Article pubs.acs.org/jced
Solubility of Polyacrylamide in Supercritical Carbon Dioxide Hai-lun Wang, Jia-rong Sang, Lin-tao Guo, Jing Zhu, and Jun-su Jin* Beijing Key Laboratory of Membrane Science and Technology, Beijing University of Chemical Technology, Beijing 100029, China ABSTRACT: To promote the application of polyacrylamide (PAM) in carbon dioxide flooding to enhance oil recovery, the solubility of PAM with different molecular weight (5 million, 7 million, 14 million, g·mol−1) was measured using dynamic method in supercritical carbon dioxide (SCCO2) at temperatures of 313, 323, and 333 K and pressures from 9.0 to 18.0 MPa. By comparing the differences of solubility data measured in SCCO2, the effects of pressure, temperature and molecular weight on the solubility of PAM in SCCO2 were investigated. The solubility data of PAM in SCCO2 was correlated with five density-based semiempirical models (Chrastil, A-L, M-T, S-S, and Bartle) and A-L model obtained the best correlated results for PAM with different molecular weight. The self-consistency of PAM solubility was verified by M-T model. The enthalpy values of PAM, including ΔHt, ΔHvap, and ΔHsolv, were estimated through Chrastil and Bartle models.
1. INTRODUCTION Enhanced oil recovery (EOR) has been a subject of continuing interest in the development of oil and gas industry. However, in low permeability reservoirs, water flooding could not satisfy the demands of oil recovery because of low permeability and complex flow patterns of the reservoirs, whereas carbon dioxide (CO2) flooding could meet the needs for EOR of the low permeability reservoirs.1 In the process of CO2 flooding, CO2 is in the supercritical state, which is called supercritical CO2 (SCCO2), whose temperature and pressure are both above the critical point. The density of the SCCO2 is close to liquid, and its viscosity and diffusion coefficient is close to gas. Especially, the physical properties of SCCO2 will change dramatically near the critical point where its temperature and pressure have small change.2 With consideration of those special properties of SCCO2, the main mechanisms for CO2 flooding have better miscibility of oil and CO2, interphase mass transfer, oil volume expansion, decrease of oil viscosity, and interfacial tension.3 Furthermore, SCCO2 also has the advantages of nontoxicity, noncorrosiveness, nonexplosive, and especially low price. All of the above are the reasons for CO2 flooding being an important process in the EOR techniques,4 especially in the tertiary oil recovery.5 It could commonly increase the oil recovery rate by 7−15% and extend the productive life of the well for 15−20 years. CO2 flooding can also curb global warming with 50−60% of CO2 injected to oil reservoirs stored underground.6−9 In the technology of CO2 flooding, water-alternating-CO2 injection usually has higher oil recovery than pure CO2 injection.10,11 Compared with pure water, a solvent with PAM played a crucial role of enhanced tertiary oil recovery by increasing the viscosity of the injected water, improving oil flow rate, increasing permeability of the flooded layer, and expanding the scope of injected water in the oil reservoirs and the water flooded thickness on the longitudinal oil layer.12 Therefore, it is an effective method to add a small quantity of PAM into the process of CO2 flooding to promote tertiary oil recovery. To © XXXX American Chemical Society
our best knowledge, the fundamental physical property data of PAM in SCCO2, such as saturated solubility, viscosity, interfacial tension, and diffusion coefficient, are still lacking. The solubility of PAM with molecular weight 5 million, 7 million, and 14 million g·mol−1 in SCCO2, all of which are widely used as polymer flooding, has never been reported to date so far, which prevents the development of the application of PAM in CO2 flooding process. In this research, the solubility of PAM (Mn = 5 million, 7 million, and 14 million g·mol−1) in SCCO2 was determined by dynamic method at the temperatures of 313, 323, and 333 K and pressures from 9.0 to 18.0 MPa, which will contribute essential and important data for the industrial process of CO2 flooding with polymer. Furthermore, five density-based semiempirical models were chosen to quantitatively explain and predict the solubility behavior of the solutes in SCCO2, which employ Chrastil model,13 Adachi and Lu model (A-L model),14 Mendez-Santiago and Teja model (M-T model),15 Sung and Shim model (S-S model),16 and Bartle model. 17 The experimental solubility data and model correlation results will contribute to understand and to industrialize the process of CO2 flooding with polymer.
