New Experimental Data and Modeling of the Solubility of Compounds

Article pubs.acs.org/IECR

New Experimental Data and Modeling of the Solubility of Compounds in Supercritical Carbon Dioxide Zhao Tang,† Jun-su Jin,*,† Ze-ting Zhang,† and Hong-tao Liu‡ †

College of Chemical Engineering and ‡College of Science, Beijing University of Chemical Technology, 15 Beisanhuan East Road, Beijing 100029, China ABSTRACT: The solid solubility of o-nitrobenzoic acid in supercritical carbon dioxide (SCCO2) was measured using a dynamic-flow technique at 308, 318, and 328 K and in the pressure range of 10.0−21.0 MPa. The experimental solubility data of the solute in SCCO2 were correlated by six different theoretical semiempirical models [the Chrastil, Kumar and Johnston, Sung and Shim (SS), Méndez-Santiago and Teja, Bartle−Clifford−Jafar−Shilstone, and Jouyban−Chan−Foster models] with the average absolute relative deviation from 4.30% to 6.61%. The correlated results indicate that the SS model provides the best fit. Solubility data from 54 different compounds of different functional groups (including carboxyl, amino, chain alkyl, heterocycle, azo, diglycolic, and anthraquinone) were collected from the literature to compare and evaluate these models. The division criteria of temperature, pressure, mole fraction solubility of the solutes, and number of experimental data points were established. The predictive capability and applicability of these models for different types of solutes and at different conditions are demonstrated in this paper.

1. INTRODUCTION Supercritical fluids have been widely applied in a variety of applications in the past few decades, such as food processing, pharmaceutical industries, separations, and chemical reactions, because of their unique properties, including their diffusivities between those of gases and liquids, compressibilities compared to those of gases, densities compared to those of liquids, and negligible surface tension, which results in more efficient mass transfer and strong solvent power.1 Supercritical carbon dioxide (SCCO2) is commonly used as a supercritical fluid because of its moderate critical properties (Tc = 304 K; Pc = 7.38 MPa), and it is nontoxic, nonflammable, nonexplosive, and inexpensive.2 In chemical processes (such as extractions and chemical reactions), it is crucial to obtain the solubility data of compounds in SCCO2 in order to determine the proper operating conditions to achieve the best outcome. Many recent studies have reviewed the solubility data of compounds in SCCO2.3−5 However, more experimental solubility data of compounds in SCCO2 are still needed. o-Nitrobenzoic acid is an intermediate of pharmaceuticals, dyestuffs, and organic synthesis and has been reported in several studies.6−9 However, no solubility data of this compound in SCCO2 have been listed in previous literature. Consequently, it is important to measure the solubility of o-nitrobenzoic acid in SCCO2. In addition, our research group has been studying the solid solubility of benzoic acid with one nitro functional group (including para and meta positions) and two nitro functional groups.10−12 In this paper, benzoic acid with one nitro functional group in the ortho position was investigated to further study the effect of the quantity and position of the nitro functional group on the solubility. Because the experimental determination of the solubility of compounds in SCCO2 at various temperatures and pressures is time-consuming, modeling of the solubility data in SCCO2 is © 2012 American Chemical Society

essential. Models used for correlating the solubility data can be broadly classified as equation of state (EOS)-based and semiempirical models.13,14 EOS-based models, like cubic equations of state or perturbed equations, need large and complicated computational methods and knowledge of the solid properties (macroscopic critical properties and sublimation pressure are needed for cubic equations of state and molecular parameters for perturbed equations). These data are normally not available for many complex structural compounds, which are calculated by group contribution methods.15,16 Because of several drawbacks, an error is produced in their estimation. On the other hand, the most common semiempirical models are based on providing a correlation between the solubility and density; hence, they are referred to as density-based models, which only need available independent variables like pressure, temperature, and density of SCCO2 instead of solid properties. They are based on simple error minimization. The only drawback is the semiempirical character, which means that solubility data are needed.17 Recently, many semiempirical models, such as the Chrastil,18 Adachi and Lu (AL),19 del Valle and Aguilera,20 Sparks−Hernandez−Estévez (SHE),21 Kumar and Johnston (KJ),22 Sung and Shim (SS),23 Bartle−Clifford− Jafar−Shilstone (BCJS),24 Méndez-Santiago and Teja (MST),25 and Jouyban−Chan−Foster (JCF) models,26 are used for correlating the solubility data of compounds in SCCO2. In these semiempirical models, some were deduced from thermodynamic theories, such as the Chrastil, KJ, SS, BCJS, MST, and JCF models, which have theoretical backgrounds. In contrast, some were the empirical modification of original Received: Revised: Accepted: Published: 5515

July 26, 2011 March 6, 2012 March 27, 2012 March 27, 2012 dx.doi.org/10.1021/ie2016224 | Ind. Eng. Chem. Res. 2012, 51, 5515−5526

Industrial & Engineering Chemistry Research

Article

with a heating electric coil so that its temperature and pressure could reach to the operating condition. SCCO2 entered into a high-pressure equilibrium cell with an available volume of 150 mL from the bottom consecutively, which was loaded with 40 or 50 g of packed solute mixed with glass beads and stainless steel sintered disks at both ends to prevent physical entrainment of the undissolved solute. The high-pressure equilibrium cell was immersed in a constant-temperature stirred water bath with preheating coils (Chongqing Yinhe Experimental Instrument Corp., model CS-503), which was controlled to ±0.5 K by a temperature controller. The temperature and pressure in the cell was measured by a calibrated internal platinum resistance thermometer (Beijing Chaoyang Automatic Instrument Factory, model XMT) and a calibrated pressure gauge (Heise, model CTUSA), respectively. The uncertainty for temperature measurement is ±0.1 K, and that for pressure is ±0.05 MPa. SCCO2 flowed out from the top of the equilibrium cell through a decompression sampling valve (wrapped with heating coils), and the solid compound was separated from CO2 and collected by two U-shaped tubes in turn. From experimental observation, the bulk of the solute was collected in the first U-shaped tube and scarcely precipitated in the second U-shaped tube. o-Nitrobenzoic acid is very soluble in water. As a result, deionized water was used to wash the analytes in the U-shaped tubes. The total volume of CO2 released during the experiment was measured by a calibrated wet-gas flowmeter (Changchun Instrument Factory, model LML-2) with an uncertainty of ±0.01 L at room temperature and atmospheric pressure. To ensure the reliability of the experimental procedure, the equilibrium time and a suitable flow rate of CO2 were determined. The flow rate experiments were carried out with a rotated flowmeter. The results showed that when the flow rate of CO2 is in the range of 0.3−1.0 L·min−1, the equilibrium of the system is maintained. The average flow rate of 0.6 L·min−1 in this work was adopted. At a suitable flow rate of CO2, the solubility of the solute was measured after 20, 30, 40, 50, and 60 min, respectively. The results showed that the solubility was roughly the same after 30 min, which shows that the system had reached equilibrium. As a result, the entire data were measured after 30 min. 2.3. Analytical Methods and Solubility Measurements. The UV spectrophotometer (UNICO, model UV2100) method was used to analyze the amount of solute collected in the U-shaped tubes. The reference solution was deionized water. The maximum UV absorption λmax of o-nitrobenzoic acid was detected at a wavelength of 268 nm.

