation in the formulation. First, the water content of geomaterials is relevant for their thermal, hydraulic and mechanical properties. Second, vaporisation consumes energy and can affect the temperature of the system. In the problem of clay-based engineered barriers in deep geological repositories for high-level radioactive waste, the formulation used must be robust for temperatures up to 150 \({}^{\circ}\)C, a temperature that could be reached in the surface of the canisters that will be surrounded with clay barriers [1]. This applies in particular to the modelling of vapour pressure as a function of temperature and to a consistent use of the specific heat capacities of liquid water and water vapour. The current international standard, as accepted by the International Association for the properties of Water and Steam (IAPWS), for saturated vapour pressure values is the equation of state in the IAPWS-95 formulation [2]. Tabulated values for temperatures between 0.01 and 150 \({}^{\circ}\)C can be found, for example, in the CRC Handbook of Chemistry and Physics [3]. In addition, the auxiliary equations of [PERSON] and [PERSON] [4] for saturated vapour pressure as a function of temperature are of comparable accuracy to the uncertainty of the experimental data. However, other simpler formulations are most frequently used in modelling. Some of them were formulated for meteorology. For instance, [PERSON] [5] developed a set of nine equations \"to be easily implemented on a calculator or computer\". The nine equations are of different complexity and are optimised for different temperature ranges. In addition, for multiple purposes, [PERSON] [6] developed an expression from the Clausius-Clapeyron equation, and fitted it to the IAPWS reference dataset for a temperature range between 0 and 100 \({}^{\circ}\)C. In the case of the thermo-hydraulic modelling of clay-based engineered barriers in deep geological repositories for high-level radioactive waste, other approximations based on exponential functional structures are common. In this way, [PERSON] and [PERSON] [7] use an expression of this kind in a general model for deformable unsaturated soil. [PERSON] et al. [8] and [PERSON] et al. [9] both used an equation with an exponential structure to model the full-scale FEBEX in situ test (Grimsel Test Site, Switzerland) for high-level nuclear waste disposal. [PERSON] et al. [10] modelled two full-scale in situ experiments analysing the behaviour of radioactive waste repositories (Buffer/Container Experiment and Isothermal Test, conducted at the Whiteshell Underground Research Laboratory, Manitoba, Canada, by Atomic Energy of Canada Limited) using an exponential function for the saturated vapour pressure. [PERSON] et al. [11] also used an expression of this kind to model a long-term laboratory heating and hydration test on bentonite pellets simulating the behaviour of a repository buffer (HE-E cells, conducted by CIEMAT in Madrid, Spain). Likewise, [PERSON] and [PERSON] [12] presented a framework for modelling unsaturated soils where an exponential expression is used. While all these works [5; 6; 7; 8; 9; 10; 11; 12] include an exponential function in their formulation of the saturated water vapour pressure, the arguments of the exponential are, in turn, different functions (polynomials, fractions) of temperature, and include a different number of parameters (two to five). These differences make the accuracy of these equations to be variable for different temperature ranges.