2. EXPERIMENT SECTION 2.1. Materials. PAM (Mn = 5 million, 7 million, 14 million, g·mol−1, CAS: 9003-05-8) used in this study was supplied by Macklin Chemistry Co. Ltd. with a mass purity of more than 98%. CO2 (mass purity more than 99.9%) was purchased from Beijing Praxair Industrial Gas Co. Ltd. Deionized water was used in this work. All chemicals were utilized without further purification. Received: July 28, 2016 Accepted: October 28, 2016
A
DOI: 10.1021/acs.jced.6b00677 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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2.2. Apparatus and Procedure. A schematic diagram of the dynamic apparatus used to measure the solubility of PAM in this work is shown in Figure 1, which has been described in
Figure 1. Schematic diagram of the experimental apparatus (1, CO2 cylinder; 2, high-pressure syringe pump; 3, surge flask; 4, pressure micrometering valve; 5, preheating cell; 6, temperature controller; 7, constant-temperature stirred water bath; 8, high-pressure equilibrium cell; 9, heating band; 10, calibrated pressure meter; 11, decompression sampling valve; 12, two U-shape tubes; 13, rotating flow meter; 14, wet gas flow meter.).
Figure 2. Determination of equilibrium time at 323 K, 13.0 MPa for PAM with (▲) Mn = 5 million, (●) Mn = 7 million, (■) Mn = 14 million.
solubility of PAM (Mn = 5 million, 7 million, 14 million g· mol−1) with different equilibrium time. It was found that the dissolution of the PAM reached phase equilibrium when the time was more than 50 min. As a result, 60 min was finally chosen as the equilibrium time. The solubility changes of PAM (Mn = 5 million, 7 million, 14 million g·mol−1) with different flow rate of CO2 were shown in Figure 3. The result showed
our previous work.18 The reliability of the apparatus used in this research has been validated in our previous work19 by comparing the solubility data of benzoic acid measured using this apparatus with the published data.20 The high-pressure equilibrium cell, both ends of which were installed with the stainless steel sintered disks to avoid physical entrainment of the undissolved PAM, was the main piece of equipment for this experiment. Before each measurement, about 6 g of solid solute PAM was packed into the highpressure equilibrium cell and distributed for three layers to avoid channeling and dead volume. First, pure CO2 in the CO2 cylinder was pumped into the high-pressure surge flask by syringe pump (Nova, model 5542121). The CO2 flowed into a preheater, which was heated with heating electric coils to achieve the operational temperature. Second, SCCO2 entered into the high-pressure equilibrium cell from the bottom of the cell. To keep the experimental temperature, the equilibrium cell was immersed in the constant-temperature stirred water bath (Chongqing Hongrui Experimental Instrument Co., model CS503F), which can maintain the temperature fluctuations within ±0.01 K. The pressure in equilibrium cell was controlled by a pressure meter (Heise, model CTUSA) with an uncertainty of ±0.05 MPa. Finally, the dissolution of PAM in SCCO2 would reach the phase equilibrium after 60 min. Then, CO2 mixed with PAM entered into a two U-shaped tubes through a decompression sampling valve from the equilibrium cell at flow rate of 0.3 L·min−1 continuously. The dissolved PAM in SCCO2 was thus separated from the CO2 and deposited in the two U-shaped tubes. A rotating flow meter was used to observe the real-time CO2 flow rate. The total CO2 volume was recorded by using a wet test meter (Changchun Instrument Factory, model LML-2) with an accuracy of ±0.01 L at operational temperature and pressure. Dynamic measurement method is that when the PAM and SCCO2 reach phase equilibrium, CO2 mixed with PAM enter into a two U-shaped tubes with a suitable flow rate. This flow rate should keep the solute and solvent equilibrium all the time. Equilibrium time should be determined to ensure that the PAM and SCCO2 system had reached phase equilibrium state. Equilibrium flow rate of CO2 should also be chosen to keep the system in phase equilibrium state. Figure 2 shows the change of
Figure 3. Determination of flow rate of SCCO2 at 323 K, 13.0 MPa for PAM with (▲) Mn = 5 million, (●) Mn = 7 million, (■) Mn = 14 million.
