Article pubs.acs.org/est
Partition Coefficients of Organics between Water and Carbon Dioxide Revisited: Correlation with Solute Molecular Descriptors and Solvent Cohesive Properties Michal Roth* Institute of Analytical Chemistry of the CAS, v. v. i., Veveří 97, 60200 Brno, Czech Republic S Supporting Information *
ABSTRACT: High-pressure phase behavior of systems containing water, carbon dioxide and organics has been important in several environment- and energy-related fields including carbon capture and storage, CO2 sequestration and CO2-assisted enhanced oil recovery. Here, partition coefficients (K-factors) of organic solutes between water and supercritical carbon dioxide have been correlated with extended linear solvation energy relationships (LSERs). In addition to the Abraham molecular descriptors of the solutes, the explanatory variables also include the logarithm of solute vapor pressure, the solubility parameters of carbon dioxide and water, and the internal pressure of water. This is the first attempt to include also the properties of water as explanatory variables in LSER correlations of K-factor data in CO2−water−organic systems. Increasing values of the solute hydrogen bond acidity, the solute hydrogen bond basicity, the solute dipolarity/polarizability, the internal pressure of water and the solubility parameter of water all tend to reduce the K-factor, that is, to favor the solute partitioning to the water-rich phase. On the contrary, increasing values of the solute characteristic volume, the solute vapor pressure and the solubility parameter of CO2 tend to raise the K-factor, that is, to favor the solute partitioning to the CO2-rich phase.
■
less able to predict them for the CO2−water−organic systems where no experimental data are available. For some composition-constrained properties such as the infinite-dilution solute partition coefficients (K-factors) in CO2−water systems, the use of models employing only pure component parameters may be expedient. To predict K-factors of organics in CO2−water systems, Lagalante and Bruno31 developed a linear solvation energy relationship (LSER) employing the following solute descriptors as the explanatory variables: the excess index of refraction, the dipolarity/polarizability, the effective hydrogen bond acidity, the effective hydrogen bond basicity and the McGowan’s characteristic volume.32 In addition, to account for the densitydependent, tunable solvent strength of CO2, the dipolarity/ polarizability of CO2 was introduced as another explanatory variable, π1, defined by
INTRODUCTION Phase behavior of systems containing water, carbon dioxide and organics has been relevant to several environment- and energyrelated fields including carbon capture and storage,1−4 CO2 sequestration5 and CO2-assisted enhanced oil recovery.6,7 A minor but distinct area of application has also been supercritical fluid extraction of aqueous media as a sample treatment technique of analytical chemistry.8−11 Consequently, partitioning of organics between supercritical CO2 and water or brine is an important topic,12 and there have been a number of experimental studies aimed either at the determination of solute partition coefficients (K-factors) in CO2−water systems at low concentrations of the organic solute13−25 or at the study of phase equilibria at finite concentrations of all components.26−28 In line with the experimental studies, several approaches to modeling the CO2−water−organic systems have been applied although the overall number of such models does not match the large attention received by the CO2−water binary system. Equation of state (EoS) models of the CO2−water−organic(s) systems such as those employing the Peng−Robinson EoS15,27,29,30 or the perturbed-chain statistical associating fluid theory28 provide good description of the phase equilibria, however, at the expense of introducing unlike interaction (binary) parameters. The unlike interaction parameters are difficult to predict beforehand and, therefore, the EoS models are well apt to correlate phase equilibrium data but somewhat © XXXX American Chemical Society
π1 = 1.15ρr − 0.98 (for ρr < 0.7)
(1)
π1 = 0.173ρr − 0.37 (for ρr > 0.7)
(2)
Received: Revised: Accepted: Published: A
June 28, 2016 September 25, 2016 October 28, 2016 October 28, 2016 DOI: 10.1021/acs.est.6b03210 Environ. Sci. Technol. XXXX, XXX, XXX−XXX
Article
Environmental Science & Technology where ρr is the reduced density of CO2 at the particular temperature and pressure. A similar model has been employed33 in modeling solid−fluid equilibria for supercritical process design. Timko et al.23 measured the CO2−water Kfactors of 18 organics at fixed conditions of 300 K and 8 MPa, and used several forms of LSERs to correlate their experimental data as well as a data set comprising all K-factor data then available (33 compounds, 332 data points). Recently, Burant et al.24 reported new K-factor data for thiophene, pyrrole, and anisole over a range of temperature and pressure, and used several training and testing data sets to develop various LSERs comprising also the solute vapor pressure and/or solute aqueous solubility as explanatory variables. In the LSER models mentioned above, the only explanatory variable used to account for temperature- and pressuredependent changes in the properties of solvents (CO2 and water) was either the reduced density of CO2 at the particular temperature and pressure or the function π1 defined by eqs 1 and 2. Therefore, the effects of temperature and pressure on water properties were not accounted for in the previous LSER models. This is understandable as the temperature and pressure region of the currently available K-factor data includes the critical region of CO2 while being rather far from the critical region of water, and so the temperature- and pressure-induced variations in the properties of CO2 may be expected to have a larger effect on the K-factors of organics than the variations in the properties of water. To obtain a more complete description, however, even the effect of variations in the water properties should be accounted for. The purpose of the present contribution is to develop correlations for K-factors of organics in CO2−water system using other temperature- and pressure-dependent solvent properties of both CO2 and water as explanatory variables. To make the correlations tractable, the mutual solubilities of CO2 and water have been neglected and pure-component properties of the two solvents have been employed.
