Supercritical regions models

The models used to predict equilibria in the supercritical region can be divided into the following groups [24] ... 

In the present work, we performed MC simulations at different operation conditions, constant fluid density and constant pressure, for calculating K2 to investigate the distribution behavior in the supercritical region. We selected C02, benzene, and graphitic slitpore as a model system by adopting the Lennard - Jones (LJ) potential function for intermolecular interactions. 

Figure 11 shows a typical example of the temperature-dependent behavior for the reactions of OH radical with aromatic compounds. The measured bimolecular rate constants of OH radical with nitrobenzene showed distinctly non-Arrhenius behavior below 350°C, but increased in the slightly subcritical and supercritical region. Feng a succeeded in modeling these data with a three-step reaction mechanism originally proposed by Ashton et while Ghandi etal. claimed to have developed a so-called multiple collisions model to predict the rates for the reactions of OH radical in sub- and super-critical water. 

The same conclusion about transferability is reached by Wallen et al [205] in a MD study of a supercritical Br solution. The ion-water interaction, described by a simple (LJ+Coulomb) two-body interaction augmented by the atomic polarizability of the ion [102] and the POLl model of water appear inadequate to reproduce quantitatively the change occurring in the solution when temperature and pressure rise to the supercritical region. 

The design of separation processes would be facilitated greatly by accurate mathematical models of the thermodynamics. Unfortunately, most standard equations of state do not represent adequately the phase behavior In the near supercritical region and In general were not developed with highly asymmetric solu-... 

Saim and Subramaniam [36] observed that the end-of-run isomerization rates decreased with isothermal increase in pressure in the subcritical region, but increased with pressure in the supercritical region. In sharp contrast to the activity maintenance observed by Tiltscher and co-workers in a macroporous catalyst, the microporous Pt/Y-Al203 catalyst used by Saim et al. deactivated even at supercritical conditions. A significant portion of the catalyst activity was lost due to the build-up of unextractable coke in the catalyst pores during the subcritical phase of reactor fill-up. In a related work, Manos and Hofmann [37] concluded that the complete in situ reactivation of a microporous zeolite catalyst by an SCF is impossible. This conclusion was based on coke desorption rates and the solubilities of model coke compounds in the SCF. The catalyst deactivation rate can be reduced at supercritical conditions, however, because freshly formed coke precursors can be dissolved by the SCF reaction medium. 

A well-rounded EoS should be able to accurately predict thermodynamic properties over a wide range of temperatures and pressure in each of the snbcritical, critical and supercritical regions. In this work, PC-SAFT is used for the prediction of thermodynamic properties. PC-SAFT is based on perturbation theory and is formnlated in terms of the residnal Helmholtz free energy, A. In the perturbation theory, A is modeled as the sirm of contributions from different intermolecular interactions over a reference fluid. In this respect. Gross and Sadowski [10] proposed the following expression which is an improvement over the original SAFT [11] ... 

Sun, Y.-R, C. E. Bunker, and N. B. Hamilton 1993, Ry scale in vapor phase and in supercritical carbon dioxide. Evidence in support of a three-density-region model for solvation in supercritical fluids . Chem. Phys. Lett. 210, 111. 

Uffindell CH, Kolesnikov AI, Li JC, Mayers J (2000) Inelastic neutron scattering study of water in the subcritical and supercritical region. Phys Rev B 62 5492-5495 Ugdale JM, Alkorla I, Elguero J (2000) Water clusters Towards an understanding based on first principles of their static and dynamic properties. Angew Chem Int Ed 39 717-721 Van der Spoel D, Van Maaien PJ, Berendsen HJC (1998) A systematic study of water models for molecidar simulation Derivation of water models optimized for use with a reaction field. J Chem Phys 108 10220-10230... 

Figure 5. Maxima and minima lines in the supercritical region of the (a) ST2 water and (b) Jagla models.

