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Thermodynamic analysis of the mutual solubilities of normal alkanes and water
Fluid Phase Equilibria 156 Ž1999. 21–33
Thermodynamic analysis of the mutual solubilities of normal alkanes and water Constantine Tsonopoulos
)
Exxon Research and Engineering, Florham Park, NJ 07932, USA
Abstract Mutual solubility data for C 5 –C 16 alkanes and water close to 298 K are investigated, along with calorimetric heats of solution, as a function of the carbon number. The solubility of alkanes in water at 298 K drops steeply with increasing CN Žcarbon number., but the rate of decrease becomes significantly smaller for CN ) 11, possibly suggesting a transition to a ‘collapsed’ conformation that reduces contact of the alkane with water. Calorimetric data for the heat of solution of normal alkanes Žand normal alkylbenzenes. in water strongly suggest that the heat of solution is a linear function of temperature, in excellent agreement with solubility data, and both calorimetric and solubility data indicate a minimum in solubility Žheat of solutions 0. at around 303 K Žvs. 290 K for the alkylbenzenes.. The solubility of water in alkanes presents a much different picture from that of alkanes in water. First, the solubility of water in alkanes at 298 K is fairly insensitive to CN, rising slightly with increasing CN, while calorimetric measurements give a heat of solution that is nearly independent of temperature and CN. Its magnitude, 35 kJ moly1 Ž8.4 kcal moly1 ., is that of a normal hydrogen-bond energy, suggesting that the dissolution of n water molecules leads to the breaking of n hydrogen bonds. The temperature dependence of the solubility data is well represented by an equation that assumes a temperature-independent heat of solution that decreases slightly with increasing CN. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Alkane solubility; Water solubility; Carbon number effect; Heat of solution
1. Introduction Knowledge of the hydrocarbonrwater mutual solubilities is frequently important in the design and operation of process equipment in refineries and petrochemical plants. Hydrocarbons, like other pollutants, must be removed from refinery and petrochemical plant wastewater streams. Accordingly,
)
Tel.: q1-973-765-1380; fax: q1-973-765-1189; e-mail: [email protected]
0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 0 2 1 - 7
22
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
the solubility and volatility of the hydrocarbons are needed to trace their phase distribution through the entire process sequence and to design separation equipment Ž such as sour water strippers. for their removal. If the water present in a hydrocarbon mixture exceeds its solubility limit, a second liquid phase will form, the ‘free’ water phase, that can affect product specifications and equipment operation. Perhaps the most common adverse process effect is corrosion. Even when a free-water phase does not form, the solubility of water in hydrocarbons at 470 K and above is so high that the phase distribution of water can affect both the operation of the equipment, say, a distillation tower, and the product quality. Sometimes, however, a water-rich phase is formed intentionally, for example, to remove salts that would otherwise deposit out. This case also requires the accurate prediction of the solubility limits. The maximum temperature of interest in water pollution abatement is about 420 K, or even 470 K in certain cases, which can be reached in sour water strippers. On the hydrocarbon-rich side, the maximum temperature of interest is the three-phase critical end point temperature, the maximum temperature at which the hydrocarbon-rich liquid phase can exist. As shown in Fig. 1, this is below the critical temperature of the hydrocarbon. In a series of publications w1–3x, we presented new mutual solubility data on C 6 –C 12 hydrocarbons and water, where we emphasized the high-temperature range. Here, we focus on temperatures closer
Fig. 1. P – T diagram of n-decanerwater Žfrom Ref. w1x..
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
23
to 298 K Žgenerally, below 400 K. and examine both the mutual solubilities and the heats of solution as a function of the carbon number. As a first step, we consider the C 5 –C 16 normal alkanes Ž along with solubility of water in liquid ethane and propane. .
2. Mutual solubilities of alkanes and water An example of the phase behavior of alkanerwater binaries is given in Fig. 1 for n-decanerwater w3x. A point below the three-phase equilibrium curve represents equilibrium between one liquid phase and the vapor, while a point above the line represents equilibrium between the hydrocarbon-rich and water-rich liquid phases. All three phases are at equilibrium at P3 , the three-phase equilibrium pressure. Because the mutual solubilities are only weakly pressure-dependent w1x, the mutual solubilities are generally measured at P slightly above P3 Žif the vapor phase is of no interest.. As it will be shown later, the two mutual solubilities have a significantly different dependence on carbon number, as well as on temperature; that is, the two heats of solution are drastically different. The solubility of alkanes in water goes through a minimum Ž where the heat of solution is zero. , while that of water in alkanes increases monotonically with increasing temperature w1–3x. We will examine the solubility and heat of solution separately for alkanes in water and water in alkanes. First we will consider the solubility at 298 K, and then the heat of solution.