K i = yi /xi
where yi is the equilibrium molar fraction of the solute in the CO2-rich phase and xi is the equilibrium molar fraction of the solute in the water-rich phase. The experimental K-factor data were taken from the original sources.13−26 However, some of the solutes, notably pentachlorophenol,19 2,3,4,5-tetrachlorophenol,21 3-methyl-4-chlorophenol,22 and 2-methyl-4,6-dinitrophenol22 and propiophenone23 were omitted because of the lack of vapor pressure data at the required temperatures (see below). Therefore, the most extensive set of experimental Kfactor data comprised 455 data points for 44 solutes of diverse structures and falling within the temperature range of 297−363 K and the pressure range of 2.5−31.5 MPa. This maximum set also involved K-factors of lower (C2−C4) alkanoic acids that were calculated from selected equilibrium compositions in the CO2−water−alkanoic acid systems reported by Panagiotopoulos et al.26 All source K-factor data are included in the Supporting Information. Solute Properties. The properties of solutes are primarily represented by the Abraham molecular descriptors36−38 including the excess molar refractivity Ei, dipolarity/polarizability Si, hydrogen bond acidity Ai, hydrogen bond basicity Bi, and the McGowan’s characteristic volume Vi.32 For most solutes, the descriptors were taken from an extensive database37 available on the Internet, with the values checked against a previous source36 wherever applicable. The descriptors of parathion were taken from the list reported by Tülp et al.38 All individual solute descriptors are compiled in the Supporting Information. In the development of the correlation, the Abraham molecular descriptors were later complemented with the logarithm of solute vapor pressure at the particular temperature as an additional explanatory variable. In most solutes, the vapor pressure values [kPa] were calculated from the Yaws’ compilation39 of the Antoine equation constants, with the vapor pressures of caffeine and parathion taken from other sources.40,41 In the largest set of K-factor data mentioned above, the range of solute vapor pressures spanned across 8 decadic orders of magnitude (from 4 × 10−7 kPa to 60 kPa), and the numerical data on solute vapor pressures are also included in the Supporting Information. Solvent Properties. The previous LSERs used in modeling solute K-factors in CO2−water systems employed the π1 variable defined by eqs 1 and 2. The variable features a discontinuity at ρr = 0.7. Alternatively, other well-defined solvent characteristics can be employed as explanatory variables, notably the cohesive energy density c and the solubility parameter δ,42
■
BACKGROUND PROPERTIES FOR EXTENDED LSER CORRELATION Basics: Starting Points. The LSERs34,35 assume that the logarithm of the modeled property ξ of a solute i can be expressed as a linear combination of k molecular descriptors usually related to the physicochemical properties of the solute, k
log ξi = log ξ0 +
∑ cjDij j=1
(4)
(3)
where Dij is the descriptor of the property j of the solute i. The coefficients cj, as well as the intercept (log ξ0), can be determined by linear regression of the vector of the properties to be modeled (log ξi) on the descriptor matrix (Dij). In data sets involving multiple solvents or fluid solvents with pressureand temperature-dependent solvating properties, some of the descriptors may relate to the properties of the solvent rather than the solute. In the previous applications of LSERs to Kfactor data in CO2−water systems, this applies to the dipolarity/polarizability of CO2 as defined by eqs 1 and 2.31,23,24 Some of the proposed LSERs also involved an explanatory variable that combined the properties of the solute and CO2.31 K-Factor Data Base. Partitioning of an organic solute i between both phases has often been characterized in terms of K-factor defined by
c=
Δuc u −u = 0 v v
δ = c1/2
(5) (6)
where Δuc is the molar cohesive energy, u is the molar internal energy at the particular temperature and pressure, u0 is the molar internal energy at the particular temperature in the ideal gas state (zero pressure), and v is the molar volume at the particular temperature and pressure. Another solvent characteristics that may be considered as an explanatory variable is the internal pressure of the solvent B
DOI: 10.1021/acs.est.6b03210 Environ. Sci. Technol. XXXX, XXX, XXX−XXX
Article
Environmental Science & Technology P int =
⎛ ∂u ⎞ ⎛ ∂P ⎞ ⎜ ⎟ = T⎜ ⎟ − P ⎝ ∂v ⎠T ⎝ ∂T ⎠v
coefficients d, p, a, b, w, and q can be determined by linear regression. The first two terms in the summation on the righthand side of eq 8 were partly inspired by the regular solution theory.42 Figure 1 shows the comparison of the experimental
(7)