models, such as the AL and SHE models, which do not have theoretical backgrounds. An excellent mathematical modeling of the solubility data in SCCO2 could provide a better understanding of the dissolution phenomenon and can be used to predict the solubility at interested pressures and temperatures after measurement of a minimum number of experimental data, which could speed up the development of SCCO2 technology.26,27 Thus, it is necessary to propose one semiempirical model on the basis of theoretical deduction to predict the solubility data of compounds in SCCO2 more accurately. In this work, the solubility of o-nitrobenzoic acid in SCCO2 was reported. These measurements were carried out over the temperature range of 308−328 K and at pressures ranging from 10.0 to 21.0 MPa. The experimental solubility data were correlated by six different theoretical semiempirical models (the Chrastil, KJ, SS, BCJS, MST, and JCF models). Solubility data from 54 different compounds of different functional groups (including carboxyl, amino, chain alkyl, heterocycle, azo, diglycolic, and anthraquinone) were taken from the literature in order to propose the most suitable model for different types of compounds at different experimental conditions.

2. EXPERIMENTAL SECTION 2.1. Chemicals. Carbon dioxide (CO2, CAS 124-38-9; more than 99.9% mass fraction) was purchased from Beijing Praxair Industrial Gas Co., Ltd. o-Nitrobenzoic acid (Figure 1;

Figure 1. Chemical structure of o-nitrobenzoic acid.

C7H5NO4, CAS 552-16-9) with an assessed minimum mass purity of 99.0% (analytical purity) was purchased from Sinopharm Chemical Reagent Beijing Co., Ltd. All chemicals were used without further purification. 2.2. Experimental Apparatus and Procedures. The solubility of o-nitrobenzoic acid in SCCO2 was measured using a dynamic-flow technique with ultraviolet spectrophotometer analysis. A schematic diagram of the experimental apparatus is shown in Figure 2. CO2 supplied to a high-pressure surge flask from a cylinder was pressurized by the compressor (Nova, model 5542121). High-pressure CO2 entered into a preheating and mixing cell

Figure 2. Schematic diagram of the experimental apparatus: 1, CO2 cylinder; 2, compressor; 3, high-pressure surge flask; 4, pressure regulating valve; 5, preheating and mixing cell; 6, high-pressure equilibrium cell; 7, decompression sampling valve; 8, U-shaped tube; 9, rotated flowmeter; 10, wet-gas flowmeter; 11, back-pressure valve; 12, safety valve; 13, pressure gauge; 14, constant-temperature stirred water bath; 15, preheating coils; 16, temperature controller; 17, thermometer; 18, heating coils. 5516

dx.doi.org/10.1021/ie2016224 | Ind. Eng. Chem. Res. 2012, 51, 5515−5526


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Table 1. Mole Fraction Solubility (y2) of o-Nitrobenzoic Acid in SCCO2 T = 308 K P (MPa)

ρ1 (g·L−1)

10.0 12.0 15.0 18.0 21.0

714.84 768.42 816.06 848.87 874.40

T = 318 K 106y2

ρ1 (g·L−1)

± ± ± ± ±

502.57 659.73 743.17 790.18 823.71

3.74 5.13 6.20 7.72 8.34

0.02 0.02 0.05 0.06 0.08

SM1 SM1 + ρM 2

ρ1 (g·L−1)

± ± ± ± ±

326.40 506.85 654.94 724.13 768.74

2.20 6.67 11.28 14.27 18.42

0.03 0.03 0.05 0.07 0.09

106y2 1.52 6.96 17.00 27.01 35.61

± ± ± ± ±

0.02 0.03 0.06 0.08 0.15

As shown in Table 1 and Figure 3, the equilibrium solubility increases with increasing pressure at three temperatures (308, 318, and 328 K). It can be attributed to the increase of the solvent’s density with increasing pressure and the specific stronger interactions between the solute and solvent molecules at higher pressure. The crossover pressure region has been observed, as shown in Figure 3. It is approximately from 10.7 to 11.7 MPa. The crossover phenomena could be attributed to the competition between the solute’s vapor pressure and the solvent’s density, whose dependences on the temperature are in opposite directions. Below the crossover pressure region, the density effect, sensitive to the solute’s vapor pressure, is dominant so that the solute is more soluble at lower temperature. However, above the crossover pressure region, the solute’s vapor pressure becomes dominant at higher temperature and the density of the solvent turns less sensitive to the solute’s vapor pressure. At the crossover point, the effects of these two competitive factors on the solid solubility balance each other. 3.2. Experimental Solubility Data Correlation. In this work, six different theoretical semiempirical models (the Chrastil, KJ, SS, BCJS, MST, and JCF models) were used to correlate the experimental results. The Chrastil Model. The Chrastil model18 is one of the most frequently used density-based models and relates the solute solubility (S, g·L−1) in SCCO2, the density of SCCO2 (ρ1, g·L−1), and temperature (T, K) as

A calibration curve was used to establish the concentration of the solute with a regression coefficient better than 0.9995. The solubility of the solute was determined by the concentration of the solute and the flow volume of SCCO2, and the solubility of the solute in mole fraction was calculated according to the following formula: y2 =

T = 328 K 106y2

(1)

where y2 is the mole fraction solubility of the solute, S is the solubility of the solute (g·L−1), M1 and M2 are the molecular weights of CO2 and the solute (g·mol−1), respectively, and ρ is the density of CO2 at room temperature and normal atmospheric pressure (g·L−1). The reliability of the experimental apparatus was verified by measurement of the solubility of the compounds in our previous work.28,29 Each data point reported in this work was the average of at least three replicated sample measurements to ensure accuracy. The uncertainty of each measurement was within ±5%.

3. RESULTS AND DISCUSSION 3.1. Experimental Data. The experimental mole fraction solubility data of o-nitrobenzoic acid in SCCO2 at 308, 318, and 328 K over the pressure range of 10.0−21.0 MPa are listed in Table 1. Figure 3 shows the solubility curve of o-nitrobenzoic

ln S = A 0 ln ρ1 +

A1 + A2 T

(2)

where A0−A2 are the adjustable parameters that can be estimated from experimental solubility data in SCCO2. Chrastil18 assumed that in an ideal case one molecule of a solute X associates with A0 molecules of a gas Y to form one molecule of a solvated complex XYA0 in equilibrium with the system X +A0Y ⇌ XYA0. Thus, A0 is an association parameter that describes the number of SCCO2 molecules in the solvated complex, to the total heat ΔHtotal of the solute (heat of solvation ΔHsol., plus heat of sublimation ΔHsub.), defined as ΔHtotal/R, where R is the gas constant, and A2 is a function of the molecular weights of the solute and SCCO2, defined as ln(M2 + A0M1) + q − A0 ln M1, where q is constant. In this work, to justify the selection of the correlation models on a more easily comparable basis, S (g·L−1 solute/SCCO2) in the Chrastil model is transformed to y2 (mole fraction solubility of solute), and the parameters of the model are redefined. According to eq 1, the solubility S can be written as follows:

Figure 3. Experimental solubility of o-nitrobenzoic acid in SCCO2 (y2) at different temperatures as a function of the pressure: (■) T = 308 K; (●) T = 318 K; (▲) T = 328 K. The solid lines represent the calculated solubility values from the SS model (eq 8).

acid in SCCO2. The density of SCCO2 obtained from the NIST fluid property database is also shown in Table 1. It can be seen that the mole fraction solubility of o-nitrobenzoic acid at 328 K and 21.0 MPa reaches a value of up to 35.61 × 10−6.