3. Solubility of alkanes in water 3.1. Solubility at 298 K The solubility of liquid normal alkanes in water at 298 K drops steeply with increasing molar volume, which is proportional to the carbon number. As shown in Fig. 2, the solubility goes from about 10 parts per million by mole for pentane to less than 10 parts per billion by mole for decane Žwhere the data w4x scatter between 1 and 7 mppb. . This steep drop in solubility with increasing carbon number is approximately given by the equation ln x hc s y3.9069 y 1.51894CN
Ž1.
which was obtained by regressing the solubility data for 5 F CN F 9 by Shaw w4x. Although the solubility continues to decrease with increasing carbon number for CN) 10, the data plotted in Fig. 2 1 w5–8x suggest, the scatter notwithstanding, a significantly weaker CN dependence for CN ) 11. This change has been attributed to the formation of micelles. The formation of such colloidal suspensions can indeed raise significantly the apparent Ž non-equilibrium. solubility w9,10x, 1
See additional information in Ref. w4x.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
24
Fig. 2. Solubility of normal alkanes in water at 298.15 K. Line calculated with Eq. Ž1..
but this could also result from a transition of the C 11 q normal alkanes to a ‘collapsed’ conformation, which would reduce contact of the alkane with water, and would thus make their solubility in water higher than that predicted by Eq. Ž 1.. Such a transition has been discussed for polymers in poor solvents w11x, and Fig. 2 raises the speculation that it may start for alkanes in water at around CN s 11. 3.2. Heat of solution Generally, it is accepted that the heat of solution includes two effects: a positive heat of cavitation and a negative heat of hydrophobic interaction between the alkane and water. These two effects cancel each other at Tmin , the temperature at which the alkane solubility goes through a minimum, with the heat of cavitation becoming the dominant effect at T ) Tmin .
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
25
The relationship between solubility and heat of solution is given by
ž
E ln x i ET
/
( P
Dhi
Ž2.
RT 2
D h i , the heat of solution, is the difference between the enthalpy of the hydrocarbon i in solution and the enthalpy of the pure hydrocarbon: D h i s h i Ž in solution. y h i Ž pure hc .
Ž3.
Thus, D h i s h Ei , the partial molar excess enthalpy of component i. Gill et al. w12,13x have measured the heat of solution of C 6 –C 9 normal alkylbenzenes and cyclohexane in water from 288.15 to 308.15 K, using a flow-microcalorimetric technique. Gill’s measurements have established that the heat of solution is a linear function of temperature; therefore, the heat capacity of solution Ž or the partial molar excess heat capacity. is constant. Such a linear dependence is also assumed for the normal alkanes, although Gill et al. w13x only measured the heat of solution at 288.15 and 298.15 K for n-pentane and n-hexane. Integration of Eq. Ž2., where D h i is expressed as a linear function of temperature, leads to Eq. Ž4. ln x hc s A q BrT q C lnT
Ž4.
where D c p s RC s 8.31451C J Ky1 moly1. The predicted minima in the solubility Ž where D h s 0. and the values of D c p from the data of Gill et al. for pentane and hexane are compared in Table 1 with the results obtained from the analysis of the solubility data of Jonsson et al. w14x for C 5 –C 8 ¨ normal alkanes in water, which confirm the linear dependence of D h on temperature. The agreement is better than what would normally be expected, because only the highly precise solubility data of Jonsson et al. were used in the comparison. Heats of solution measured calorimetrically and derived ¨ from solubility data are compared in Fig. 3 Žfrom Ref. w2x.. The minimum in the solubility of C 5 –C 8 alkanes in water is at around 303 K, with perhaps a slight decrease in Tmin with increasing carbon number. The more extensive calorimetric data of Gill et al. w12,13x for C 6 –C 9 normal alkylbenzenes give a minimum at 291 K Ž with a slight increase in Tmin with increasing CN. , which is confirmed by the solubility data of Bohon and Claussen w15x, which give Tmin s 290 " 1 K. Thus, the minimum in the liquid hydrocarbon solubility in water is very Table 1 Comparison of calorimetric and solubility data D c p ŽJ Ky1 moly1 . Pentane Hexane Heptane Octane Nonane a
Calorimetric
Solubility
Calorimetric
Solubility
400"70 440"45
399 448 474 495 515a
303 298
303.0 302.9 302.5 301.8 303b
Extrapolated value. Assumed average for alkanes.