where T is the temperature and P the pressure. The properties c, δ, and Pint of the two solvents can be calculated from high precision equations of state for carbon dioxide43 and water44 employing an interactive software package.45 The ideal gas state of either fluid, needed when calculating the cohesive energy and the derived properties c and δ (eqs 5 and 6), was always approximated by setting the pressure equal to 10−6 Pa. In all correlations mentioned below as well as in the Supporting Information, the units of c, δ, and Pint are J·cm−3, (J·cm−3)1/2 and MPa, respectively. The reason for considering also the internal pressure as an explanatory variable, in addition to the cohesive energy-derived properties c or δ, comes from an early suggestion by Wiehe and Bagley.46 They proposed that while the cohesive energy density measures the total interaction energy per unit volume of the fluid, including the hydrogen bonds, the internal pressure only reflects the part of the total interaction energy that is due to nonspecific interactions, with hydrogen bonds supposedly remaining intact on an infinitesimal change of the fluid’s volume. Therefore, because of very different abilities of water and CO2 for hydrogen bonding, the ratio c/Pint can be expected to behave differently in the two solvents. Table 1 shows a few
Figure 1. Calculated (eq 8) versus experimental K-factors in the set containing the data of Brudi et al.18 Solutes: (+) phenol, (○) benzyl alcohol, (□) benzoic acid, (■) 2-hexanone, (△) cyclohexanone, (▲) caffeine, (▽) vanillin.
and calculated values of Ki when the regression via eq 8 was applied to the K-factor data set of Brudi et al.18 It appears that the overall correlation tends to break apart to separate regions pertaining to the individual solutes. Hence, eq 8 fails to meet the intended purpose to embrace solutes of different structural classes within a single correlation. Moreover, eq 8 clearly underestimates the effects of temperature and pressure on the K-factor because, in most solutes, the variation of the calculated values is rather flat as compared with the variation in the respective experimental data. The flatness of the calculated profiles most probably results from the particular functional form of eq 8. There is apparently some offset among the effects of temperature and pressure on the cohesive energy densities and internal pressures of both CO2 and water. Therefore, to provide more flexibility in handling the effects of temperature and pressure on solute K-factor, improved correlation has been sought in the form of summation of simple terms. After testing with several different K-factor data sets and several different forms of the correlations, the most efficient correlation equation is
Table 1. Ratio of Cohesive Energy Density to Internal Pressure for Water and for CO2 c/Pint T (K)
P (MPa)
water
CO2
305 305 320 320 340 340 350 350
8 20 8 20 8 20 8 20
10.45 10.47 7.09 7.17 5.06 5.14 4.46 4.53
1.40 1.08 1.11 1.12 1.08 1.16 1.07 1.17
examples of c/Pint values for the two solvents at several temperatures and pressures within the scope of experimental Kfactor data. It appears that, in water, variations of c/Pint with temperature are relatively larger as compared with those in CO2. Therefore, both c (or δ) and Pint of water have been included as the explanatory variables. Because the currently available experimental K-factor data cover a rather narrow range of temperature, the cohesive properties of water are not expected to make the explanatory variables of primary importance. Nevertheless, they should provide additional, easy-to-obtain explanatory variables to cover a part of the residual variance that has not been covered by the previous correlations.31,23,24
log K i = eEi + sSi + aAi + bBi + wVi + dδCO2 + pδ H2O + tPHint2O + u log Pisat + q
where the coefficients e, s, a, b, w, d, p, t, u, and q are again determined by linear regression. Instead of the cohesive energies of both solvents, the solubility parameters were employed in eq 9. The internal pressure of CO2 was no longer considered as an explanatory variable because of relatively large standard error in the estimation of the respective coefficient, and the varying solvent power of CO2 has already been represented by the solubility parameter δCO2. Compared with eq 8, eq 9 performs considerably better when applied to the data set of Brudi et al.18 as illustrated in the Supporting Information. Application of eq 9 to a set of 207 data points18,20,23 is illustrated by Figure 2. This set contains 23 solutes of various
■
RESULTS AND DISCUSSION The original version of the proposed correlation was sought in the form int log K i = d(cCO2 − c H2O)Ei + p(PCO − PHint2O)Si + aAi 2
+ bBi + wVi + q
(9)
(8) int
where the solvent properties c and P always refer to the same temperature and pressure as the solute K-factor Ki, and the C