that the solubility remained unchanged when the flow rate of CO2 at range from 0.1 to 0.4 L·min−1. The final appropriate flow rate also should take consideration of small fluctuations of flow rate existing in the apparatus. Thus, 0.3 L·min−1 was adopted as the final CO2 flow rate in this research. The UV spectrophotometer (PERSEE, model TU-1810) was chosen to analyze the concentration of PAM. The maximum UV absorption wavelength of PAM with three molecular weights was 200 nm. Three standard curves of PAM (Mn = 5 million, 7 million, and 14 million g·mol−1) were obtained and shown in Figure 4. The regressed coefficients of all three standard curves are better than 0.9991. The solute collected in B
DOI: 10.1021/acs.jced.6b00677 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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2.3. Correlation with Density-Based Semiempirical Models. Semiempirical models are widely used to correlate the solubility for polymers because of lacking thermochemical data of polymers. Density-based semiempirical models are used to establish the relationship between solubility of polymers and density of SCF. In this research, five density-based semiempirical models (Chrastil, A-L, M-T, S-S, and Bartle) are chosen to correlate the experimental solubility of PAM in SCCO2. Chrastil derived a density-based model in 1982. It is based on the assumption that the molecules of the solute and the solvent form a solvate-complex, which is in equilibrium with the solvent. According to Chrastil model, a logarithmic relationship among the solute solubility (S, g·L−1) in SCCO2, the density of SCCO2 (ρ, g·L−1), and the operational temperature (T, K) was derived as follows ln S = A1 +
B1 + C1 ln ρ T
(1)
where S is the solubility of solute in SCCO2 (g·L−1); ρ is density of SCCO2 (g·L−1); T is the operating temperature (K). A1, B1, and C1 are the adjustable parameters correlated by fitting experimental data. A1 is a function of the molecular weights of the solute and SCCO2. C1 represents the number of solvent molecules that associate with one solute molecule. B1 is a function of solvation and sublimation enthalpies of the solute and by eq 2 total heat of solution (ΔHt, kJ/mol) can be obtained, which is the sum of solvation enthalpy (ΔHsolv, kJ/ mol) and sublimation enthalpy (ΔHvap., kJ/mol) of the solute. R is the molar gas constant, typically taken as 8.314 J/mol·K. ΔHt = −B1R
(2)
Adachi and Lu proposed a modified model based on the Chrastil model by considering the quantity C1 to be density dependent as C1= C2+ D2ρ+ E2ρ2. Adachi and Lu model (A-L model) is described as follows: ln S = A 2 +
B2 + (C2 + D2ρ + E2ρ2 )ln ρ T
(3)
where A2, B2, C2, D2, and E2 are the adjustable parameters of AL model. M-T model was proposed based on the theory of dilute solution. Because the proposed equation has a limitation that the sublimation pressure of solute is often unavailable, the model was developed by the Clausius−Clapeyron equation. The expression of M-T model was finally proposed as T ln(yP) = A3 + B3T + C3ρ
(4)
where y is the equilibrium mole fraction of the solute in SCCO2; P is the operating pressure (MPa); T is the operating temperature (K); and A3, B3, and C3 are the adjustable parameters of M-T model. M-T model can also be used to evaluate the self-consistency of solubility data. S-S model showed a linear relationship between ln y and ln ρ and introduced a function of temperature. S-S model was illustrated as
Figure 4. Standard curves of PAM for (a) Mn = 5 million, (b) Mn = 7 million, (c) Mn = 14 million at 200 nm.
