4.1.1. P-V-T diagram calculation with equations of state

To describe the P-V-T diagram behavior, it is necessary to use precise equations of state (EOS) with specific parameters for pure substances. In the case of carbon dioxide, the equations of Bender [19] and Span and Wagner [37] are the most used. The Bender equation is presented below, where the parameters were determined from experimental PVT data of carbon dioxide. Table 1 shows the parameters of the Bender equation.


Table 1. Bender equation constants for CO2 [19].

$$P = \frac{T}{V} \left[ R + \frac{B}{V} + \frac{C}{V^2} + \frac{D}{V^3} + \frac{E}{V^4} + \frac{F}{V^5} + \left( G + \frac{H}{V^2} \right) \frac{1}{V^2} \exp\{-a\_{20} / \ \slash\!V^2\} \right] \tag{1}$$

where

4. High-pressure carbon dioxide properties

critical CO2. ( ) 50C, ( ) 60C, and ( ) 70C isotherms [17].

150 bar 190 bar

220 bar

of the item 2.2 for the isotherms T1 > T2 > T3 > T4 > T5.

4.1.1. P-V-T diagram calculation with equations of state

Table 1 shows the parameters of the Bender equation.

calculated by volumetric properties (P-V-T) using equation of state.

The influence of the density in the solvation power by the tunable operating conditions (P, T) is

LABP 700 800 900

Figure 8. Total anthocyanins compounds content in lyophilized açaí berry pulp before and after extraction with super-

 **Density (Kg/m3**

**)**

 **CO2**

220 bar

270 bar

320 bar

350 bar

420 bar

490 bar

Above the critical point, the supercritical extraction process can operate over a wide range of operating conditions (P, T) and the simplest density behavior can be obtained through an isotherm, being possible to select a wide range of operating pressures, as shown in Figure 3

The density is defined by the inverse of specific volume, and for practical purpose, could be

To describe the P-V-T diagram behavior, it is necessary to use precise equations of state (EOS) with specific parameters for pure substances. In the case of carbon dioxide, the equations of Bender [19] and Span and Wagner [37] are the most used. The Bender equation is presented below, where the parameters were determined from experimental PVT data of carbon dioxide.

the most important thermodynamic effect in the high-pressure fluid processes.

4.1. Thermodynamic properties

0

20

40

60

80

100

**Anthocyanins Content (mg/100g)**

120

140

160

180

220 Carbon Dioxide Chemistry, Capture and Oil Recovery

$$B = a\_1 - \frac{a\_2}{T} - \frac{a\_3}{T^2} - \frac{a\_4}{T^3} - \frac{a\_5}{T^4} \tag{2}$$

$$C = a\_6 + \frac{a\_7}{T} + \frac{a\_8}{T^2} \tag{3}$$

$$D = a\_{\phi} + \frac{a\_{10}}{T} \tag{4}$$

$$E = a\_{11} + \frac{a\_{12}}{T} \tag{5}$$

$$F = \frac{a\_{1\frac{\nu}{\nu}}}{T} \tag{6}$$

$$G = \frac{a\_{14}}{T^3} + \frac{a\_{15}}{T^4} + \frac{a\_{16}}{T^9} \tag{7}$$

$$H = \frac{a\_{1\overline{\gamma}}}{T^3} + \frac{a\_{1\overline{\mathfrak{s}}}}{T^4} + \frac{a\_{1\overline{\mathfrak{s}}}}{T^5} \tag{8}$$

$$a\_{20} \approx V\_C^2 \tag{9}$$

Figure 9 shows the calculation with Bender equation [19] of state for the P-V-T diagram isotherms and saturation curve, including an isotherm close to the critical temperature of the carbon dioxide. The calculations were performed using a Microsoft Excel spreadsheet. The equation presents accuracy in calculations when compared to data taken from IUPAC International Thermodynamic Table.

Figure 9. P-V-T diagram of carbon dioxide calculated with Bender EOS and compared to IUPAC data (symbols).

However, for applications of supercritical technology, it is necessary to calculate other thermodynamic properties. The thermodynamic properties of the pure solvent (density, enthalpy, and entropy) and the thermodynamic properties of the solute/solvent mixture, among which the equilibrium compositions, enthalpies, and mixing entropies, must be calculated in the operating conditions throughout the process. The cubic equation of state, also called Van der Waals type equation, represents an alternative, since the Bender-type equation described above is complex. In these cases, the cubic equations of state of Peng-Robinson (PR) [38] and Soave Redlich-Kwong (SRK) [39] are presented as the most commonly applied options in process simulations (Table 2). These equations of state use various thermodynamic properties and the following physical properties of the pure substance: critical pressure, critical temperature, and the acentric factor, which are tabulated, in the case of carbon dioxide.

