Saturated fluid density: correlation

In the original presentation of PC-SAFT parameters were correlated against vapour pressure and saturated liquid density data for 78 non-associating pure fluids and shown to work well in the description of mixture systems. Subsequently the equation has been successfully applied to the study of a wide range of industrially important fluids from simple binary mixtures involving hydro-carbons to associating fluids, " " pharmaceuticals, and asphaltenes, and, in particular, polymer systems. ... 

Current work is focused on the expansion of this concept with additional constraints for various properties with the intent of permitting equations to be fitted when the experimental data are extremely limited. This strategy implies the resulting equation of state will probably have the correct behaviour even though there might be only a few vapour pressures and saturated liquid densities for the regression. When additional measurements are made the results can be compared to values obtained from the equation of state to confirm or deny the predicted values. But as is the case with so many fluids where correlations have not been developed, these techniques provide methods to obtain equations of state for the vast number of fluids where equations were hitherto unavailable. 

Our method for the calculation of p(P,W) is a statistical mechanical approach known as mean-field theory (refs. 1 and 5). In this approach, the properties of the nitrogen within the graphite pore are obtained directly from the forces between the constituent molecules. The parameters of the intermolecular forces are determined by (a) ensuring that the saturation pressure and saturated liquid density of the model fluid are equal to the experimental values for nitrogen at its normal boiling point (77 K, which is the temperature at which the adsorption experiments are carried out) and (b) matching the model adsoq)tion on an isolated surface to the experimental t-curve of de Boer et al. (ref. 10). Having fixed the values for these parameters, the theory is then used to calculate model isotherms for pores of a variety of widths, which are then correlated (ref. 1) as a function of pressure and pore width to yield the individual pore isotherm p(P,W). Mean-field theory is known to become less accurate as the pore size is made very small (ref. 11) even for very small pores, however, this approach is more realistic than methods based on the Kelvin equation. 

Without the external field, the Stockmayer fluid near the wall exhibits symmetric density oscillations that die out as they reach the middle of the film. Near the surface, the fluid dipoles are oriented parallel to the walls. Upon turning on the electric field, the density profile of the Stockmayer fluid exhibits pronounced oscillations throughout the film. The amplitude of these oscillations increases with increasing field strength until a saturation point is reached at which all the fluid dipoles are oriented parallel to the field (perpendicular to the walls). The density profile remains symmetric. The dipole-dipole correlation function and its transverse [] and longitudinal [] com-... 

Supercritical fluid extraction is a potential technique for the purification of pharmaceutical products containing residual solvents. The solubilities of three inhibitors of inflammatory activity, Ketoprofen, Piroxicam, and Nimesulide, in supercritical CO2, measured using a dynamic saturation technique, were reported at pressures between 100 bar and 220 bar and at two temperatures 312.5 K and 331.5 K. The solubilities exhibit a clear dependence on the solvent density, and this has been used to provide a simple and precise correlation of the data (Macnaughton et al., 1996). 

Fig. 5. Density profile p z) for a fluid at a surface near a wetting transition. In the nun-wet state of the surface the local density p at the surface is less than the density piiq at the liquid branch of the coexistence curve describing gas-liquid condensation (upper part). Then the density profile p(z) decays to the gas density pgas in the bulk at a microscopic distance which is of the order of the correlation length f). In the wet state of the surface (lower part), the bulk gas is saturated must have the value of the gas branch of the coexistence curve) and /q > piiq, and a (macroscopic) liquid layer condenses at the surface, separated at large distances from the gas by a liquid-gas interface centered at z = h(x, y).

As the triggering process of CHF in flow boiling is very complex, CHF predictions rely heavily on empirical correlations based on dimensionless numbers derived from experimental CHF databases. These dimensionless numbers include parameters that influence the CHF values measured, such as mass velocity, subcooling at the channel inlet, fluid properties, heated length and the diameter of the channel. Due to differences in the apparent mechanisms, correlations are normally separately proposed for CHF under subcooled and under saturated conditions. Most of these correlations were developed based on databases for water and macroscale charmels because the majority of studies on CHF focused mainly on nuclear applications. Recently, this scenario has been changing because of the necessity to dissipate high power densities in microprocessors and power electronics and data for a wider variety of fluids are now appearing in the literature. 

Presenting the process model as a mass transfer correlation is also conunon. This requires an understanding of the process s physical properties, namely, the density and viscosity of the SC-CO2 and the mass diffusion of the solute in SC-CO2. Dimensionless numbers, namely, Reynolds (Re) (Equation 5.16), which is related to fluid flow Schmidt (Sc) (Equation 5.17), which is related to mass diffusivity Grashof (Gr) (Equation 5.18), which is related to mass transfer via buoyancy forces due to difference in density difference between saturated SC-CO2 with solute and pure SC-CO2 and Sherwood (Sh) (Equation 5.19), which is related to mass transfer, are important in these correlations. In supercritical extraction, natural convection is not significant (Shi et al., 2007) and in this case, Shp is related only to Re and Sc, as shown in Equation 5.19. 

For pure fluids, it is most common to represent the saturated vapor and saturated liquid transport properties as simple polynomial functions in temperature, although polynomials in density or pressure could also be used. Exponential expansions may be preferable in the case of viscosity (Bmsh 1962 Schwen Puhl 1988). For mixtures, the analogous correlation of transport properties along dew curves or bubble curves can be similarly regressed. In the case of thermal conductivity, it is necessary to add a divergent term to account for the steep curvature due to critical enhancement as the critical point is approached. Thus, a reasonable form for a transport property. 

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