T

Temperature

Figure 1. Pressure-temperature phase diagram of a pure substance.

Table 1. Ranges of Some Physical Properties Associated with Different Fluid States

Density, Diffusivity, kg/m3 m2/s

Viscosity, MPa.s

P = 101.3 kPa 0.6-2 (0.1-0.4) X 10"4 (1-3) X 10"4 T = 288-303 K

Supercritical

T = TJ3 = Pc 200-500 0.7 X 10"7 (1-3) X 10"4

T = T,P = 4PC 400-900 0.2 X 10"7 (3-9) X 10"4

Liquid

T = 288-303 K 600-1600 (0.22) x HT9 (0.2-3) X 10"2 Source: Ref. 11.

low solubility in the ordinary gaseous state of the same fluid. However, the solubility of compounds in a SCF also depends on solute and solvent properties. The dissolved compounds can be recovered from the fluid by decreasing the pressure or increasing the temperature, both of which reduce fluid density and allow it to be separated from the dissolved compound.

The reason SCF technology has been slow to find commercial applications has been due in part to the lack of available thermodynamic data to develop large-scale operations. Thermodynamic principles that can be used for quantitative and mathematical descriptions of solvent power of the SCF are models of phase equilibria and equations of state. For a process that involves the dissolution of a solute or a mixture of solutes from a solid matrix or a liquid mixture at constant temperature and pressure, the equilibrium conditions for the system would be given by fî"'d(T, P, xt) = ffCF(T, P, yi) (1)

ffod = food system component fugacity ~ffCF = SCF component fugacity where

T is the temperature, P is the pressure, %i is the mole fraction of solute in food, and yt is the mole fraction of solute in SCF phase.

Earlier studies have considered the food as an inert solid containing the soluble material. Then, the problem was treated similarly to the calculation of water activity (12). Later, it was confirmed that the solid matrix interacts with the soluble material; therefore, it is not appropriate to consider it as inert. For example, the solubility of pure caffeine in C02 can be 200 times larger than its solubility in C02 when dissolved in coffee beans (13). Therefore, for complex materials such as black pepper, clove buds, ginger rhizomes, and so on, an empirical treatment is advisable, since currently there is no equation available to describe their thermodynamic behavior. If, however, the system involves extraction or concentration of solutes present in a liquid phase, equation 1 can be used together with any appropriate cubic equation of state (EOS), such as Peng-Robinson (PR) or Soave-Redlich-Kwong (SRK). A simplified thermodynamic description of the calculation of solubility of a food system in C02 follows (14,15). The solute can be a mixture of substances like orange essential oil, a mixture of fatty acids or any similar system. For constant temperature and pressure, equation 1 is written for each component of the mixture, plus one for C02. Therefore, for a mixture with the following composition:

nc equations similar to equation 1 should be written, where Z* is the composition vector, Z* is the molar fraction of component in the mixture, and (nc — 1) is the number of substances from the original mixture that will be treated with C02.

The data required for SCF plant scale-up is the solubility of the mixture (food system) with the composition represented by equation 2 in the SC solvent for a given temperature and pressure. This is accomplished by combining equation 1 with an appropriate EOS capable of calculating the fugacity for a given temperature, pressure, and composition. From thermodynamics we have (14,16):

where ^ is the fugacity coefficient of component i, fi is the fugacity of component, i, T is the temperature, P is the pressure, xt is the mole fraction of component i, V is the specific volume of the mixture, and Z = PV/RT is the compressibility factor.

To evaluate the fugacity coefficients for all substances that form the mixture, the PR EOS for a mixture can be used:

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