(69g) Extension of the Tait Equation to Mixtures

The advent of high precision densitometers, especially since the mid 1980's, has resulted in an abundance of high quality liquid density measurements over full concentration ranges, and up to significantly high pressures. However, the correlation of these data remains an important challenge. Over the years, the Redlich-Kister and Tait equation have emerged as the winners.

For a long time, the Tait Equation has remained the workhorse for describing the pressure dependence of liquid density for pure substances. Liquid densities at high pressures are modeled with respect to a reference density at low pressure, usually the saturated liquid density. However, only limited success has been achieved in the extension of the Tait equation to mixtures. Consequently, the standard procedure has been to correlate the composition dependence of excess molar volume (Vex) at individual pressures via the Redlich-Kister correlation, and to tabulate and publish the resulting correlation parameters.

The COSTALD correlation (Thomson, 1982) is a notable example of the application of the Tait Equation to describe the pressure dependence of liquid densities for mixtures. The B-parameter in the Tait equation is modeled as a function in reduced temperature (Tr), while the critical temperature (Tc) is obtained via a three-parameter corresponding states approach. While this implementation is a useful, generalized method for engineering calculations, the model does not allow adjustable interaction parameters, which are crucial for the correlation of high precision or highly non-ideal density data.

Recently, Sen and co-workers (2007, 2008) have demonstrated a technique employing virial-based mixing rules (VBMR) to describe the concave, convex, and S-shaped curves representing the composition dependence of liquid phase excess thermophysical properties (such as molar volume, enthalpy and viscosity). The VBMR methodology draws upon the exact science of mixing rules that has been established for the virial coefficients of gases. Perturbations from ideal mixing are modeled akin to successive terms in the virial expansion; hence the name ?Virial-Based Mixing Rules? (VBMR). Each perturbation reduces to zero for pure components, and adopts the composition order of the corresponding virial coefficient it represents. For example, the first perturbation represents the second virial coefficient and implements a quadratic mixing rule, while allowing one adjustable binary interaction parameter. The next term employs cubic mixing and allows multiple interaction parameters, including a ternary interaction parameter which may be fine-tuned for ternary and higher mixtures. All interaction parameters are initialized to zero.

While the mixing rule parameters can be cross-correlated against pressure, this investigation takes a different approach. In a manner similar to the COSTALD correlation, it is recognized that model parameters may be composition-dependent. This dependence is described via the VBMR methodology. In a first-order, computationally-efficient scenario, the composition dependence of low-pressure density (or Vex) is assumed to be decoupled from that of the Tait equation parameters. While this assumption roughly holds for simple systems, the generalized scenario requires the simultaneous correlation of these dependencies.

Both scenarios are investigated for densities of several systems over their full composition range and up to significant pressures. It is noted that an useful corollary of this investigation is the application of the Tait equation to correlate other mixture thermophysical properties under pressure.