S= 5517

ρM 2y2 M1(1 − y2 )

(3)



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Table 2. Correlated Results of Six Different Semiempirical Models for the Solubility of o-Nitrobenzoic Acid in SCCO2 model

correlated parameters

AARD (%)

Chrastil KJ SS BCJS MST JCF

A1 = −9656.6; A2 = −5.9642; A3 = 3.7773 B0 = 6.7361 × 10−3; B1 = −10234.8; B2 = 15.7774 C0 = −10.7023; C1 = 4706.3; C2 = −40912.2; C3 = 90.183 D0 = 8.7780 × 10−3; D1 = −12381.8; D3 = 23.7872 E0 = 2.8381; E1 = 30.4437; E2 = −14537.5 F0 = −19.6265; F1 = −1.6832; F2 = 2.8638 × 10−3; F3 = 4.7292 × 10−3; F4 = −1.1930 × 10−1; F5 = 1.9345

5.91 6.61 4.30 5.08 4.68 6.03

Considering that, in the supercritical state, ρ can be substituted by ρ1. Combining eqs 2 and 3, one gets ln

ρ1M 2y2 M1(1 − y2 )

= A 0 ln ρ1 +

A1 + A2 T

pressure. In addition, a corrective parameter with a reference density should be introduced. Therefore, considering these latest constraints and eq 9, it is possible to describe the BCJS model as follows: ⎛ P ⎞ D ln⎜⎜y2 ref ⎟⎟ = D0(ρ1 − ρref ) + 1 + D2 T P ⎝ 2 ⎠

(4)

Simplifying eq 4, one gets ⎛ M ⎞ A = ⎜A 0 − ln 2 ⎟ln ρ1 + 1 + A 2 ln M T 1 − y2 ⎝ 1⎠ y2

In eq 10, ρref is a reference density (a value of 700 g·L−1 was chosen) and P2ref is the reference pressure, typically taken as 0.1 MPa. In this model, the parameter D1 is related to the enthalpy of sublimation of the solid solute (ΔHsub) by the expression ΔHsub = −RD1. Equation 10 can be transformed as

(5)

The term 1 − y2 approximately equals 1 because the mole fraction solubility of the solute y2 is much smaller than 1. In addition, the term A0 − ln(M2/M1) can be redefined as a new association parameter A3. Therefore, eq 5 becomes A ln y2 = A3 ln ρ1 + 1 + A 2 T

ln(y2 P) = D0ρ1 + (6)

B1 + B2 T

ln(y2 P) = D0ρ1 +

(7)

D1 + D3 T

⎛ P ⎞ T ln E = T ln⎜⎜y2 sub ⎟⎟ = ln E0′ρ1 + E1′ ⎝ P2 ⎠

(12)

(13)

In eq 13, E is the enhancement factor. Méndez-Santiago and Teja tested the validity of this expression. However, it is necessary to predetermine the sublimation pressures P2sub. Its value is substituted by a Clausius−Clapeyron-type expression. Therefore, Méndez-Santiago and Teja25 proposed a modified model:

(8)

where C0−C3 are adjustable parameters. The BCJS Model. Bartle et al.24 related the enhancement factor (ratio of the actual solubility to the ideal solubility) of the solute and density of the solvent: ⎛ P ⎞ ln⎜⎜y2 sub ⎟⎟ = D0ρ1 + D0′ ⎝ P2 ⎠

(11)

Equation 12 is used to correlate the solubility data in this work. The MST Model. Another density-based model was proposed by Mendez-Santiago and Teja.25 This model comes from the linear relationship between T ln(E) and ρ1, which was derived from the theory of dilute solutions.

where B0−B2 are adjustable parameters. The parameter B1 is the same as the parameter A1 of the Chrastil model, defined as ΔHtotal/R. The SS Model. Sung and Shim23 discussed the temperature effects on the solubility and pointed out that in the log−log plot the solubility isotherms were linear but their slopes were decreasing with temperature. Therefore, they modified the KJ model containing temperature effects into another form as follows: ⎛ C ⎞ C ln y2 = ⎜C0 + 1 ⎟ ln ρ1 + 2 + C3 ⎝ ⎠ T T

D1 + (D2 − D0ρref + ln P2 ref ) T

Because the reference conditions for the density (ρref.) and pressure (P2ref) are constant, the term D2 − D0ρref + ln P2ref can be redefined as a new association parameter D3, and eq 11 is simplified as

Equation 6 is used to correlate the solubility data in this work. The KJ Model. Kumar and Johnston22 pointed out that the linear relationships observed between ln y2 and ln ρ1, and in some cases between ln y2 and ρ1, are system-dependent, and neither can be validly generalized. Similar to eq 2, the linear expression between ln y2 and ρ1 could be given as ln y2 = B0 ρ1 +

(10)

T ln(y2 P) = E0ρ1 + E1T + E2

(14)

where E0, E1, and E2 are adjustable parameters. All other variables in eq 14 are the same as those defined in eq 13. The JCF Model. Jouyban et al.26 considered the nonlinear relationship between ln y2 and the pressure in isothermal conditions, the nonlinear relationship between ln y2 and the temperature in isobaric conditions, and the linear relationship between ln y2 and ln ρ1 in a certain range of pressure and temperature. They proposed another density-based model. Though the use of this model was low,17 the model was in good agreement with experimental solubility data, which can

(9)

In eq 9, P is the pressure (MPa), the parameter D0 is related to the solvation of the solute, and D0′ comes from the vapor pressure of the solute. To solve some of the inconveniences that involve the estimation of the sublimation pressure P2sub, Bartle et al.24 changed the sublimation pressure with a reference 5518



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be confirmed in the ensuing text. The JCF model can be written as 2 ln y2 = F0 + FP 1 + F2P + F3PT + F4

T + F5 ln ρ1 P

(15)

where F0−F5 are adjustable parameters. The average absolute relative deviation (AARD) of the model from experimental data was calculated according to the following formula: AARD (%) =