Table 3 shows the calculated values of the carbon dioxide densities for some isotherms above the critical point using the equations of Peng-Robinson [38] and Soave-Redlich-Kwong [39]. The computational package PE 2000 developed by Pfohl et al. [40] was used for calculations. The results are compared to data taken from IUPAC International Thermodynamic Table and from NIST Chemistry Webbook (NIST Standard Reference Database). The Peng-Robinson equation of state presented the best results for the carbon dioxide density calculation in the conditions of pressure and temperature of Table 3 when compared with different databases.

Figure 10 shows the calculation with Peng-Robinson [38] equation of state for P-V-T diagram isotherms and saturation curve, including an isotherm close to the critical temperature of the carbon dioxide. The Peng-Robinson equation of state was able to describe all the phases of the carbon dioxide P-V-T diagram for the isotherms studied when compared to data taken from

Pressure (bar) Temperature (C/K) CO2 density (kg/m3

 36.85/310 617.3 563.0 683.4 686.5 847.8 763.8 855.5 857.0 941.1 846.6 921.5 922.7 46.85/320 418.1 390.6 444.6 449.4 781.5 707.9 801.5 803.1 845.3 763.8 848.0 849.5 893.0 805.9 882.4 883.7 963.2 868.2 933.2 934.4 66.85/340 260.5 246.2 258.1 258.6 643.2 589.3 678.7 680.5 731.7 666.7 751.9 753.3 794.4 721.8 800.6 801.8 882.9 799.6 866.7 867.9

)

PR SRK NIST IUPAC

Carbon Dioxide Use in High-Pressure Extraction Processes

http://dx.doi.org/10.5772/intechopen.71151

223

IUPAC International Thermodynamic Table.

Table 3. Carbon dioxide density calculated with different equations of state.

Cubic equations

Table 2. Cubic equations of state.


Table 2. Cubic equations of state.

However, for applications of supercritical technology, it is necessary to calculate other thermodynamic properties. The thermodynamic properties of the pure solvent (density, enthalpy, and entropy) and the thermodynamic properties of the solute/solvent mixture, among which the equilibrium compositions, enthalpies, and mixing entropies, must be calculated in the operating conditions throughout the process. The cubic equation of state, also called Van der Waals type equation, represents an alternative, since the Bender-type equation described above is complex. In these cases, the cubic equations of state of Peng-Robinson (PR) [38] and Soave Redlich-Kwong (SRK) [39] are presented as the most commonly applied options in process simulations (Table 2). These equations of state use various thermodynamic properties and the following physical properties of the pure substance: critical pressure, critical temperature, and

Figure 9. P-V-T diagram of carbon dioxide calculated with Bender EOS and compared to IUPAC data (symbols).

**Specific Volume (cm3**

100 1000 10000

**/mol)**

 SAT T=250 K T=310 K T=410 K T=510 K T=610 K Bender

Table 3 shows the calculated values of the carbon dioxide densities for some isotherms above the critical point using the equations of Peng-Robinson [38] and Soave-Redlich-Kwong [39]. The computational package PE 2000 developed by Pfohl et al. [40] was used for calculations. The results are compared to data taken from IUPAC International Thermodynamic Table and from NIST Chemistry Webbook (NIST Standard Reference Database). The Peng-Robinson equation of state presented the best results for the carbon dioxide density calculation in the conditions

the acentric factor, which are tabulated, in the case of carbon dioxide.

0

100

200

**Pressure (bar)**

300

400

222 Carbon Dioxide Chemistry, Capture and Oil Recovery

of pressure and temperature of Table 3 when compared with different databases.


Table 3. Carbon dioxide density calculated with different equations of state.

Figure 10 shows the calculation with Peng-Robinson [38] equation of state for P-V-T diagram isotherms and saturation curve, including an isotherm close to the critical temperature of the carbon dioxide. The Peng-Robinson equation of state was able to describe all the phases of the carbon dioxide P-V-T diagram for the isotherms studied when compared to data taken from IUPAC International Thermodynamic Table.

Under supercritical conditions, the thermal conductivity is influenced by both temperature and pressure and at constant pressure this property increases with increasing temperature, and on the other hand, at constant temperature, the thermal conductivity increases with pressure [42]. Carbon dioxide and other supercritical solvents have low viscosity and high diffusivity values. The viscosity and thermal conductivity of gases and liquids differ by one to two orders of magnitude, and the diffusivity values of gases and liquids differ by four orders of magnitude [41]. In the supercritical state, the substances have intermediate characteristics between the properties of a gas and a liquid, which contributes to more favorable hydrodynamic properties than the liquids, with diffusion coefficients close to those of a gas, which provides a fast and efficient mass transfer. Another feature of the supercritical fluid includes its low viscosity, which facilitates the penetration of the fluids into a solid matrix. Therefore, high diffusivity and low viscosity lead to a faster extraction time providing a dissolving power so that the

Carbon Dioxide Use in High-Pressure Extraction Processes

http://dx.doi.org/10.5772/intechopen.71151

225

Table 4 shows that supercritical fluids are characterized by transport properties (viscosity and diffusivity) between gases and liquids. The viscosity of a supercritical fluid is smaller than the viscosity of a gas and the diffusivity of the liquid is greater than the diffusivity of a supercritical fluid. In summary, the scheme of Figure 11 shows the basic properties of supercritical

Viscosity Pa s 10<sup>5</sup> 10<sup>4</sup> to 10<sup>5</sup> 10<sup>3</sup>

Unit Gas SCF Liquid

/s 10<sup>1</sup> 10<sup>3</sup> to 10<sup>4</sup> 10<sup>6</sup>

carbon dioxide, which become fundamental in high pressures extraction processes.

supercritical fluid is considered a solvent.