The presence of an LLCP and extrema lines in the supercritical region not only affects the thermodynamic properties of the liquid but also affects its dynamics. Recent computer simulations, based on atomistic [41], silica [39], and different water models [41], show that there is an intimate relationship between the C p line and the dynamic properties of the liquids, LDL and HDL. Specifically, it is found that in the more ordered liquid (i.e., the liquid with less entropy), the temperature dependence of the diffusion coefficient at constant pressure is given by D(T) exp(-EAT) (where Ep, is a constant), indicating that such a liquid is Arrhenius [51]. Instead, the less ordered liquid is found to be non-Arrhenius. Interestingly, in the supercritical region of the P-T plane, the dynamics of the fluid... 

EOS is normally either the Soave-Redlich-Kwong (SRK) or the Peng-Robinson (PR). Both are cubic EOSs and hence derivations of the van der Waals EOS, and like most equations of state, they use three pure component parameters per substance and one BIP per binary pair. There are other more complex EOSs (see Table 8.4). EOS models are appropriate for modeling ideal and real gases (even in the supercritical region), hydrocarbon mixtures, and light-gas mixtures. However, they are less reliable when the sizes of the mixture components are significantly different or when the mixture comprises nonideal liquids, especially polar mixtures. 

Belyakov et al. (1997) developed a parametric crossover model for the phase behavior of H2O + NaCl solutions that corresponds to the Leimg-Criffiths model in the critical region and is transformed into the regular classical expansion far away from the critical point. The model was optimized, and leads to excellent agreement with vapor-liquid equilibrimn data for dilute aqueous solutions of NaCl near the critical points. This crossover model is capable of representing the thermodynamic surface of H2O + NaCl solutions in the critical and supercritical regions. 

Figure 5. Adsorption isotherms for the supercritical region [23], Dots experimental Curves predicted by model...

The SCRELA code was developed for large LOCA analyses for the SCFR, an early version of the Super FR [72, 73]. The SPRAT-DOWN, including the downward flow water rod model for the Super LWR, was extended to the SPRAT-DPWN-DP code for the large LOCA analyses [71]. The critical flow at supercritical pressure is not known. Then, the correlation at the subcritical pressure has also been used in the supercritical pressure for the LOCA analyses since the duration of supercritical pressure is very short. Both codes were verified in comparison with the REFLA-TRAC code. The SPRAT-DOWN code was applied to the small LOCAs of the Super LWR because the system pressure stays in supercritical region at the small LOCAs [71]. 

Although modeling of supercritical phase behavior can sometimes be done using relatively simple thermodynamics, this is not the norm. Especially in the region of the critical point, extreme nonideahties occur and high compressibilities must be addressed. Several review papers and books discuss modeling of systems comprised of supercritical fluids and soHd orHquid solutes (rl,i4—r7,r9,i49,r50). 

Hm for steam + n-heptane calculated by the above method is shown by the dashed lines in figure 6. Considering the simplicity of the model and the fact that no adjustable parameters have been used, agreement with experiment is remarkable. For mixtures of steam + n-hexane, benzene and cyclohexane agreement with experiment is much the same. At low densities the model reproduces the curvature of the lines through the results better than the virial equation of state. The method fails to fully reproduce the downward turn of the experimental curves at pressures near saturation, but does marginally better in this region than the P-R equation with k. = -0.3. At supercritical temperatures the model seems to... 

Fig. 5.3. Locus of Hopf bifurcation points in K-fi parameter plane for thermokinetic model with the full Arrhenius temperature dependence and y = 0.21. The nature of the Hopf bifurcation point and, hence, the stability of the emerging limit cycle changes along this locus at k = 2.77 x 10 3. Supercritical bifurcations are denoted by the solid curve, subcritical bifurcations occur along the broken segment, i.e. at the upper bifurcation point for the lowest k. The stationary-state solution is unstable and surrounded by a stable limit cycle for all parameter values within the enclosed region. Oscillatory behaviour also occurs in the small shaded region below the Hopf curve, where the stable stationary state is surrounded by both an unstable and...

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