Using the compressibility factor Z, equation 4 can be written as (17):

where Z = PV/RT, a' = (-1 + B), fi' = (A - 3B2 - 2B), / = (-AB +B2 + B3),A = a(T)P/(RT)2, andB = bP/RT. In general, the parameter a(T) is referred to as the attractive parameter and b as the volumetric parameter, and they are given by:

a(T) = 2 XiXjOij dij = ajti b = 2 XiXjbij bu = bh, =

where % is the attractive parameter for binary i-j, by is the volumetric parameter for the binary i-j, au is the at-

tractive parameter for component i, bu is the volumetric parameter for component i, ka.. is the attractive binary interaction parameter, and kb. . is the volumetric binary interaction parameter. The pure components' attractive and volumetric parameters are calculated using the critical properties of the solute. For instance (17):

Peng-Robinson's EOS

where w is the acentric factor.

To solve equation 1, which is a nonlinear problem, a nonlinear trial-and-error solution is required. The objective function to be minimized is defined accordingly with the available experimental data. The following information is needed: (1) the system temperature and pressure, (2) the composition vector Z*, and (3) the matrices of binary attractive and volumetric interaction parameters given by equations 6 and 7. This should include binary systems such as component-iVC02 and component-t/ component-^'. Then, there will be nc binary parameters of the kind component i-C02, plus (nc)2/2 parameters of the kind component-i/component-J. Binary liquid-SC and liquid-vapor equilibrium data are required to evaluate these parameters. Currently, scarce information is available in the literature for systems involving foods; therefore, some difficulties can be anticipated to solve the preceding equations. Finally, one should be aware that to solve equation 1, equation 4 is solved twice, once for each phase in equilibrium.

The procedure just described was used to evaluate the solubility of orange essential oil in C02 (15,16). The problem was treated as a dewpoint problem; therefore, the oil solubility in C02 was considered to be the amount of carbon dioxide required to dissolve a given oil sample. Defining a as the essential oil fraction in the final SC mixture (essential oil and C02), the composition vector in the C02 rich phase (SCF) when the oil phase is completely dissolved is given by:

The solubility of the essential oil in the SC phase will be:

yco2MCo2 (1 - a)MCo2

where Sb is the solubility of the oil (mg of oil/g of C02), /nf are the mass fractions of essential oil components, are the molecular mass of essential oil components, and y/ are molar fractions of essential oil components, respectively. Figure 2 shows the experimental and calculated solubilities of the orange oil (oil-phase) in C02 made using both

Peng-Robinson's EOS

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