100 N

N

∑ 1

|y2 cal − y2 exp | y2 exp

(16)

y2cal

where is the calculated value of the mole fraction solubility of the solute, y2exp is the experimental value of the mole fraction solubility of the solute, and N is the number of experimental data points. The name and version of the software that we used to fit the experimental and calculated data was MS-Excel 2007. The correlated results and optimal parameters of the experimental solubility data using six different semiempirical models are listed in Table 2. As shown in Table 2, the application of these models to correlate the solubility proved to be successful. Among these models, the SS model gave the best fit to the solubility data with a AARD value of 4.30. On the contrary, the AARD value of the KJ model is 6.61, which is the highest in all of the models. Furthermore, the solubility data of the solute in SCCO2 are better correlated by the SS, BCJS, and MST models than the Chrastil, KJ, and JCF models. In a comparison between the expressions of the models, this may result from the complexity between the solubility of the solute and the density of SCCO2. By means of transformation of the expressions of the models, the Chrastil, KJ, and JCF models suggest that the relationship between the logarithm of solubility (ln y2) and the solvent’s density (ln ρ1 or ρ1) is linear, while the SS, BCJS, and MST models considered the temperature (T) and pressure (P) effects on the solubility (y2). In particular, the SS model indicated the temperature effects on the log−log solubility−density relationship. Because of the fact that the solvent’s density (ρ1) is a function of the temperature (T) and pressure (P), the relationship between the logarithm of solubility (ln y2) and the solvent’s density (ln ρ1 or ρ1) in these three models is more complex than linear. Likewise, the correlated results also indicate differentiation of these models: the AARD values of the Chrastil, KJ, and JCF models are from 5.91 to 6.61; the AARD values of the BCJS and MST models are 4.68 and 5.08, respectively; the AARD value of the SS model is 4.30. Consequently, the SS model is more suitable to correlate the solubility data of o-nitrobenzoic acid in SCCO2. Figure 3 shows the calculated solubility values using the SS model. Sung and Shim23 discussed the temperature effects on the solubility and pointed out that in the log−log plot the solubility isotherms were linear but their slopes were decreasing with temperature. Figure 4 shows the log−log relationship between the experimental solubility of o-nitrobenzoic acid in SCCO2 (y2) and the density of SCCO2 (ρ1) at different temperatures. Likewise, the slopes of the solubility isotherms in Figure 4 are not parallel to each other but are decreasing gradually with increasing temperature. In addition, as stated by the Chrastil, KJ, and BCJS models, the respective coefficients of the Chrastil and KJ models can be related to the total heat of reaction (ΔHtotal), while the heat of

Figure 4. log−log relationship between the experimental solubility of o-nitrobenzoic acid in SCCO2 (y2) and the density of SCCO2 (ρ1) at different temperatures: (■) T = 308 K; (●) T = 318 K; (▲) T = 328 K. The solid lines represent the calculated solubility values from the SS model (eq 8).

sublimation (ΔHsub) can be estimated from the coefficients of the BCJS model. The heat of solvation (ΔHsol) is calculated by subtracting ΔHsub from ΔHtotal. The values of ΔHtotal, ΔHsub, and ΔHsol of o-nitrobenzoic acid, presented in Table 3, were calculated from the correlated results. Table 3. Total Heat of Reaction, Heat of Sublimation, and Heat of Solvation Calculated for o-Nitrobenzoic Acid

a

ΔHatotal (kJ·mol−1)

ΔHbtotal (kJ·mol−1)

−80.3

−85.1

ΔHcsub (kJ·mol−1)

ΔHdsol (kJ·mol−1)

102.9

−185.6

b

Obtained from the Chrastil model. Obtained from the KJ model. Obtained from the BCJS model. dObtained from the difference between the ΔHcsub and (ΔHatotal + ΔHbtotal)/2. c

Figure 5. Solubility of o-nitrobenzoic acid in SCCO2. Symbols represent the experimental solubility: (■) T = 308 K; (●) T = 318 K; (▲) T = 328 K. The solid line represents the solubility correlation from the MST model (eq 14). 5519



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Table 5. Details of Solubility Data (Temperature T, Pressure P, Mole Fraction Solubility of the Solutes y2, and Number of Experimental Data Points N)

Table 4. Details and References of Compounds no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

solute 3,5-dinitrobenzoic acid 3-nitrobenzoic acid 4-nitrobenzoic acid 4-methylbenzoic acid 4-methoxybenzoic acid 4-aminobenzoic acid 4-methoxyphenylacetic acid hexadecanoic acid octadecanoic acid mandelic acid p-toluenesulfonamide sulfanilamide salicylamide n-phenylacetamide 2-methyl-N-phenylacetamide 4-methyl-N-phenylacetamide n-(4-ethoxyphenyl)ethanamide acetamide acrylamide cholesterol β-carotene lycopene naproxen anastrozole phenylbutazone lovastatin rosuvastatin dutasteride flurbiprofen solvent brown 1 disperse orange 3 disperse blue 79 disperse yellow 54 disperse red 73 disperse yellow 119 disperse yellow 16 disperse yellow 232 C.I. disperse blue 56 C.I. disperse violet 1 C.I. disperse yellow 82 1-[(4-aminophenyl)azo]-2-naphthol C.I. disperse orange 30 1,4-bis(n-alkylamino)-9,10-anthraquinone 1,4-bis(octylamino)-9,10-anthraquinone didecyl-2,2′-oxidiacetate didodecyl-2,2′-oxidiacetate diundecyl-2,2′-oxidiacetate N-hexyl-N-(4-pyridyl) pentadecafluorooctanamide N-hexyl-N-(4-pyridyl)octanamide 2,2′-Oxybis(N,N-diethylacetamide) 2,2′-oxybis(N,N-dibutylacetamide) 1-amino-2-methyl-9,10-anthraquinone 1,4-dihydroxy-9,10-anthraquinone 1-hydroxy-4-(prop-2′-enyloxy)-9,10anthraquinone

formula

ref

C7H4N2O4 C7H5NO4 C7H5NO4 C8H8O2 C8H8O3 C7H7NO2 C9H10O3 C16H32O2 C18H36O2 C8H8O3 C7H9NO2S C6H8N2O2S C7H7NO2 C8H9NO C9H11NO C9H11NO C10H13NO2 C2H5NO C3H5NO C27H46O C40H56 C40H56 C14H14O3 C17H19N5 C19H20N2O2 C24H36O5 C22H28FN3O6S C27H30F6N2O2 C15H13FO2 C16H14N4 C12H10N4O2 C24H27BrN6O10 C18H11NO3 C18H16N6O2 C15H13N5O4 C16H14N4O C20H17ClN2O3 C14H9BrN2O4 C14H10N2O2 C20H19N3O2 C16H13N3O C19H17N5O4Cl2 C16H12N2O2 C30H40N2O2 C20H42O5 C24H50O5 C22H46O5 C19H17F15N2O4

11 11 10 30 31 32 33 34 34 35 36 36 37 38 38 38 39 40 40 41 42 43 44 45 37 46 46 47 48 49 50 50 51 52 52 53 54 55 56 57 57 58 59 60 61 61 62 63

C19H32N2O4 C12H24N2O3 C20H40N2O3 C15H11NO2 C14H8O4 C17H12O4

63 64 64 65 66 66

no.

