Thermodynamic model of supercritical

Thermodynamic Modeling of Supercritical Fluid-Solute Phase Behavior... 

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). 

Sverjensky D. A. (1987) Calculation of the thermodynamic properties of aqueous species and the solubilities of minerals in supercritical electrolyte solutions. In Thermodynamic Modeling of Geological Materials Minerals, Fluids, and Melts, Reviews in Mineralogy (eds. I. S. E. Carmichael and H. P. Eugster). Mineralogical Society of America, Washington, DC, vol. 17, pp. 177-209. 

To date little or no thermodynamic modeling of the phase behavior of the ligand/C02 or metal chelate/C02 systems has been conducted. However, in order for supercritical fluid extraction to be considered as a possible replacement for organic solvent extraction, accurate models must be developed to predict the phase behavior of these systems to allow for both equipment and process design. Equation of state (EOS) modeling was chosen here to model the vapor-liquid equilibrium of the P-diketone/C02 systems studied. Cubic EOSs are the most widely used in modeling high pressure and supercritical fluid systems. This is... 

There are three essential elements that make up the thermodynamic foundations of supercritical fluids. These elements are experimental and identification techniques for elucidating the phase behavior, models for dense gases, and eomputation methods. 

This model has the 4-point geometry (Fig. lb), but a much more complicated functional form with parameters derived from ab initio quantum chemical calculations. The flexible version for this model (MCYL) has also been developed (Lie and dementi 1986). The MCY model was used by Impey et al. (1981) in their MD studies of the structure of water at elevated temperatures and high density, and by O Shea and Tremaine (1980) in the MC simulations of thermodynamic properties of supercritical water. It is well known, however, that this potential reproduces poorly the pressure at a given density (or the density at a given pressure). Even the... 

There are three essential elements that make up the thermodynamic foundations of supercritical fluids. These elements are experimental and identification techniques for elucidating the phase behavior, models for dense gases, and computation methods. 20.1.2.1.1 Experimental methods There are two basic approaches to experimental determination of the high-pressure phase behavior of a system, synthetic and analytic. In the synthetic approach, phase boundaries of a fixed (known) eomposition system are observed, usually visually, in a cell with sight windows, by manipulation of the system pressure and temperature. These experimental systems, one shown as Figure 20.1.10 allow determination of cloud point, dew point, bubble point, and eritieal point of partieular binary systems including polymers. Unlike earlier custom-... 

Various authors have considered the glassy state behaviour, and in particular the sorption of gases and supercritical fluids. The main dificulty is to find a thermodynamic model suitable for the description of the properties of the glassy state. Also, the normal equations of state specially developed for polymeric systems are not directly applicable to the non-equilibrium conditions of this state. 

Thermodynamic Model. Solubility of a condensed phase, y2, in a vapor phase at supercritical conditions (12) can be defined as ... 

The effect of temperature on retention has been described experimentally,(4-8) but the functional dependence of k with temperature has only recently been described.W A thermodynamic model was outlined relating retention as a function of temperature at constant pressure to the volume expansivity of the fluid, the enthalpy of solute transfer between the mobile phase and the stationary phase and the change in the heat capacity of the fluid as a function of temperature.(9) The solubility of a solid solute in a supercritical fluid has been discussed by Gitterman and Procaccia (10) over a large range of pressures. The combination of solute solubility in a fluid with the equation for retention as a function of pressure derived by Van Wasen and Schneider allows one to examine the effect of solubility on solute retention. 

In our research, we were led to characterise thermodynamically the mixtures composed of an organic compound and supercritical CO2 in a relatively wide range of temperatures, including several types of phase equilibrium. We looked for a single thermodynamic model which would be predictive (no parameters to adjust to the experimental data), valid for a wide range of temperatures and pressures, and also capable of representing solid-fluid and liquid-fluid equilibria. 

In front of the diversity and the complexity of supercritical fluid extraction, we dispose of all experimental and theoretical tools to compute and extrapolate pilot plant experimental data to an industrial unit. A lot of theoretical thermodynamic and kinetic data are now available, and experimental extractions carried out on pilot plants allow to build extrapolation models, from the very simple ones (like it is described in this case study) to the very sophisticated ones based on a numerical simulation software and taking into account hydrodynamic, thermodynamic and kinetic phenomena. 

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