the two U-shaped tubes was dissolved with deionized water in 50 mL volumetric flask and analyzed the absorbance by the UV spectrophotometer. Each data reported was an average of three or more repeated measurements, and the relative uncertainty of each data was within ±5%.
ln y = A4 +
⎛ B4 D⎞ + ⎜C4 + 4 ⎟ln ρ ⎝ T T⎠
(5)
where A4, B4, C4, and D4 are the adjustable parameters of S-S model. C
DOI: 10.1021/acs.jced.6b00677 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 1. Experimental Solubility Data of PAM in SCCO2 at Temperature T = 313−333 K and pressure P = 9.0−18.0 MPa 1010·y (mol·mol−1)c a
T (K)
P (MPa)
313
9.0 11.0 13.0 15.0 18.0 9.0 11.0 13.0 15.0 18.0 9.0 11.0 13.0 15.0 18.0
323
333
a
−1 b
ρ (g·L )
Mn = 5 million
492.75 685.58 744.41 781.32 820.39 286.12 505.69 637.96 701.08 758.11 235.91 359.16 507.26 605.6 688.34
2.34 2.99 3.33 3.88 4.02 2.61 3.67 4.36 5.01 5.83 3.26 4.32 5.39 6.45 7.72
± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
Mn = 7 million
0.05 0.05 0.04 0.06 0.06 0.05 0.05 0.06 0.07 0.05 0.06 0.06 0.07 0.06 0.07
1.55 1.94 2.13 2.35 2.60 1.69 2.35 2.92 3.51 3.90 2.16 2.89 3.65 4.44 5.24
± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
Mn = 14 million
0.03 0.02 0.02 0.04 0.04 0.03 0.04 0.05 0.04 0.04 0.03 0.05 0.04 0.04 0.03
0.59 0.82 0.97 1.05 1.10 0.71 1.03 1.21 1.45 1.63 0.98 1.25 1.59 1.80 2.29
± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
0.01 0.01 0.02 0.02 0.01 0.02 0.02 0.02 0.01 0.01 0.02 0.02 0.02 0.01 0.02
Standard uncertainties u are u(T) = 0.01 K, u(P) = 0.05 MPa. bρ is the density of pure CO2 at different experimental temperatures and pressures, which is obtained from the NIST fluid property database. cy is the equilibrium mole fraction of the solute in SCCO2.
a
molecular motion theory, it could be determined with the entropic value of solute molecules and interactions between solute and solvent molecules. On one hand, according to Flory’s theory as expressed in eq 8
Bartle model was a new linear expression that added a reference pressure and reference density, and can be expressed as follows ⎛ P⎞ B ln⎜y ⎟ = A5 + 5 + C5(ρ − ρref ) T ⎝ P2 ⎠
−
(6)
where P2 is the reference pressure, typically taken as 0.1 MPa; ρref is a reference density, typically taken as 700 g·L−1; A5, B5, and C5 are the adjustable parameters of Bartle model. In this model, B5 can be applied to calculate the ΔHvap (kJ/mol) of PAM by eq 7 ΔH vap = −B5R
ΔG ΔS = RT R
(8)
The Gibbs free energy (ΔG) of single polymer chain and steric hindrance of ploymer both increase with molecular weight increasing25 and ΔS, which represents chaos degree of solute molecules, decreases with ΔG increasing. Therefore, solute solubility decreases with molecular weight increasing. On the other hand, it can be determined that with molecular weight increasing, the intermolecular forces between PAM become stronger than that between PAM and solvent molecules, which reduces the solute dissolution. 3.2. Prediction of Solubility and Thermodynamic Properties. The solubility data of PAM in SCCO2 are correlated using Chrastil, A-L, M-T, S−S, and Bartle models. The average absolute relative deviation (AARD, %) is used to compare the correlated precision for models. The value of AARD is calculated by eq 9
(7)
3. RESULTS AND DISCUSSION 3.1. Experimental Solubility of PAM in SCCO2. The mole fraction solubility y of PAM (Mn = 5 million, 7 million, 14 million, g·mol−1) in SCCO2 at different temperatures and pressures are tabulated in Table 1 and illustrated in Figure 5. The value range of y is from 2.34 × 10−10 to 7.72 × 10−10 for PAM with molecular weight 5 million g·mol−1, 1.55 × 10−10 to 5.24 × 10−10 for PAM with molecular weight 7 million g·mol−1 and 0.59 × 10−10 to 2.29 × 10−10 for PAM with molecular weight 14 million g·mol−1. These fundamental solubility data is essential for process design and can scale-up