4.2 Application of theory to liquid mixtures of hydrocarbons

In order to check the reliability of the thermodynamic model, theoretical results are first tested against the non-equilibrium molecular dynamics simulation results using the same (Exp-6) intermolecular potential function for a binary mixture of pentane and decane (C5 + C10) [26]. Note that the optimized parameters were used in the non-equilibrium molecular dynamics simulations to represent the experimental data of thermal diffusion factors of (C5 + C10) mixture.

Figure 1 compares the theoretical results with the simulation results of α<sup>T</sup> for the mixture of pentane and decane (C5 + C10) at 300 K and 0.1 Mpa [26]. These results show that the thermodynamic model can describe α<sup>T</sup> reasonably well with the uncertainties of simulation results. Also included in the Figure 1 are measured data for the system (C5 + C10). The model is seen to compare well with both simulation and measured results within their data uncertainties.

The above results suggest that the thermodynamic model with the pressure dependent collision integrals offers reliable prediction of α<sup>T</sup> as a function of both temperature and concentration in binary mixtures. Therefore, we adopted the unlike potential parameter and pressure dependent collision integrals to first

Figure 1. Thermal diffusion factor for mixture (C5 + C10) from theory, simulation and experiment.

correlate a value of α<sup>T</sup> in liquid hydrocarbon mixtures at a single temperature and equimolar condition, and extended that to all other conditions. When several data points of thermal diffusion factor were available in different non-ideal conditions of temperature, pressure and concentration, we re-evaluated the single point parameters by incorporating several data points in parameters regression. Also, in most of the cases the three parameters p1, p2 and p3 can describe well the diffusion factors and can depend on the temperature, pressure, concentration and interaction parameters.

Figure 2 presents results for the collision integrals independent of pressure. The calculated collision integral results are physically consistent and agree with the literature data very well [25].

Figure 3 shows theoretical predictions and experimental data [27] of α<sup>T</sup> for mixture (C1 + C3) at a given temperature T = 346 K and P = 5.5 Mpa as a function of composition of C1. Figure 4 presents theoretical and experimental results of α<sup>T</sup> for T = 346 K, and composition, x1(C1) = 0.34 as the function of pressure. The latter

Figure 2. Collision integrals from calculation and literature.

Figure 3. Thermal diffusion factor for mixture (C1 + C3) from theory and experiment.

Thermodynamics of Thermal Diffusion Factors in Hydrocarbon Mixtures DOI: http://dx.doi.org/10.5772/intechopen.75639

Figure 4. Thermal diffusion factor for mixture (C1 + C3) from theory and experiment.

condition is close to the critical point of the mixture (C1 + C3). In both cases the theoretical results are in agreement with the measured data well within the experimental uncertainty.

Figure 5 compares theoretical predictions with experimental data [23] of α<sup>T</sup> for mixture of methane and butane (C1 + C4) for temperature 346 K and composition x1(C1) = 0.34. Figure 6 presents similar comparisons at the lower temperature of 319 K and composition of x1(C1) = 0.49. The variations of thermal diffusion coefficients with pressure are investigated. The comparison between theory and experiment is very good for all the tested conditions.

To further examine the reliability of our models, Figure 7 compares theoretical and experimental results of α<sup>T</sup> for the more non-ideal mixture of Heptane and Hexadecane (C7 + C16) [28]. The model can describe α<sup>T</sup> reasonably well over the whole range of the composition.

Figure 5. Thermal diffusion factor for mixture (C1 + C4) from theory and experiment.

Figure 6. Thermal diffusion factor for mixture (C1 + C4) from theory and experiment.

Figure 7. Thermal diffusion factor for mixture (C7 + C16) from theory and experiment.