DOI: 10.1021/acs.est.6b03210 Environ. Sci. Technol. XXXX, XXX, XXX−XXX
Article
Environmental Science & Technology
Figure 2. Calculated (eq 9) versus experimental K-factors in the set containing the data of Brudi et al.,18 Wagner et al.20 and Timko et al.23 (n = 207). Solutes: (○) acetophenone,23 (□) benzaldehyde,23 (△) bromobenzene,23 (▽) methyl vinyl ketone,23 (◊) chlorobenzene,23 (×) cyclohexane,23 (+) cyclohexene,23 (green ○) cyclopentene,23 (green □) ethylbenzoate,23 (green △) fluorobenzene,23 (green ▽) hexane,23 (green ◊) methylbenzoate,23 (green ×) propylbenzoate,23 (green +) tetrahydrofuran,23 (red ○) toluene,23 (red □) phenol,18 (red △) benzyl alcohol,18 (red ▽) benzoic acid,18 (red ◊) 2hexanone,18 (red ×) cyclohexanone,18 (red +) caffeine,18 (blue ○) vanillin,18 (blue □) aniline,20 (blue △) benzaldehyde, GC-SPME detection,20 (blue ▽) benzaldehyde, UV/vis detection.20
Figure 3. Calculated (eq 9) versus experimental K-factors in the set containing the data of Sengupta et al.,16 Brudi et al.,18 Wagner et al.,20 Timko et al.,23 Burant et al.,24 and Bryce et al.25 (n = 282). Solutes: (○) acetophenone,23 (□) benzaldehyde,23 (△) bromobenzene,23 (▽) methyl vinyl ketone,23 (◊) chlorobenzene,23 (×) cyclohexane,23 (+) cyclohexene,23 (green ○) cyclopentene,23 (green □) ethylbenzoate,23 (green △) fluorobenzene,23 (green ▽) hexane,23 (green ◊) methylbenzoate,23 (green ×) propylbenzoate,23 (green +) tetrahydrofuran,23 (red ○) toluene,23 (brown ○) thiophene,24 (brown □) pyrrole,24 (brown △) anisole,24 (brown ▽) benzene,25 (brown ◊) 1,2dichloroethane,16 (brown ×) 1,1,2-trichloroethane,16 (brown +) 1,1,2,2-tetrachloroethane,16 (orange □) phenol,18 (orange △) benzyl alcohol,18 (orange ▽) benzoic acid,18 (orange ◊) 2-hexanone,18 (orange ×) cyclohexanone,18 (orange +) caffeine,18 (blue ○) vanillin,18 (blue □) aniline,20 (blue △) benzaldehyde, GC-SPME detection,20 (blue ▽) benzaldehyde, UV/vis detection.20
chemical structures, and the solute vapor pressures in the set span across 5 decadic orders of magnitude. There is no apparent relation between the solute structure and the deviation of the calculated from the experimental K-factor. The statistical parameters of the correlation are summarized in Table 2. In most regression coefficients, the ratio of the coefficient to the standard error of the coefficient exceeds the critical value47 of the t distribution at the 97.5% confidence level and the respective number of the degrees of freedom, meaning that the coefficient is statistically significant. It should be noted, however, that the relatively satisfactory performance of the correlation in Figure 2 may partly result from the fact that all experimental K-factor data by Timko et al.23 refer to a single temperature and pressure setting (300 K and 8 MPa, respectively). Figure 3 shows the correlation by eq 9 of a more extensive K-factor data set16,18,20,23−25 comprising 282 data points for 30 solutes. Performance of eq 9 with this data set still appears to be relatively acceptable, and the statistical parameters of the correlation are listed in Table 3.
Finally, eq 9 was employed to correlate the K-factor data in the most extensive data set mentioned above (455 data points for 44 solutes),13−26 including the K-factor values for lower alkanoic acids calculated from selected phase equilibrium data reported by Panagiotopoulos et al.26 Calculated and experimental values are compared in Figure 4, and the statistical parameters of the correlation are given in Table 4. Regardless of the number of explanatory variables, any model to correlate a diverse set of experimental data faces the problem of origin of the data scattering around the model prediction: What part of the scattering comes from inadequacy of the model, and what part comes from inconsistencies or errors in the set of experimental data measured by different methods in different laboratories? There is probably no definite way to safely distinguish between the two sources of scattering. However, the resultant correlation can provide some (although
Table 2. Regression of K-Factor Data18,20,23 with eq 9
a
coefficient
e
s
a
b
value std error |value/error|
−0.165 0.102 1.62
−0.462 0.046 9.96
−1.894 0.102 18.64
−2.026 0.164 12.37
d [(J·cm−3)−1/2]
w
4.461 0.112 0.226 0.008 19.71 14.78 n = 207a AAD = 0.148b med = 0.118c RMSE = 0.182d R2 = 0.971e
Number of data points in the set, n. bAverage absolute deviation AAD =
d − log Kexp median|ni=1| log Kcalc i i |. Root-mean-square error, RMSE =
1 n
1 n
p [(J·cm−3)−1/2]
t (MPa−1)
u
q
−0.726 0.258 2.81
−0.006 0.002 4.16
0.377 0.030 12.42
34.074 12.636 2.70
n
∑i = 1 |log K icalc − log K iexp|. cMedian value of absolute deviations, med = n
∑i = 1 (logK icalc − logK iexp)2 . eCoefficient of determination, R2. D
DOI: 10.1021/acs.est.6b03210 Environ. Sci. Technol. XXXX, XXX, XXX−XXX
Article
