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THERMAL PROPERTIES OF SC CO2 BY MC SIMULATIONS 409 FIGURE 4 Isothermal compressibility (k) as a function of pressure. Legend as in Fig. 2. CO2 ðL 1⁄4 0:699Þ does predict lower densities, especially on the liquid-like branch of the sub- critical isotherm studied ðT 1⁄4 288:37 KÞ; but the agreement between simulation results and the 2CLJQ EOS improves in the supercritical region, especially at the higher temperatures and pressures. In general, good agreement is also found between these results and the predictions of the Span and Wagner EOS, except in the extended critical region where deviations in densities up to 5% can be found. The extended critical region includes a temperature range of 20 K and a pressure range of 10 MPa around the critical point. Mo ̈ller and Fischer obtained similar results from constant pressure – constant temperature molecular dynamics simulations in this region. The volume expansivity (bP) and the isothermal compressibility (k) as functions of pressure are shown in Figs. 3 and 4, respectively. The discrepan- cies between the 2CLJQ model (both simulations and EOS) and the Span–Wagner EOS are obvious in the extended critical region for both quantities. The volume expansivity is overpredicted by the 2CLJQ model by more than 90% at 330K, as shown by comparisonwiththeSpan–WagnerEOS,andevenat 288 and 374K deviations up to 80% can be found. However, these deviations are not surprising since it is known that these derivatives, as well as other properties such as heat capacities, diverge at the critical point, so that any discrepancies between the molecular model and the Span – Wagner EOS are bound to be greatly magnified in this region. In fact, it is known that the 2CLJQ model fails to reproduce the critical point of CO2 exactly; from the correlations developed by Stoll et al. [23] for the 2CLJQ fluid, we expect for CO2 a model-predicted critical tempera- ture Tc 1⁄4 307:83 K from simulations and Tc 1⁄4 318:4K from the 2CLJQ EOS, higher than the accepted experimental value Tc 1⁄4 304:128 K which the Span – Wagner EOS is designed to reproduce. Thus, for instance, for CO2 at 330.39K the 2CLJQ model gives results that are more near-critical (reduced temperature Tr 1⁄4 T* =T*c 1⁄4 1:07) than in the actual case ðTr 1⁄4 1:09Þ: The corresponding “spikes” in the isotherms in Figs. 3 and 4 are therefore more pronounced for the 2CLJQ model than for the Span–Wagner EOS. A substantially closer agreement between both sets of data would be obtained by computing the isotherms from the reference EOS at the same reduced temperature as the simulations. On the other hand, these differences become less significant at higher temperatures and pressures, away from the extended critical region. At pressures above 40 MPa the agreement between the Span – Wagner EOS and the 2CLJQ model is very good for all temperatures; for temperatures higher than 374 K the agreement is excellent in the entire range of pressures as can be seen in the inset of Fig. 3. A similar behavior for the isothermal compressibility is shown in Fig. 4 (and the inset therein). Figure 5 illustrates the isobaric heat capacity obtained in this work as a function of density. We have chosen to plot these results (as well as those in the following figures) in terms of density for visual clarity, but the analysis from a CP vs. P plot shows the same tendency. Deviations smaller than 3% are found between the 2CLJQ model and the Span– Wagner EOS except in the already mentioned extended critical region. Nevertheless, the deviations of CP in the extended critical region are considerablyPDF Image | Thermal Properties of Supercritical Carbon Dioxide
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