New equations for density, entropy, heat capacity, and potential temperature of a saline thermal fluid

A set of fitted polynomial equations for calculating the physical variables density, entropy, heat capacity and potential temperature of a thermal saline fluid for a temperature range of 0–374 °C, pressure range of 0.1–100 MPa and absolute salinity range of 0–40 g/kg is established. The freshwater components of the equations are extracted from the recently released tabulated data of freshwater properties of Wagner and Pruß [2002. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Journal of Physical and Chemical Reference Data 31, 387–535]. The salt water component of the equation is based on the near-linear relationship between density, salinity and specific heat capacity and is extracted from the data sets of Feistel [2003. A new extended Gibbs thermodynamic potential of seawater. Progress in Oceanography 58, 43–114], Bromley et al. [1970. Heat capacities and enthalpies of sea salt solutions to 200 °C. Journal of Chemical and Engineering Data 15, 246–253] and Grunberg [1970. Properties of sea water concentrates. In: Third International Symposium on Fresh Water from the Sea, vol. 1, pp. 31–39] in a temperature range 0–200 °C, practical salinity range 0–40, and varying pressure and is also calibrated by the data set of Millero et al. [1981. Summary of data treatment for the international high pressure equation of state for seawater. UNESCO Technical Papers in Marine Science 38, 99–192]. The freshwater and salt water components are combined to establish a workable multi-polynomial equation, whose coefficients were computed through standard linear regression analysis. The results obtained in this way for density, entropy and potential temperature are comparable with those of existing models, except that our new equations cover a wider temperature—(0–374 °C) than the traditional (0–40 °C) temperature range. One can apply these newly established equations to the calculation of in-situ or onboard density, specific volume (therefore, the porosity), and potential temperature change that are usually measured on shipboard by the Ocean Drilling Project (ODP) and other hydrothermal-fluid studies.