Environmental Science & Technology Table 3. Regression of K-Factor Data16,18,20,23−25 with eq 9 coefficient
e
s
a
b
value std error |value/error|
0.375 0.080 4.69
−0.572 0.051 11.27
−2.124 0.115 18.41
−1.392 0.119 11.66
d [(J·cm−3)−1/2]
w
4.081 0.096 0.215 0.007 19.02 13.00 n = 282 AAD = 0.173 med = 0.131 RMSE = 0.230 R2 = 0.952
p [(J·cm−3)−1/2]
t (MPa−1)
u
q
−0.747 0.282 2.65
−0.007 0.002 3.91
0.444 0.029 15.59
35.184 13.821 2.55
inconclusive) guide as regards the relative accuracy of different sources of experimental K-factor data for a particular solute. In the set of experimental data employed here, this concerns primarily the sources of K-factor data of benzene.13,14,25 The present correlation indicates that the benzene data of Bryce et al.25 are more accurate than those of Yeo and Akgerman13 and Ghonasgi et al.14 Compared with most previous K-factor correlations in CO2− water systems,31,23,24 the present LSER correlations employ more explanatory variables. Consequently, larger effort is required here to assemble the set of explanatory variables. However, the cohesive properties of CO2 and water are readily available from high-precision, pure component EoSs for the two fluids in a wide range of temperature and pressure employing a user-friendly software package. Compared with the previous correlations, this makes the preparation of the present set of explanatory variables somewhat more time-consuming and tedious rather than actually more difficult. Relative importance of the individual explanatory variables in the correlation described by eq 9 can be assessed from the ratio of the respective coefficient to its standard error although the resultant trends certainly apply only to the present selection of the organic solutes. With some variations in the order among the three data sets in Tables 2−4, the most important explanatory variables are the solute characteristic volume, the solute hydrogen bond acidity, the logarithm of solute vapor pressure, the solubility parameter of CO2, and the solute hydrogen bond basicity. The importance of the internal pressure of water and the solubility parameter of water as the explanatory variables is generally lower. Nevertheless, in relatively coherent data sets (Figures 2 and 3), even the cohesive properties of water contribute to the satisfactory performance of eq 9 in correlating the K-factor values in CO2− water systems. The signs (plus or minus) of the individual coefficients in Tables 2−4 reflect the effect of the respective explanatory variable (eq 9) on the solute K-factor. Apparently, increasing values of the solute hydrogen bond acidity, the solute hydrogen bond basicity, the solute dipolarity/polarizability, the internal
Figure 4. Calculated (eq 9) versus experimental K-factors in the largest data set (n = 455). Solutes: (○) benzene,13 (□) toluene,13 (△) naphthalene,13 (▽) parathion,13 (◊) phenol,14 (×) m-cresol,14 (+) pchlorophenol,14 (blue ○) benzene,14 (blue □) phenol,17 (blue △) pchlorophenol,17 (blue ▽) phenol,22 (blue ◊) salicylic acid,22 (blue ×) 2-nitrophenol,22 (blue +) 4-nitrophenol,22 (dark green ○) 2chlorophenol,22 (dark green □) 2,4-dichlorophenol,22 (dark green △) 2,4,6-trichlorophenol,22 (dark green ▽) 2,4-dimethylphenol,22 (dark green ◊) acetophenone,23 (dark green ×) benzaldehyde,23 (dark green +) bromobenzene,23 (light green ○) methyl vinyl ketone,23 (light green □) chlorobenzene,23 (light green △) cyclohexane,23 (light green ▽) cyclohexene,23 (light green ◊) cyclopentene,23 (light green ×) ethylbenzoate,23 (light green +) fluorobenzene,23 (brown ○) hexane,23 (brown □) methylbenzoate,23 (brown △) propylbenzoate,23 (brown ▽) tetrahydrofuran,23 (brown ◊) toluene,23 (brown ×) thiophene,24 (brown +) pyrrole,24 (red ○) anisole,24 (red □) benzene,25 (red △) 2,4-dichlorophenol,15 (red ▽) 1,2-dichloroethane,16 (red ◊) 1,1,2-trichloroethane,16 (red ×) 1,1,2,2-tetrachloroethane,16 (red +) phenol,18 (blue ○) benzyl alcohol,18 (blue □) benzoic acid,18 (blue △) 2-hexanone,18 (blue ▽) cyclohexanone,18 (blue ◊) caffeine,18 (blue ×) vanillin,18 (blue +) aniline,20 (olive ○) benzaldehyde, GC-SPME detection,20 (olive □) benzaldehyde, UV/vis detection,20 (olive △) acetic acid,26 (olive ▽) propionic acid,26 (olive ◊) butyric acid.26
Table 4. Regression of K-Factor Data in the Largest Set13−18,20,22−26 with eq 9 coefficient
e
s
a
b
value std error |value/error|
0.281 0.108 2.60
−0.406 0.062 6.56
−1.906 0.105 18.12
−1.887 0.157 12.01
d [(J·cm−3)−1/2]
w
3.497 0.084 0.187 0.008 18.74 10.42 n = 455 AAD = 0.278 med = 0.182 RMSE = 0.389 R2 = 0.885 E
p [(J·cm−3)−1/2]
t (MPa−1)
u
q
−0.126 0.271 0.46
−0.004 0.002 2.06
0.456 0.037 12.48
5.666 13.327 0.43
DOI: 10.1021/acs.est.6b03210 Environ. Sci. Technol. XXXX, XXX, XXX−XXX
Article
Environmental Science & Technology
Academy of Sciences (Institutional Research Plan RVO:68081715).