of CO2 flooding with PAM. The densities of SCCO2 were obtained from the National Institute of Standards and Technology Web site,21 and they are also listed in Table 1, which could be used in densitybased semiempirical models correlation. Table 1 and Figure 5 show that at all of the listed temperatures, the solubility of PAM in SCCO2 increases with the pressure of SCCO2 increasing, following the expected trends because the solvation power of SCCO2 increases with the density of SCCO2. The influence of temperature of PAM in SCCO2 is the same as that of pressure, and the main reason is that the solubility increases with the solute vapor pressure of SCCO2. The solubility data also show that the solubility of PAM decreases with the PAM molecular weight increasing, and the result in this research was consistent with most solubility studies on different polymers in SCCO2.22−24 According to the
AARD(%) =
100 n
n
∑ 1
|ycal − yexp | yexp
(9)
where yexp is the experimental solubility; ycal is the calculated solubility using density-based semiempirical models; and n is the number of experimental points. According to the expression of M-T model, the solubility can be presented by a single straight line when plotting T ln(yP) − B3T versus the density of solvent ρ. The comparison between the experimental solubility values and the calculated results for PAM in SCCO2 is shown in Figure 6. It can be concluded that most of the experimental solubility are in the vicinity of the straight line and solubility of PAM in SCCO2 increases with increasing density. Therefore, the satisfactory self-consistency of PAM solubility was obtained. The correlation results including the adjustable parameters and AARD (%) of each model for PAM with three molecular weights are listed in Table 2. The multiple linear regression was D
DOI: 10.1021/acs.jced.6b00677 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Figure 6. Solubility of PAM for (▲) Mn = 5 million, (●) Mn = 7 million, (■) Mn = 14 million in SCCO2 correlated by M-T model at temperatures of 313, 323, and 333 K (▲, ●, ■, experimental results; , calculated results).
experimental solubility. A-L model has the minimum value of AARD (2.61% for PAM with Mn = 5 million g·mol−1, 3.15% for PAM with Mn = 7 million g·mol−1, 2.18% for PAM with Mn = 14 million g·mol−1), which indicates that A-L model could be finally chosen to predict the solubility of PAM in SCCO2 at other operational conditions in the experimental operation range to provide basic data for the application of PAM in CO2 flooding. In this work, the statistical test method was carried out to evaluate the effects of the number of parameters on correlated precision for each model. The AARD′ was established using the following equation AARD′(%) =
100 n−z
n
∑ 1
|ycal − yexp | yexp
(10)
where z is the number of parameters in each model, n, ycal, and yexp are same with the eq 9. The values of AARD′ of five models are listed in Table 3. The differences of AARD′ (%) between these models with different number of parameters are statistically significant (variance analysis; p = 1.31 × 10−6 < 0.01). The result indicates that A-L model has the best correlation results because of most number of parameters, which could be concluded that more parameters result in better correlation results. The thermodynamic properties of PAM (ΔHt, ΔHsolv, and ΔHvap) can be calculated by Chrastil and Bartle models. The value of ΔHt can be obtained by eq 2; while that of ΔHvap is through eq 7. Thus, the value of ΔHsolv can be obtained by subtracting ΔHvap from ΔHt. The thermodynamic properties of PAM are listed in Table 4, which could provide help for the research on phase equilibrium of PAM in SCCO2.
Figure 5. Experimental solubility of PAM for (a) Mn = 5 million, (b) Mn = 7 million, (c) Mn = 14 million in SCCO2 at (■) 313 K, (●) 323 K, and (▲) 333 K.