b
T ŽK. at minimum solubility
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
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Fig. 3. Heat of solution of hydrocarbons in water Žfrom Ref. w3x..
definite, but the different affinity that alkanes and alkylbenzenes have for water possibly leads to a different Tmin . In view of the high precision of Jonsson’s solubility data Ž and their agreement with calorimetric ¨ data., an extrapolation was made to nonane on the basis of the following assumptions: D h s 0 at 303 K D c p s 515 J Ky1 moly1 The value of A in Eq. Ž4. was determined with the solubility value calculated with Eq. Ž1.. Selected data for the solubility of C 5 –C 9 normal alkanes w1,2,14,16–20x and the values calculated with Eq. Ž 4. Žwith the parameters given in Table 2. are compared in Fig. 4. Although there is
Table 2 Solubility of normal alkanes in water with Eq. Ž4. Alkane
A
B
C
Pentane Hexane Heptane Octane Nonanea
y333.59719 y374.90804 y396.93979 y415.7563 y433.434
14 537.472 16 327.128 17 232.298 17 975.386 18 767.82
47.97436 53.89582 56.95927 59.55451 61.940
a
Extrapolated; see text and Table 1.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
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Fig. 4. Solubility of C 5 –C 9 normal alkanes in water from 273 to 413 K. Lines calculated with Eq. Ž4. and the parameters in Table 2.
considerable scatter in the data, Eq. Ž4. with parameters based only on the data of Jonsson et al. w14x ¨ for C 5 –C 8 Žand extrapolated for C 9 . , does reasonably well up to around 400 K.
4. Solubility of water in alkanes 4.1. Solubility at 298 K The solubility of water in liquid alkanes at 298 K presents a much different picture from that of alkanes in water. Unlike the sharp drop in solubility with increasing CN shown in Fig. 2, the solubility of water in normal alkanes is fairly insensitive to CN, rising slightly with increasing CN.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
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Fig. 5 includes data for water in liquid ethane and propane from Parrish et al. w21x, in C 5 –C 8 from Polak and Lu w22x, in C 6 from Roddy and Coleman w23x, and in C 7 –C 16 from Schatzberg w24x. The dependence of the solubility of water on CN is given by ln x w s
y79.6677 y 6.6547CN
Ž5. 9.5470 q CN The solubility of water in n-hexadecane is only 60% greater than that in n-pentane, unlike the larger than four orders of magnitude difference between the solubility of these hydrocarbons in water Ž Fig. 2.. 4.2. Heat of solution The relationship between solubility and heat of solution is given by Eqs. Ž 2. and Ž 3.. However, here h i is the enthalpy of water in solution and h i is the enthalpy of pure liquid water. An important
Fig. 5. Solubility of water in normal alkanes at 298.15 K. Line calculated with Eq. Ž5..
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
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Table 3 Solubility of water in normal alkanes with Eq. Ž6. Alkane
A
B
D h w ŽkJ moly1 .
Pentane Hexane Heptane Octane Decane Hexadecane
6.951930 6.698073 6.76126 a 6.839365 6.476563 6.418156
y4381.365 y4291.186 Žy4290.7. b y4290.165 y4179.296 y4089.393
36.4 35.7 Ž35.7. b 35.7 34.7 34.0
a b
Determined with the solubility of water at 298.15 K from Eq. Ž5. and the interpolated value for B. Interpolated values.
difference is that the heat of solution for water in alkanes is always positive and is nearly the same for all alkanes.
Fig. 6. Solubility of water in n-octane. Line calculated with Eq. Ž6. and the parameters in Table 3.