pressure of water and the solubility parameter of water all tend to reduce the K-factor, that is, to favor the solute partitioning to the water-rich phase. On the contrary, increasing values of the solute characteristic volume, the solute vapor pressure and the solubility parameter of CO2 tend to raise the K-factor, that is, to favor the solute partitioning to the CO2-rich phase. These findings largely conform to what one would expect. The finding that increasing solute characteristic volume (= solute molecular size) tends to favor solute partitioning to the CO2-rich phase obviously reflects the fact that bulkier solute molecules require more energy to break the water−water hydrogen bonds to create the cavity to accommodate the solute molecule in the hydrogen-bonded structure of water. To quantify the importance of water properties (cohesive energy density and internal pressure) as explanatory variables in correlating the K-factor data, the regressions presented in Tables 2−4 and Figures 2−4 were repeated with a truncated equation
■
log K i = eEi + sSi + aAi + bBi + wVi + dδCO2 + u log Pisat + q
(10)
with the water properties absent from the regression model. The resultant regression coefficients and other statistical parameters are listed in the Supporting Information. It appears that when replacing eq 10 with eq 9 as the model (i.e., when including the properties of water in the set of explanatory variables), the average absolute deviation drops by about 8% to 12%, the median of absolute deviations drops by about 13% to 21%, and the root-mean-square error drops by about 6% to 13%, depending on the K-factor data set. The effect of including the water properties turns out to be most important in the smallest data set (Table 2, Figure 2) and the least important in the largest set (Table 4, Figure 4). The probable reason is that the largest set of K-factor data is also the least consistent, with diverse sources of experimental data and the largest burden of experimental errors.
■
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.est.6b03210. Literature K-factor data of organic solutes at the listed temperature and pressure together with the explanatory variables including the Abraham molecular descriptors of the solutes, cohesive properties of water, cohesive properties of CO2, and vapor pressures of the solutes, as well as an illustration of the different performance of eqs 8 and 9 and an illustration of importance of the water property terms in the correlation (XLS)
■
REFERENCES
(1) Azar, C.; Lindgren, K.; Larson, E.; Möllersten, K. Carbon Capture and Storage From Fossil Fuels and Biomass − Costs and Potential Role in Stabilizing the Atmosphere. Clim. Change 2006, 74 (1), 47−79. (2) Gibbins, J.; Chalmers, H. Carbon capture and storage. Energy Policy 2008, 36 (12), 4317−4322. (3) Boot-Handford, M. E.; Abanades, J. C.; Anthony, E. J.; Blunt, M. J.; Brandani, S.; Mac Dowell, N.; Fernández, J. R.; Ferrari, M.-C.; Gross, R.; Hallett, J. P.; Haszeldine, R. S.; Heptonstall, P.; Lyngfelt, A.; Makuch, Z.; Mangano, E.; Porter, R. T. J.; Pourkashanian, M.; Rochelle, G. T.; Shah, N.; Yao, J. G.; Fennell, P. S. Carbon capture and storage update. Energy Environ. Sci. 2014, 7 (1), 130−189. (4) Kemper, J. Biomass and carbon dioxide capture and storage: A review. Int. J. Greenhouse Gas Control 2015, 40, 401−430. (5) De Silva, G. P. D.; Ranjith, P. G.; Perera, M. S. A. Geochemical aspects of CO2 sequestration in deep saline aquifers: A review. Fuel 2015, 155, 128−143. (6) Alvarado, V.; Manrique, E. Enhanced Oil Recovery: An Update Review. Energies 2010, 3 (9), 1529−1575. (7) Olea, R. A. CO2 retention values in enhanced oil recovery. J. Pet. Sci. Eng. 2015, 129, 23−28. (8) Ehntholt, D. J.; Thrun, K.; Eppig, C.; Ringhand, P. The Concentration of Model Organic Compounds Present in Water at Parts-per-Billion Levels using Supercritical Fluid Carbon Dioxide. Int. J. Environ. Anal. Chem. 1983, 13 (3), 219−235. (9) Hedrick, J.; Taylor, L. T. Quantitative Supercritical Fluid Extraction/Supercritical Fluid Chromatography of a Phosphonate from Aqueous Media. Anal. Chem. 1989, 61 (17), 1986−1988. (10) Thiebaut, D.; Chervet, J.