4. CONCLUSIONS The mole fraction y of PAM in SCCO2 was obtained using dynamic method from 313 to 333 K and 9.0 to 18.0 MPa, which was 2.34−7.72 × 10−10 for 5 million g·mol−1, 1.55−5.24 × 10−10 for 7 million g·mol−1 and 0.59−2.29 × 10−10 for 14 million g·mol−1 molecular weight. The self-consistency of PAM solubility was evaluated by M-T model. Five density-based semiempirical models (Chrastil, A-L, M-T, S−S, and Bartle
used to calculated the adjustable parameters by correlating the experimental solubility of PAM in SCCO2. As is shown in Table 2, the values of AARD of five models are in the range of 2.18−7.94%, which indicates that the calculated solubility has a good agreement with the E
DOI: 10.1021/acs.jced.6b00677 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 2. Correlated Results of Semiempirical Models for the Solubility of PAM in SCCO2 models
106·Mn (g·mol−1)
Chrastil
5 7 14 5 7 14 5 7 14 5 7 14 5 7 14
A-L
M-T
S−S
Bartle
adjustable parameters A1 A1 A1 A2 A2 A2 A3 A3 A3 A4 A4 A4 A5 A5 A5
= = = = = = = = = = = = = = =
no.
Chrastil
A-L
M-T
S−S
Bartle
Mn = 5 million Mn = 7 million Mn = 14 million
6.59 6.23 7.91
3.92 4.73 3.27
9.93 9.84 9.14
6.74 6.61 7.17
9.91 9.55 9.45
Table 4. Thermodynamic Properties of PAM no.
ΔHt (kJ/mol)
ΔHvap (kJ/mol)
ΔHsolv (kJ/mol)
Mn = 5 million Mn = 7 million Mn = 14 million
35.50 38.33 38.99
52.05 54.79 55.70
−16.55 −16.46 −16.71
models) were employed to correlate the solubility, and the AARD, AARD′ and adjustable parameters for each model were calculated, respectively. A-L model got the best AARD of 2.61% for PAM with 5 million g·mol−1, 3.15% for PAM with 7 million g·mol−1, and 2.18% for PAM with 14 million g·mol−1. The values of the total heat of solution, the enthalpies of vaporization (or sublimation), and solvation of PAM in SCCO2 were calculated. Finally, A-L model could be applied to predict the solubility of PAM in SCCO2 for the application of PAM in CO2 flooding.
AUTHOR INFORMATION
Corresponding Author
*E-mail address:
[email protected]. Tel.: +86 10 64434788. Fax: +86 10 64436781. Funding
This research was financially supported by the funds awarded by National Natural Science Foundation of China (No. 21476008) and the Ministry of Education of the People’s Republic of China (No. JD1504). The authors are grateful to the support of this research from the Mass Transfer and Separation Laboratory in Beijing University of Chemical Technology. Notes
The authors declare no competing financial interest.
