MULTIPROPERTY FIT OF EQUATIONS OF STATE BY GENERALIZED NONLINEAR LEAST SQUARES: APPLICATION TO THE CO2-H2O SYSTEM

The description of geochemical fluid-phase equilibria frequently requires equations of state (EOS) capable of simultaneously representing the pressure-density isotherms of the single-phase fluids, and the pressure-composition-density relationships in the liquid-vapor coexistence region. The literature contains many examples of EOS that are forced to reproduce one of these fluid properties, but are found to predict erroneous values of the others. Such difficulties are usually attributed to limitations inherent in the analytical form of the equations, rather than the statistical methods by which the EOS parameters are estimated. We show that application of Generalized Nonlinear Least Squares (GNLS) - in which the conventional distinction between dependent and independent variables is abandoned - can greatly enhance the ability of EOS to provide self-consistent representations of various fluid properties. GNLS differs from conventional Weighted Nonlinear Least Squares (WNLS) in its use of simultaneous iteration for the model-dependent parameters and estimates of the error-free values of the measurements; the postulated functional relationship enters as a constraint to be satisfied by these estimated variables.

Existing GNLS algorithms, designed for fit of a single equation, require modification to deal with the large composite data sets on which equations of state are often based. A new procedure incorporating these modifications is described, and applied to the fit of a cubic EOS to pvT and saturation data for CO2, H2O, and CO2-H2O mixtures. It is concluded that accurate representations of vapor pressures and pressure-density isotherms for pure fluids are not mutually exclusive, as is commonly supposed.

Research sponsored by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy under contract DE-AC05-00OR22725. Oak Ridge National Laboratory is managed and operated by UT-Battelle, LLC.