-P.; van Noort, R. W.; de Jong, G. J.; Brinkman, U. A. Th.; Frei, R. W. Supercritical-fluid extraction of aqueous samples and on-line coupling to supercritical-fluid chromatography. J. Chromatogr. 1989, 477 (1), 151−159. (11) Kane, M.; Dean, J. R.; Hitchen, S. M.; Dowle, C. J.; Tranter, R. L. Extraction of surfactants from aqueous media by supercritical fluid extraction. Analyst 1995, 120 (2), 355−359. (12) Burant, A.; Lowry, G. W.; Karamalidis, A. K. Partitioning Behavior of Organic Contaminants in Carbon Storage Environments: A Critical Review. Environ. Sci. Technol. 2013, 47 (1), 37−54. (13) Yeo, S.-D.; Akgerman, A. Supercritical extraction of organic mixtures from aqueous solutions. AIChE J. 1990, 36 (11), 1743−1747. (14) Ghonasgi, D.; Gupta, S.; Dooley, K. M.; Knopf, F. C. Supercritical CO2 extraction of organic contaminants from aqueous streams. AIChE J. 1991, 37 (6), 944−950. (15) Akgerman, A.; Carter, B. D. Equilibrium Partitioning of 2,4Dichlorophenol between Water and Near-Critical and Supercritical Carbon Dioxide. J. Chem. Eng. Data 1994, 39 (3), 510−512. (16) Sengupta, S.; Gupta, S.; Dooley, K. M.; Knopf, F. C. Measurement and Modeling of Extraction of Chlorinated Hydrocarbons from Water with Supercritical Carbon Dioxide. J. Supercrit. Fluids 1994, 7 (3), 201−209. (17) Chang, C. M. J.; Huang, I. Separation of Phenolic Pollutants from Dilute Solutions Using Supercritical Carbon Dioxide and Nitrous Oxide. Sep. Sci. Technol. 1995, 30 (5), 683−695. (18) Brudi, K.; Dahmen, N.; Schmieder, H. Partition Coefficients of Organic Substances in Two-Phase Mixtures of Water and Carbon Dioxide at Pressures of 8 to 30 MPa and Temperatures of 313 to 333 K. J. Supercrit. Fluids 1996, 9 (3), 146−151. (19) Curren, M. S.; Burk, R. C. Supercritical Fluid Extraction of Acidic, Polar Solutes from Aqueous Matrices: Partitioning Data for Pentachlorophenol between Carbon Dioxide and Water. J. Chem. Eng. Data 1998, 43 (6), 978−982. (20) Wagner, K.-D.; Brudi, K.; Dahmen, N.; Schmieder, H. Partition coefficients of aromatic organic substances in two-phase mixtures of water and carbon dioxide at pressures from 8 to 30 MPa and at temperatures of 313 to 333 K. Part II. J. Supercrit. Fluids 1999, 15 (2), 109−116.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: +420 532 290 171. Fax: +420 541 212 113. Notes
The author declares no competing financial interest.
■
ACKNOWLEDGMENTS This contribution has been supported by the Czech Science Foundation (Project No. 16-03749S) and by The Czech F
DOI: 10.1021/acs.est.6b03210 Environ. Sci. Technol. XXXX, XXX, XXX−XXX
Article
Environmental Science & Technology (21) Curren, M. S. S.; Burk, R. C. Partitioning of Acidic Solutes between Water and Supercritical Carbon Dioxide. Effect of pH and Ionic Strength. J. Chem. Eng. Data 2000, 45 (5), 746−750. (22) Karásek, P.; Pól, J.; Planeta, J.; Roth, M.; Vejrosta, J.; Wičar, S. Partition Coefficients of Environmentally Important Phenols in a Supercritical Carbon Dioxide-Water System from Cocurrent Extraction without Analysis of the Compressible Phase. Anal. Chem. 2002, 74 (16), 4294−4299. (23) Timko, M. T.; Nicholson, B. F.; Steinfeld, J. I.; Smith, K. A.; Tester, J. W. Partition Coefficients of Organic Solutes between Supercritical Carbon Dioxide and Water: Experimental Measurements and Empirical Correlations. J. Chem. Eng. Data 2004, 49 (4), 768−778. (24) Burant, A.; Thompson, C. J.; Lowry, G. W.; Karamalidis, A. K. New Linear Partitioning Models based on Experimental Water − Supercritical CO2 Partitioning Data of Selected Organic Compounds. Environ. Sci. Technol. 2016, 50 (10), 5135−5142. (25) Bryce, D. A.; Shao, H. B.; Cantrell, K. J.; Thompson, C. J. Determination of Organic Partitioning Coefficients in Water-Supercritical CO2 Systems by Simultaneous In Situ UV and Near-Infrared Spectroscopies. Environ. Sci. Technol. 