A NEW EQUATION FOR THE DENSITY OF A SALINE THERMAL FLUID

A new polynomial equation for calculating the density ρ(t,p,S) of a thermal saline fluid for a temperature range of 0-374 °C, pressure range of 0.1-100 MPa and practical salinity range of 0-40 is established and shown underneath.

The freshwater components of the equation are extracted from the tabulated data of freshwater properties of Wagner and Pruß (2002, J. Phys. Chem. Ref. Data, 31, 387-535). The salt water components of the equation are based on the near-linear relationship between density and salinity and are extracted from the data set of Feistel (2003, Progr. Oceanogr., 58, 43-114), Bromley et al. (1970, J. Chem. Eng. Data, 15, 246–253), Grunberg (1970, 3rd Int. Symp. on Fresh Water from the Sea. Vol.,1, 31-39), and Millero et al. (1980, Deep-Sea Res., 27A, 255–264) in a temperature range 0-200°C, practical salinity range 0-40 and varying pressure. The freshwater and salt water components were combined to set up a workable multi-polynomial equation whose coefficients are computed through standard linear regression analysis. The results obtained in this way for the density are comparable with those of existing models, except that our new equation covers a wider temperature- (0-374 °C) than the traditional (0-40 °C) temperature range. One can apply this newly developed equation to the calculation of in-situ or onboard density, specific volume (therefore, the porosity) that are usually measured on shipboard by the Ocean Drilling Project (ODP) and other hydrothermal-fluid studies.

ρ(t,p,S)= 9.9920571E+02 + 9.5390097E-02 × t - 7.6186636E-03 × t² + 3.1305828E-05 × t³ -6.1737704E-08 × t⁴ + 4.3368858E-01×p + 2.5495667E-05 × p × t² - 2.8988021E-07× p×t³ +9.5784313E-10 × p × t⁴ +1.7627497E-03 × p² - 1.2312703E-04 ×p² × t +1.3659381E-06 × p² × t² -4.0454583E-09 × p²× t³ - 1.4673241E-05 × p³ + 8.8391585E-07× p³ × t - 1.1021321E-08 × p³× t² +4.2472611E-11× p³×t³ -3.9591772E-14 × p³×t⁴ -7.99992230E-01 × S +2.40936500E-03 ×S × t -2.58052775E-05× S× t² + 6.85608405E-08×S× t³ +6.29761106E-04 p×S - 9.36263713E-07 ×p²×S

For terms without S, adjusted R²= 0.99992; for terms with S,adjusted R²= 0.99991. Units: t,°C;S, unitless; p, MPa.