Tmin/K to Tmax/K

Pmin/MPa to Pmax/ MPa

y2,min × 104 to y2,max × 104

N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

308.00−328.00 308.00−328.00 308.00−328.00 313.20−333.20 308.20−328.20 308.00−328.00 308.20−328.20 308.00−328.00 308.00−338.00 308.15−328.15 308.00−328.00 308.00−328.00 308.20−328.20 308.20−328.20 308.20−328.20 308.20−328.20 308.00−328.00 308.20−323.20 308.20−323.20 313.15−333.15 313.20−333.20 323.15−353.15 313.10−333.10 308.00−348.00 308.20−328.20 308.00−348.00 308.00−348.00 308.00−348.00 303.15−323.15 353.20−393.20 353.20−393.20 353.20−393.20 353.20−393.20 343.00−383.00 343.00−383.00 323.15−383.15 308.00−348.00 353.15−393.15 353.20−393.20 353.15−373.15 353.15−373.15 313.15−393.15 310.00−340.00 310.10−324.70 313.00−333.00 313.00−333.00 343.00−363.00 313.00−343.00 313.00−333.00 313.00−333.00 313.00−333.00 308.00−348.00 308.15−348.15 308.15−348.15

10.00−21.00 10.00−21.00 8.00−21.00 11.00−24.60 14.08−24.60 8.00−21.00 11.61−23.61 12.85−22.65 12.85−22.65 10.10−23.06 11.00−21.00 11.00−21.00 10.00−22.00 10.44−22.50 12.16−22.50 12.16−22.50 9.00−19.00 9.00−40.00 9.00−40.00 10.00−25.00 12.00−28.00 20.00−40.00 8.96−19.31 12.20−35.50 10.00−22.00 12.16−35.46 12.16−35.46 12.20−35.50 10.76−22.12 18.10−30.40 16.00−28.00 18.00−30.00 15.00−30.00 12.00−28.00 12.00−28.00 10.00−25.00 12.10−35.50 15.00−30.00 15.00−30.00 20.00−30.00 20.00−35.00 11.28−32.57 8.80−18.80 8.80−15.00 9.30−15.20 9.20−14.50 13.70−18.10 8.80−14.40 9.30−13.40 8.70−13.30 8.80−13.10 12.20−35.50 12.16−40.54 12.16−40.54

0.0044−0.0421 0.0144−1.0986 0.20−3.22 0.430−7.02 281−906 0.01302−0.05661 0.47−6.34 2.58−21.40 0.74−11.10 0.27−29.04 0.222−0.512 0.00195−0.00433 0.0845−2.10 0.293−4.562 0.197−4.633 0.384−4.802 0.091−0.428 2.383−31.62 1.193−16.31 0.0230−1.45 0.0003−0.00580 0.00651−0.01712 0.019−0.318 0.036−3.799 0.199−26.5 0.11−1.14 0.03−2.44 0.001−1.607 0.242−1.584 0.0129−0.208 0.0145−0.174 0.00520−0.499 0.00194−0.103 0.030−0.31 0.0080−0.20 0.009245−2.694 0.0020−0.0770 0.00033−0.0258 0.00053−0.0349 0.0060−0.0414 0.0095−1.16 0.0801−0.8432 0.00282−0.0287 0.00068−0.0781 8.50−35.18 6.40−18.73 0.65−1.55 12.1−21.6 8.86−18.2 22.3−117.1 15.2−86.0 0.046−1.096 0.13−3.14 0.09−4.98

15 15 15 18 18 15 22 15 20 21 15 15 21 24 21 21 16 30 28 24 13 20 18 45 21 45 45 45 17 17 17 20 12 15 15 15 42 12 12 6 8 45 15 20 15 15 15 15 15 15 15 43 40 38

single line on a graph of T ln(y2P) − E1T versus the density of solvent, ρ1. Figure 5 shows that the experimental solubility data for o-nitrobenzoic acid obey this criterion.

Finally, as stated by the MST model, it can be used to test the consistency of the solubility data measured. Thus, the experimental data are consistent, if all isotherms collapse to a 5520



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Table 6. AARD Values of Each Model with Compounds of Different Functional Groups no.

Chrastil

(1) Carboxyl 1 4.82 2 9.41 3 11.79 4 1.98 5 3.00 6 6.43 7 4.01 8 2.04 9 8.16 10 18.76 23 8.15 29 9.09 X̅ 1a 7.30 SD1b 4.59 (2) Amino 11 3.21 12 2.88 13 3.56 14 7.61 15 5.65 16 6.98 17 8.46 18 3.44* 19 8.40 X̅ 2a 5.58 SD2b 2.21 (3) Chain Alkyl 20 7.14 21 3.69 22 5.48 X̅ 3a 5.44 SD3b 1.41 (4) Heterocycle 24 11.01 25 4.59 26 5.32 27 8.65 28 11.23

KJ

SS

BCJS

MST

4.95 9.49 12.74 6.80 3.56 6.49 5.07 4.71 7.51* 4.73 4.10* 8.62 6.56 2.56

3.00* 6.87 10.46 1.86* 2.80 6.36 4.08 1.83 8.51 13.23 6.92 9.26 6.27 3.51

6.43 5.40 6.60* 4.35 4.09 8.21 3.72* 1.10 9.40 8.30 6.89 9.81 6.19 2.47

1.78* 2.75 9.54 6.19 6.41 8.66 5.69 9.40 7.00 6.38 2.57

2.30 2.74* 3.50* 5.96 4.57 6.71 6.87 3.54 6.71 4.77* 1.72

7.94 7.55 6.96 6.71 4.27* 6.49 9.01 10.25 14.81 8.22 2.81

7.41 7.05 6.98 5.04 5.03 6.82 8.06 9.16 13.64 7.69 2.44

2.76 4.44 5.42 4.77* 4.55 4.69* 5.08* 7.07 6.37* 5.02 1.16*

7.84 5.87 5.31 6.34 1.09*

6.83 3.31 2.60* 4.25 1.85

6.15 3.78 7.88 5.94 1.68

6.59 3.61 7.13 5.78 1.55

4.89* 2.45* 2.60* 3.31* 1.12

7.25 7.77 4.46* 3.85* 5.78*

6.73* 7.81 5.51 5.24 11.52

10.15 4.55* 7.90 7.69 10.80

9.51 13.66 9.66 9.73 14.03

9.81 4.75 5.06 9.13 10.70

5.36 5.48 7.15 4.14 3.22 8.00 4.16 0.84* 8.58 7.19 6.59 9.43 5.85 2.36

JCF

no.