2016, 50 (11), 5766−5773. (26) Panagiotopoulos, A. Z.; Willson, R. C.; Reid, R. C. Phase Equilibria in Ternary Systems with Carbon Dioxide, Water, and Carboxylic Acids at Elevated Pressures. J. Chem. Eng. Data 1988, 33 (3), 321−327. (27) Lazzaroni, M. J.; Bush, D.; Jones, R.; Hallett, J. P.; Liotta, C. L.; Eckert, C. A. High-pressure phase equilibria of some carbon dioxide− organic−water systems. Fluid Phase Equilib. 2004, 224 (1), 143−154. (28) Fouad, W. A.; Yarrison, M.; Song, K. Y.; Cox, K. R.; Chapman, W. G. High Pressure Measurements and Molecular Modeling of the Water Content of Acid Gas Containing Mixtures. AIChE J. 2015, 61 (9), 3038−3052. (29) Roop, R. K.; Akgerman, A. Entrainer Effect for Supercritical Extraction of Phenol from Water. Ind. Eng. Chem. Res. 1989, 28 (10), 1542−1546. (30) Roop, R. K.; Akgerman, A. Distribution of a Complex Phenolic Mixture between Water and Supercritical Carbon Dioxide. J. Chem. Eng. Data 1990, 35 (3), 257−260. (31) Lagalante, A. F.; Bruno, T. J. Modeling the Water-Supercritical CO2 Partition Coefficients of Organic Solutes Using a Linear Solvation Energy Relationship. J. Phys. Chem. B 1998, 102 (6), 907−909. (32) Abraham, M. H.; McGowan, J. C. The Use of Characteristic Volumes to Measure Cavity Terms in Reversed Phase Liquid Chromatography. Chromatographia 1987, 23 (4), 243−246. (33) Bush, D.; Eckert, C. A. Prediction of solid−fluid equilibria in supercritical carbon dioxide using linear solvation energy relationships. Fluid Phase Equilib. 1998, 150−151, 479−492. (34) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. Linear Solvation Energy Relationships. 23. A Comprehensive Collection of the Solvatochromic Parameters, π*, α, and β, and Some Methods for Simplifying the Generalized Solvatochromic Equation. J. Org. Chem. 1983, 48 (17), 2877−2887. (35) Kamlet, M. J.; Doherty, R. M.; Abboud, J. L. M.; Abraham, M. H.; Taft, R. W. Solubility: A New Look. CHEMTECH 1986, 16 (9), 566−576. (36) Abraham, M. H.; Chadha, H. S.; Whiting, G. S.; Mitchell, R. C. Hydrogen bonding. 32. An analysis of water−octanol and water− alkane partitioning and the Δlog P parameter of Seiler. J. Pharm. Sci. 1994, 83 (8), 1085−1100. (37) Open Abraham Descriptor Data. http://lxsrv7.oru.edu/~alang/ abrahamdescriptors/ 20120223AcreeCompilationDescriptorsAddedToWebService.csv. (38) Tülp, H. C.; Goss, K.-U.; Schwarzenbach, R. P.; Fenner, K. Experimental Determination of LSER Parameters for a Set of 76 Diverse Pesticides and Pharmaceuticals. Environ. Sci. Technol. 2008, 42 (6), 2034−2040. (39) Yaws, C. L. The Yaws Handbook of Vapor Pressure. Antoine Coefficients, 2nd ed.; Elsevier: Amsterdam, 2015.
(40) Emelyanenko, V. N.; Verevkin, S. P. Thermodynamic properties of caffeine: Reconciliation of available experimental data. J. Chem. Thermodyn. 2008, 40 (12), 1661−1665. (41) Spencer, W. F.; Shoup, T. D.; Cliath, M. M.; Farmer, W. J.; Haque, R. Vapor Pressures and Relative Volatility of Ethyl and Methyl Parathion. J. Agric. Food Chem. 1979, 27 (2), 273−278. (42) Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall PTR: Upper Saddle River, NJ, 1999; pp 309−326. (43) Span, R.; Wagner, W. A New Equation of State for Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa. J. Phys. Chem. Ref. Data 1996, 25 (6), 1509−1596. (44) Wagner, W.; Pruss, A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31 (2), 387−535. (45) Wagner, W.; Overhoff, U. ThermoFluids: Interactive software for the Calculation of Thermodynamic Properties for More than 60 Pure Substances; Springer-Verlag: Berlin-Heidelberg, 2006. (46) Wiehe, I. A.; Bagley, E. B. Estimation of Dispersion and Hydrogen Bonding Energies in Liquids. AIChE J. 1967, 13 (5), 836− 838. (47) Critical Values of the Student’s t Distribution. http://www.itl. nist.gov/div898/handbook/eda/section3/eda3672.htm.
G
DOI: 10.1021/acs.est.6b03210 Environ. Sci. Technol. XXXX, XXX, XXX−XXX