■
5.27 4.98 6.33 2.61 3.15 2.18 7.94 7.87 7.31 4.94 4.85 5.26 7.93 7.64 7.56
(2) Vargaftik, N. B. Tables on Thermophsical Properties of Liquids and Gases, 2nd ed.; Halsted Press, Division of John Wiley & Sons, Inc.: New York, 1975. (3) Holm, L. W. A comparison of propane and carbon dioxide solvent flooding processes. AIChE J. 1961, 7, 179−184. (4) Doscher, T. M.; El-Arabi, M. High pressure model studies of oil recovery by carbon dioxide. Soc. Pet. Eng. J. 1981, DOI: 10.2118/9787MS. (5) Qin, J. S.; Han, H. S.; Liu, X. L. Application and enlightenment of carbon dioxide flooding in the United States of America. Pet. Explor. Dev. 2015, 42, 232−240. (6) Koottungal, L. 2014 worldwide EOR survey. Oil Gas J. 2014, 112, 79−91. (7) Espie, A. A.; Brand, P. J.; Skinner, R. C.; Hubbard, R. A.; Turan, H. I. Obstacles to the storage of CO2 through EOR operations in the North Sea. Greenhouse Gas Control Technol., Proc. Int. Conf., 6th 2003, 1, 213−218. (8) Quintella, C. M.; Dino, R.; Musse, A. P. S. CO2 Enhanced oil recovery and geologic storage: an overview with technology assessment based on patents and articles. Soc. Pet. Eng. J. 126122 2010, DOI: 10.2118/126122-MS. (9) Jablonowski, C.; Singh, A. A survey of CO2-EOR and CO2 storage project costs. Soc. Pet. Eng. J. 139669 2010, DOI: 10.2118/ 139669-MS. (10) Teklu, T. W.; Alameri, W.; Graves, R. M.; Kazemi, H.; Alsumaiti, A. M. Low-salinity water-alternating-CO2 EOR. J. Pet. Sci. Eng. 2016, 142, 101−118. (11) Rogers, J. D.; Grigg, R. B. A literature analysis of the WAG injectivity abnormalities in the CO2 process. Soc. Pet. Eng. J. 59329 2000, DOI: 10.2118/59329-MS. (12) Rahul, R.; Jha, U.; Sen, G.; Mishra, S. A novel polymeric flocculant based on polyacrylamide grafted inulin: Aqueous microwave assisted synthesis. Carbohydr. Polym. 2014, 99, 11−21. (13) Chrastil, J. Solubility of solids and liquids in supercritical gases. J. Phys. Chem. 1982, 86, 3016−3021. (14) Adachi, Y.; Lu, C. Y. Supercritical fluid extraction with carbon dioxide and ethylene. Fluid Phase Equilib. 1983, 14, 147−156. (15) Méndez-Santiago, J.; Teja, A. S. The solubility of solids in supercritical fluids. Fluid Phase Equilib. 1999, 158-160, 501−510. (16) Sung, H. D.; Shim, J. Solubility of C. I. disperse red 60 and C. I. disperse blue 60 in supercritical carbon dioxide. J. Chem. Eng. Data 1999, 44, 985−989. (17) Bartle, K. D.; Clifford, A.; Jafar, S. A.; Shilstone, G. F. Solubilities of solids and liquids of low volatility in supercritical carbon dioxide. J. Phys. Chem. Ref. Data 1991, 20, 713−756. (18) Tang, Z.; Jin, J. S.; Yu, X. Y.; Zhang, Z. T.; Liu, H. T. Equilibrium solubility of pure and mixed 3,5-dinitrobenzoic acid and 3nitrobenzoic acid in supercritical carbon dioxide. Thermochim. Acta 2011, 517, 105−114.
Table 3. AARD′ (%) of Five Models
■
AARD (%)
−1.783; B1 = −4.27 × 103; C1 = 1.800 −0.984; B1 = −4.61 × 103; C1 = 1.827 −0.866; B1 = −4.69 × 103; C1 = 1.822 −4.168; B2 = −4.56 × 103; C2 = 2.547; D2 = 7.19 × 10−4; E2 = 5.22 × 10−7 −1.084; B2 = −4.84 × 103; C2 = 2.194; D2 = 4.41 × 10−4; E2 = 3.49 × 10−7 −0.011; B2 = −5.02 × 103; C2 = 1.934; D2 = 3.88 × 10−4; E2 = 3.75 × 10−7 −6.89 × 103; B3 = 0.377; C3 = 1.052 −7.27 × 103; B3 = 0.994; C3 = 1.069 −7.35 × 103; B3 = 0.486; C3 = 1.073 −0.139; B4 = −8.62 × 103; C4 = −1.273; D4 = 6.77 × 102 −7.442; B4 = −6.42 × 103; C4 = −0.034; D4 = 2.81 × 102 17.23; B4 = −1.47 × 104; C4 = −3.979; D4 = 1.57 × 103 2.996; B5 = −6.26 × 103; C5 = 3.24 × 10−3 3.622; B5 = −6.59 × 103; C5 = 3.30 × 10−3 3.115; B5 = −6.70 × 103; C5 = 3.31 × 10−3
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DOI: 10.1021/acs.jced.6b00677 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