Table 4. Order of magnitude of transport properties.

Diffusivity cm2

Figure 11. Carbon dioxide properties.

Figure 10. PVT diagram of carbon dioxide calculated with Peng-Robinson EOS and compared to IUPAC data (symbols).

From a process point of view, the accuracy of the cubic equations of state was good, considering that the operating conditions commonly applied in CO2 extraction at high pressures are close to the values of temperature and pressure used in Table 3.

## 4.2. Other high-pressure carbon dioxide properties

The application of the high-pressure fluid extraction technologies in both laboratory and industrial scales requires not only the knowledge of the physical and thermodynamic properties of the solvent, but also requires the understanding of thermal and transport properties behavior. Among them, the most commonly cited are viscosity, diffusivity, thermal conductivity, and dielectric constant.

The dielectric constant describes the ability of a solvent to be polarized. The dielectric constant value is associated with the ability to dissolve electrolytes or polar compounds. The dielectric constant increases with temperature for most substances [41]. The dielectric constant of supercritical carbon dioxide with approximate value of a hydrocarbon alone does not characterize it as an important solvent; it only identifies it as a non-polar substance. Its solvation power is mainly related to the considerable increase of its density in the supercritical region with the properties as viscosity and diffusivity complementing the characteristics that makes supercritical carbon dioxide a differentiated solvent.

Under supercritical conditions, the thermal conductivity is influenced by both temperature and pressure and at constant pressure this property increases with increasing temperature, and on the other hand, at constant temperature, the thermal conductivity increases with pressure [42].

Carbon dioxide and other supercritical solvents have low viscosity and high diffusivity values. The viscosity and thermal conductivity of gases and liquids differ by one to two orders of magnitude, and the diffusivity values of gases and liquids differ by four orders of magnitude [41].

In the supercritical state, the substances have intermediate characteristics between the properties of a gas and a liquid, which contributes to more favorable hydrodynamic properties than the liquids, with diffusion coefficients close to those of a gas, which provides a fast and efficient mass transfer. Another feature of the supercritical fluid includes its low viscosity, which facilitates the penetration of the fluids into a solid matrix. Therefore, high diffusivity and low viscosity lead to a faster extraction time providing a dissolving power so that the supercritical fluid is considered a solvent.

Table 4 shows that supercritical fluids are characterized by transport properties (viscosity and diffusivity) between gases and liquids. The viscosity of a supercritical fluid is smaller than the viscosity of a gas and the diffusivity of the liquid is greater than the diffusivity of a supercritical fluid. In summary, the scheme of Figure 11 shows the basic properties of supercritical carbon dioxide, which become fundamental in high pressures extraction processes.


Table 4. Order of magnitude of transport properties.

From a process point of view, the accuracy of the cubic equations of state was good, considering that the operating conditions commonly applied in CO2 extraction at high pressures are

Figure 10. PVT diagram of carbon dioxide calculated with Peng-Robinson EOS and compared to IUPAC data (symbols).

**Specific Volume (cm3**

100 1000 10000

**/mol)**

 SAT T = 220 K T = 250 K T = 310 K T = 410 K T = 510 K T = 610 K Peng-Robinson

The application of the high-pressure fluid extraction technologies in both laboratory and industrial scales requires not only the knowledge of the physical and thermodynamic properties of the solvent, but also requires the understanding of thermal and transport properties behavior. Among them, the most commonly cited are viscosity, diffusivity, thermal conductiv-

The dielectric constant describes the ability of a solvent to be polarized. The dielectric constant value is associated with the ability to dissolve electrolytes or polar compounds. The dielectric constant increases with temperature for most substances [41]. The dielectric constant of supercritical carbon dioxide with approximate value of a hydrocarbon alone does not characterize it as an important solvent; it only identifies it as a non-polar substance. Its solvation power is mainly related to the considerable increase of its density in the supercritical region with the properties as viscosity and diffusivity complementing the characteristics that makes supercrit-

close to the values of temperature and pressure used in Table 3.

4.2. Other high-pressure carbon dioxide properties

ical carbon dioxide a differentiated solvent.

ity, and dielectric constant.

0

100

200

**Pressure (bar)**

300

400

224 Carbon Dioxide Chemistry, Capture and Oil Recovery

Figure 11. Carbon dioxide properties.