Chrastil

(4) Heterocycle 33 11.37 37 10.21 48 9.02 49 5.84 X̅ 4a 8.58 SD4b 2.53* (5) Azo 30 6.98 31 5.25 32 14.36 34 9.14 35 12.02 36 14.29 40 6.27 41 2.76 42 16.22 X̅ 5a 9.70 SD5b 4.45 (6) Diglycolic 50 5.57 51 5.39 52 4.25 45 6.70 46 9.16 X̅ 6a 6.21 SD6b 1.67 (7) Anthraquinone 38 6.26* 39 7.68 47 11.05 53 12.35 54 11.54 43 4.06 44 12.34 X̅ 7a 9.33 SD7b 3.07 X̅ ga 7.69 SDgb 3.72

6.34 5.22* 8.97 3.02 1.96* 5.33* 3.92 5.03 9.30 4.50* 4.74 7.92* 5.52* 2.16*

KJ

SS

BCJS

MST

JCF

22.13 11.86 9.32 5.18 11.68 4.46

9.91 10.20 8.22 3.53 7.92 2.57

22.47 10.82 11.06 4.32 8.64 5.50

28.79 10.98 11.62 4.02 10.25 7.09

6.82* 9.95* 2.04* 2.26* 6.91* 3.12

7.36 13.74 10.09 11.82 9.81* 29.52 6.73 3.99 7.32 11.15 7.05

6.96 5.27 10.86 6.23* 10.15 4.09* 4.50 1.54* 12.86 6.94* 3.45*

7.59 13.70 10.01 11.25 11.29 31.16 5.85 2.17 13.30 11.81 7.68

10.20 18.07 14.79 12.98 13.64 44.69 5.81 4.03 14.58 15.42 11.17

5.12* 4.85* 6.95* 7.39 12.80 18.69 0.37* 2.98 5.43* 7.18 5.17

5.31 6.33 4.39 7.40 9.03 6.49 1.62

5.66 5.18 4.25 6.56 8.42 6.01 1.42

6.01 6.23 4.62 7.84 8.53 6.65 1.39

6.82 6.66 4.86 8.73 9.05 7.22 1.53

4.01* 4.65* 2.33* 5.81* 3.22* 4.00* 1.19*

19.42 19.26 8.06 5.38* 10.42 8.96 3.62 10.73 5.83 8.67 4.96

6.54 6.82 8.58 8.79 10.58 2.69* 6.86 7.27 2.29 6.40 2.94*

19.20 19.30 11.65 10.73 9.43 8.20 4.10 11.80 5.21 8.63 5.15

24.27 24.97 9.33 8.99 8.89 11.66 3.26* 13.05 7.68 9.54 7.19

6.86 5.32* 7.89* 6.47 8.30* 4.91 4.85 6.37* 1.30* 5.79* 3.01

a

X̅ is the mean AARD value of each model for each group. bSD is the standard deviation of each model. 1−7: compounds of different functional groups. g: global.

4. COMPARISON AND EVALUATION OF THE SEMIEMPIRICAL MODELS

authors. Otherwise, the densities of SCCO2 are obtained from the NIST fluid property database. 4.2. Correlated Results with Semiempirical Models. The correlated results with the different kinds of compounds of each model are shown in Table 6. The lowest error fit is marked with an asterisk (*). The mean AARD values of each model and their corresponding standard deviation (SD) can be observed in Table 6 and Figure 6. As shown in Table 6, the overall AARD value is 5.79% and 6.40% for the JCF and SS models, respectively, which are much better than those obtained by the other models. The MST model is shown to give the poorest correlated results with a global AARD of 9.54%. In addition, the accuracy of another three models, the Chrastil, KJ, and BCJS models, with AARD is 7.69%, 8.67%, and 8.63%, respectively. In order to better compare the accuracy of the models, SD has also been calculated in our study. Compared with the values of SD of other models, the SS

4.1. Details of the Solubility of Compounds. In order to compare the accuracy of these models, the available solubility data (in mole fraction) of 54 different kinds of compounds have been collected from the literature (including 1155 data points).10,11,30−66 The details of compounds (names and formulas) and their references are listed in Table 4. The details of the solubility data (temperature, pressure, mole fraction solubility of the solutes, and number of experimental data points) are presented in Table 5. Because we are looking for an accurate semiempirical model to correlate the solubility data of solutes in SCCO2 and the accuracy of different models are compared with each other, it has been assumed that all published data are correct. All published data listed in Table 5 have been checked to avoid the input error. In this study, the densities of SCCO2 were obtained from literature listed by 5521



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Statistical tests of the KJ and SS models were carried out. The results in Table 7 indicate that the AARD′ differences between these two models are not statistically significant (paired t test; P = 0.015997 > 0.01), which proves that the SS model has better correlative and predictive capability than the KJ model not with more adjustable parameters but with containing temperature effects on solubility. The BCJS model [ln(y2P) vs ρ1] provides results in terms of AARD and SD (8.63% and 5.15%) similar to those of the KJ model (8.67% and 4.96%). In a comparison between the expressions of these two models, there are no significant differences in the relationship between the solute’s solubility and solvent’s density, which may result in similar correlated results. The MST model [T ln(y2P) vs ρ1] is shown to give the poorest correlated results with AARD of 9.54% and SD of 7.19% in all of the models, perhaps because of the oversimplified treatments used to derive this model.25 In general, in terms of the number of adjustable parameters, the models with three parameters have higher values of AARD and SD than those of models with 4 or even more parameters. In our opinion, the accuracy of the models depends on the expression of the relationship between the solute’s solubility and solvent’s density and the number of parameters, which is remarkable. The increase in the complexity of the expression and the number of parameters can enhance the accuracy of the models. Compared with four original models (the Chrastil, KJ, BCJS, and MST models), the SS and JCF models are modifications of the original models. The SS model considered temperature effects on solubility and modified the KJ model by increasing the complexity expression of the relationship between the solute’s solubility and solvent’s density, while the JCF model modified the Chrastil model by increasing the number of parameters about temperature and pressure. As shown in Table 6 and Figure 6, the correlated results obtained with different models are in accordance with our opinion. All of the modifications of the models give better fit than the original models. The results of statistical tests indicate that the JCF model has the best correlated result because it uses more adjustable parameters, while the better correlative capability of the SS model is independent of the number of parameters. In addition, the models that have similar semilogarithmic solubility−density relationships (the KJ, BCJS, and MST models) have worse correlated results, while the models that have the log−log solubility−density relationship (the JCF and SS models) have better correlated results, except the Chrastil model. With regard to the Chrastil model, this log−log model with three parameters was developed earlier and it did not consider more complicated effects of temperature and pressure on solubility. Therefore, the Chrastil model has worse correlated results (as shown in Figure 6). However, it still correlated better than the semilogarithmic models. The results indicate that the solubility of compounds in SCCO2 is described better by the log−log solubility−density relationship. Furthermore, from published experimental solubility data of compounds, there are many different types of functional groups. Consequently, 54 different compounds collected in this work were classified by 7 different kinds of functional groups (including carboxyl, amino, chain alkyl, heterocycle, azo, diglycolic, and anthraquinone, which are frequently used in industry). The solubility data of different kinds of compounds were correlated by these models separately in order to discuss which model is suitable for certain types of compounds. The correlated results are listed in Table 6.

