389657 Description of Thermophysical Properties of Multi-Component Mixtures Employing Virial-Based Mixing Rules (VBMR)
The last several decades have witnessed the development of a number of high fidelity methods for describing thermophysical properties of pure substances in condensed phases. They include corresponding states techniques and component-specific correlations, as well as statistical thermodynamics approaches. However, the science for describing mixtures has consistently trailed behind, often being limited to ideal mixing or similar formulations. For example, the mixing rules (typically implemented in process simulators) for liquid viscosity and thermal conductivity, are the Kendall-Monroe and Li correlations, respectively.
While the attractive feature of such mixing rules is that they do not require interaction parameters (IP’s), their downside is that the do not allow IP’s, even when appropriate. In many applications, they incorrectly predict only a small deviation from ideal mixing, often with incorrect sign. Thus, while these mixing rules perform reasonably for hydrocarbon systems, their efficacy for non-ideal systems is questionable.
The state-of-the-art is the Redlich-Kister correlation (RKC), which can incorporate additional higher-order terms to improve the fit of data with higher precision. It is often the correlation of choice for the applied thermodynamics research community, and has been successfully applied to precisely correlate a variety of thermophysical properties for binary mixtures. However, the RK correlation does not naturally extend to multi-component systems.
This investigation draws upon the exact mathematics of mixing rules established for virial coefficients of gases. Perturbations from ideal mixing are modeled akin to successive terms in the virial expansion, resulting in 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.
Applying the VBMR methodology, Sen and co-workers have recently demonstrated excellent results for the correlation of several thermophysical properties for a number of binary liquid mixtures, including density, enthalpy, and viscosity. In this investigation, the VBMR methodology is extended to ternary (and multicomponent systems), yielding non-zero ternary (and higher-order) interaction parameters accounting for three-body interations, without compromising the goodness-of-fit for binary constituents. Comparisions are made with RKC, emphasizing how the VBMR naturally extends to multicomponent systems, while the RKC does not.
The VBMR model separates the temperature dependence of pure component and interaction parameters. This is postulated as a key reason for the smooth as well as weak temperature dependence of the interaction parameters. By contract, the temperature dependence of model parameters for the RKC is often siginifcantly jagged. This investigation implements and demonstrates the smotth temperature dependence for several binary and multicomponent mixtures.