Figure 6. Mean AARD (solid box) of each model with their corresponding SD (dashed box).

model gives the lowest overall SD of 2.94%; on the contrary, the MST model gives the highest overall SD of 7.19%. In order to provide the relationship between the predictive capability of the model and the number of parameters, statistical tests were carried out in this work. As a general rule, the more curve-fitting parameters, the more accurate the correlations are expected to be. In order to provide a reliable accuracy criterion to compare the accuracy of the models possessing different numbers of curve-fitting parameters, the new AARD (AARD′) was calculated by AARD′ (%) =

100 N−Z

N

∑ 1

|y2 cal − y2 exp | y2 exp

(17)

y2cal, y2exp,

where and N are the same as those in eq 16 and Z is the number of curve-fitting parameters for each model. The AARD′ values of each model for different compounds are listed in Table 7. The Chrastil model (ln y2 vs ln ρ1) is a common densitybased model with three adjustable parameters. The mean AARD and SD are 7.69% and 3.72%, respectively. The JCF model (ln y2 vs ln ρ1) provides a better correlated result than the Chrastil model. The mean AARD and SD are 5.79% and 3.01%, respectively. Although the expression of the relationship between the solute’s solubility and solvent’s density in the JCF model is similar to the Chrastil model, the JCF model has more adjustable parameters of temperature and pressure. Jouyban et al.27 have indicated that the AARD′ differences between these two models are statistically significant. Likewise, the result of statistical tests of the Chrastil and JCF models in Table 7 indicates that the AARD′ differences between these two models are statistically significant (paired t test; P = 0.003943 < 0.01), which is identical with the above viewpoint. As a result, the number of added parameters in the JCF model has a significant effect on the predictive capability of the model. The KJ model (ln y2 vs ρ1) is similar to the Chrastil model with three adjustable parameters. Compared with the Chrastil model, the fit was worse. It was improved by the SS model, which reduced AARD from 8.67% to 6.40% and SD from 4.96% to 2.94%. The SS model (ln y2 vs ln ρ1 + ln ρ1/T) has four adjustable parameters, which also improved the accuracy of the expression of the density’s function in the KJ model. 5522



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Table 7. AARD′ Values of Four Models with Different Compounds no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Chrastil

JCF

KJ

SS

no.

Chrastil

JCF

KJ

SS

6.03 11.76 14.74 2.38 3.60 8.04 4.64 2.55 9.60 21.89 10.19 11.36 3.75 3.29 4.15 8.88 6.95 7.76 9.48 3.93 10.92 8.40 4.43 5.87 12.85 4.92 5.70 9.27

8.65 7.12 12.23 3.88 2.52 7.27 4.79 6.86 11.63 5.56 6.46 10.80 3.41 5.33 6.70 5.89 6.07 5.41 5.93 8.48 9.20 6.11 3.15 2.85 12.54 4.99 8.67 8.44

6.18 11.86 15.93 8.16 4.28 8.11 5.87 5.89 8.83 5.52 2.23 3.44 11.13 7.07 7.48 10.10 7.01 10.45 7.84 8.96 7.62 6.25 4.92 10.19 15.93 10.35 10.43 15.03

4.09 9.37 14.27 2.39 3.60 8.67 4.99 2.50 10.64 16.34 3.14 3.73 4.32 7.15 5.65 8.29 9.17 4.09 7.83 8.20 4.79 3.25 8.90 10.77 5.86 5.55 10.02 11.74

29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 mean SD

13.64 13.81 12.40 10.61 7.79 8.73 6.56 17.95 9.84 16.03 19.05 12.54 4.42 17.38 4.39 13.40 6.96 6.34 5.31 8.38 11.45 7.83 9.60 13.81 15.44 12.41 9.32a 4.50

14.12 8.92 13.01 2.55 3.39 6.98 6.61 9.48 8.17 19.20 28.04 1.11 5.96 5.96 5.46 5.42 5.47 5.81 3.18 7.92 4.39 9.35 7.25 10.76 8.82 9.15 7.54a 4.32

10.46 8.93 16.68 11.87 29.51 14.77 12.26 36.90 12.77 25.90 25.68 13.46 6.38 7.84 9.69 3.93 6.64 7.91 5.49 11.65 6.48 9.24 11.29 8.67 5.82 11.32 10.56b 6.34

12.11 9.11 6.89 13.58 14.87 8.50 13.84 5.58 11.28 9.82 10.23 13.50 3.08 14.11 2.99 7.67 7.72 7.06 5.79 11.21 4.81 8.95 11.48 9.46 9.77 11.82 8.37b 3.82

a

The mean AARD′ differences between the Chrastil and JCF models are significant (paired t test; P = 0.003943 < 0.01). bThe mean AARD′ differences between the KJ and SS models are significant (paired t test; P = 0.015997 > 0.01).

Table 6 indicates that the SS model provides the best correlation with amino and azoic compounds; with regard to five other kinds of compounds (carboxyl, chain alkyl, heterocyclic, diglycolic, and anthraquinone), the JCF model is the best model. The reason could be attributed to the different intermolecular interactions between different solutes and CO2 molecules. The carboxyl and amino functional groups have strong polarity, which may restrain interactions between the solute and CO2 molecules. The compounds containing the chain alkyl, heterocyclic, diglycolic, or anthraquinone listed have macromolecules, which signify that they have larger molecular volumes such that association with CO2 molecules becomes difficult. Considering most of the dyes, they have specific chemical structures−azoic functional group, which could impact interactions between the solute and CO2 molecules. Huang et al.67 have analyzed the solubility of about 30 dyes correlated by the Chrastil, KJ, BCJS, and MST models in detail, and their correlated results are similar to ours. 4.3. Influential Factors on the Different Models. The expression of models indicates that major parameters of the models are the temperature, pressure, and density of the solvent, respectively. The solvent’s density depends on the temperature and pressure. In addition, the number of experimental data points and the range of solubility of the solutes are other major influential factors in the process of the calculation of AARD. For this purpose, the effects of four factors (temperature, pressure, mole fraction solubility of the solutes, and number of experimental data points) on the accuracy of different models were discussed. The results are listed in Table 8.

The criterion (classifying the data shown in Table 5) was to consider the temperature range and final temperature. A final temperature value of around 348 K was established. This is explained because on several occasions the vicinities of the upper critical end point (UCEP) were not reached; depending on the temperature, the shape of the solubility curve is between the UCEP and Chrastil’s shape. Compared with the temperature range and final temperature listed in Table 5, the final temperature for several compounds is 348 K. As a result, a final temperature value of around 348 K was established. According to Table 8, when the final temperature is less than 348 K, all of the models provided better results than those of more than 348 K. All of the differences of the mean AARD value of each model are above 2.00, except the SS model. This situation suggests that with higher temperature, when the UCEP or its proximities is reached, a large increase in solubility is produced, which may increase the error. Also, it is observed that, with a small temperature range and a final temperature lower than 348 K, the best fit was obtained with the JCF model. The mean AARD and SD were 5.01% and 1.95%, respectively. With a final temperature higher than 348 K, the lowest mean AARD of 7.02% was still obtained with the JCF model. In addition, the lowest difference of the mean AARD value, which is 1.66, was obtained with the SS model, while the highest difference was 6.93, obtained with the MST model. Likewise, the criterion was to consider the pressure range and final pressure. A final pressure value of around 30 MPa was established. The reason is that when the UCEP or its proximities is reached, the change in the solubility with pressure 5523



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Table 8. Differences of the Mean Value of AARD for Each Model at Different Conditions (Temperature T, Pressure P, Mole Fraction Solubility of the Solutes y2, and Number of Experimental Data Points N) T < 348 K T > 348 K

P < 30 MPa P ≥ 30 MPa

y2 < l × 10−4 y2 ≥ l × 10−4

N < 30 N ≥ 30

X̅ a SDb X̅ a SDb ΔX̅ c X̅ a SDb X̅ a SDb ΔX̅ c X̅ a SDb X̅ a SDb ΔX̅ c X̅ a SDb X̅ a SDb ΔX̅ c

Chrastil

KJ

SS

BCJS

MST

JCF

6.74 3.48 9.17 3.61 2.44 6.98 3.64 8.98 3.52 2.17 7.87 3.63 7.57 3.77 −0.30 7.14 3.57 10.10 3.42 2.97

6.92 2.63 11.43 6.31 4.51 7.76 4.74 10.35 4.91 3.31 9.00 5.52 8.46 4.55 −0.54 8.47 5.36 9.54 2.25 1.06

5.76 2.70 7.41 3.01* 1.66* 5.71 2.63* 7.67 3.04 2.16 6.38 2.99 6.41 2.90* 0.03* 5.83 2.69* 8.93 2.61 3.10

6.96 2.55 11.26 6.82 4.31 7.69 4.77 10.36 5.36 3.18 10.23 4.86 7.61 5.07 −2.61 8.60 5.51 8.75 3.06 0.15*

6.84 2.62 13.77 9.64 6.93 8.30 7.06 11.82 6.87 4.16 11.77 6.96 8.12 6.98 −3.65 9.64 7.86 9.09 2.70 −0.55

5.01* 1.95* 7.02* 3.86 2.02 5.36* 3.16 6.58* 2.54* 1.88* 5.49* 2.56* 5.98* 3.25 0.49 5.25* 3.00 8.17* 1.61* 2.91

a X̅ is the mean AARD value of each model. bSD is the standard deviation for each model. cΔX̅ is the difference of the mean value of AARD at each condition.

AARD of 5.25%. When the number of data points is higher than 30, the JCF model still gives the best correlation (AARD of 8.17%). All results can be summarized as follows: with upper temperature and pressure, all of the accuracy of the models obviously decreases; with a higher mole fraction solubility of the solute, most of the accuracy of the models increases a little; with more experimental data points, most of the accuracy of the models decreases. Whether the values of the temperature, pressure, mole fraction solubility, or number of experimental data points are high or low, the JCF model is superior to other models.

becomes more drastic, which may result in the uncertainty of the solubility. Similar to the determination of the temperature, a final pressure value of around 30 MPa was established. It is observed that the results are similar to the temperature in Table 8. With a final pressure lower than 30 MPa, all of these models give better correlations. The best fit was obtained with the JCF model. The mean AARD was 5.36%. With a final pressure higher than 30 MPa, the JCF model still provides the lowest AARD of 6.58%. In addition, the lowest difference of the mean AARD value, which is 1.88, was also obtained with the JCF model. Then, the criterion was to consider the mole fraction solubility of the solutes. As shown in Table 5, there exists a larger difference of the mole fraction solubility for different solutes. As a result, a final mole fraction value of around 1 × 10−4 was established, which makes the difference obvious. It is observed that the result is opposite to that of the temperature and pressure mentioned above. As shown in Table 8, with a final mole fraction higher than 1 × 10−4, most of the models provide a lower AARD than that of the mole fraction lower than 1 × 10−4 except the SS and JCF models, which only have slight increases. The differences of the mean AARD value obtained are all less than 1.00 except the BCJS and MST models, which are −2.61 and −3.65, respectively. In addition, the best model is the JCF models either for the higher mole fraction solubility or for the lower mole fraction solubility. The last influencing factor considered was the number of data points in the experiment. In view of the number of data points listed in Table 5, the minimum value of the number is 15, while the maximum value is 45. Consequently, a final value of around 30 was established, which also makes the difference obvious. The results that are shown in Table 8 indicate that most of the mean AARD values of the models were raised by increasing the number of data points, with the exception of the MST models. With a final number of data points value of lower than 30, the best model was the JCF model, which provides an

5. CONCLUSIONS In this work, the solubility of o-nitrobenzoic acid in SCCO2 was determined at 308, 318, and 328 K, over a pressure range from 10.0 to 21.0 MPa. The crossover pressure region for the binary system was from 10.7 to 11.7 MPa, and the thermodynamic properties (ΔHtotal, ΔHsub, and ΔHsol) of the solid solute were obtained. The six different theoretical semiempirical models (the Chrastil, KJ, SS, BCJS, MST, and JCF models) were used to correlate the experimental data. The results showed that the SS model correlated the solubility data of o-nitrobenzoic acid in SCCO2 more accurately. The six different semiempirical models have been applied to fit the solubility data of 54 different kinds of compounds (including 1155 data points). In general, the SS and JCF models as the modification of models correlated the solubility data better than the other four original models. Statistical analysis was performed to discuss the relationship between the predictive capability of these models and the number of parameters. The results indicated that the correlative and predictive capability of the models depend on the accuracy of the expression of the density’s function and the increase in the number of parameters. Moreover, the compounds collected were classified by seven different kinds of functional groups 5524



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(including carboxyl, amino, chain alkyl, heterocycle, azo, diglycolic, and anthraquinone) to evaluate the application of these models. In addition, the division criteria of four different influential factors (temperature, pressure, mole fraction solubility of the solutes, and number of experimental data points) on the different models were established at 348 K, 30 MPa, 1 × 10−4, and 30, respectively. The results indicated that in any case the JCF model is shown to be the best model because it has more adjustable parameters of temperature and pressure.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was financially supported by a fund awarded by the National Natural Science Foundation of China (Grant 21176012); support from the Petrochina Company Ltd. through the Applied Research ProProject (Grant 2009A3801-02), the Fundamental Research Funds for the Central Universities (Grant ZZ1103), and the Science and Technology Bureau of the City of Changzhou (Grant CJ20110013) is gratefully acknowledged. The authors are also grateful to the Mass Transfer and Separation Laboratory of the Beijing University of Chemical Technology for its support.

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REFERENCES

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New Experimental Data and Modeling of the Solubility of Compounds

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