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C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
Nilsson w25x measured the heat of solution for water in C 7 –C 12 normal alkanes at 298 K and concluded that, within experimental uncertainty, it is independent of CN and equal to Ž34.9 " 1.1. kJ moly1. What is striking about this large value for the heat of solution is that its magnitude is close to that of the hydrogen-bond energy. Typical values for the energy of a ‘normal’ hydrogen bond range between 20 and 40 kJ moly1 Ž5 to 10 kcal moly1 .. Thus, not surprisingly, the magnitude of the heat of solution suggests that dissolution of n water molecules leads to the breaking of n hydrogen bonds, which to a good approximation is independent of both carbon number and temperature. As a result, the solubility and the heat of solution of water in alkanes have only a weak dependence on carbon number and temperature. Among hydrocarbons, alkanes have the least affinity for water. That is, they must have the smallest Žin absolute sense. heat of hydrophobic interaction. Since this makes a negative contribution to the heat of solution, the heat of solution of water in other hydrocarbons should be less than that in alkanes. Indeed, Nilsson’s w25x calorimetric measurements in benzene give D h s 24.4 kJ moly1. This difference of ; 10 kJ moly1 between benzene and alkanes is a measure of the difference in the
Fig. 7. Solubility of water in n-heptane. Line calculated with Eq. Ž6. and the parameters in Table 3.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
31
respective heats of hydrophobic interaction with water. Ž X-ray diffraction data suggest that water forms weak hydrogen bonds to the aromatic p electrons of an aromatic compound in the solid state w26x.. If we assume that D h is constant, then D c p s 0 and integration of Eq. Ž2. gives ln x w s A q BrT
Ž6.
This simple equation, with the parameters in Table 3, fits the data remarkably well to within ; 30 K of the three-phase critical temperature, as can be seen in Fig. 6 for water in n-octane w2,22,27–30x. 2 ŽTo fit x w up to the three-phase critical temperature, 539 K, it is necessary to use the more complex equation derived in ŽRef. w2x; Eq. Ž 6. .. In agreement with the calorimetric data, the parameters B Žs 8.31451D h. are very slightly dependent on CN and give an average D h s 35.3 " 0.8 kJ moly1. However, the solubility data Ž which are not as smooth as those of Jonsson et al. w14x for alkanes in ¨ water. suggest that D h decreases slightly with increasing CN. Finally, Fig. 7 shows that the interpolated parameters for water in n-heptane Žsee Table 3. fit reasonably well the widely scattered solubility data 2 w22,24,27–29,31–33x, especially considering that the data of Black et al. w27x and Englin et al. w29x for water solubility in other hydrocarbons have always been found to be too high Ž see also Fig. 6. . Essentially no information is available for water in C 9 and C 11 –C 15 alkanes, except for the data of Schatzberg at 298 and 313 K w24x. 5. Conclusions and recommendations There is good agreement between solubility and calorimetric measurements, for both the solubility of alkanes in water and of water in alkanes. At 298 K, Fig. 2 clearly demonstrates that the solubility of alkanes in water decreases steeply with increasing carbon number, although around CN s 11 there appears to be a transition to a much slower solubility decrease with CN, possibly due to folding of the C 11 q alkanes. On the other hand, the solubility of water in alkanes at 298 K increases only slightly with CN ŽFig. 5.. There are two contributions to the heat of solution: a positive heat of cavitation and a negative heat of hydrophobic interaction. On the water-rich side, there is a definite minimum in the solubility around 303 K ŽFig. 4. , where the two contributions cancel each other. The heat of solution Ž either measured calorimetrically or derived from solubility data. is a linear function of temperature Ž Fig. 3. , thus, giving a constant heat capacity of solution. The solubility of water in alkanes increases monotonically with temperature ŽFigs. 6 and 7.. To an excellent approximation, the heat of solution of water in alkanes is a constant that changes only slightly with CN, because it is primarily influenced by the breaking of hydrogen bonds in water. The resulting two-parameter equation for the solubility of water in alkanes is very satisfactory to within about 30 K of the three-phase critical end point temperature ŽFig. 6.. It is hoped that the recommendations reached here on the mutual solubilities of alkanes and water ŽEqs. Ž1., Ž4. – Ž 6. ; Tables 2 and 3. will be useful both in engineering application and theoretical investigations. In the latter case, having a relatively clear picture on how the mutual solubilities depend on carbon number and temperature may facilitate the development of molecular models and 2
Data and later references are given in Ref. w4x.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
32
simulations that will explain at least some of the observations summarized in the previous paragraphs. It may then be possible to predict with some confidence the mutual solubilities of water with heavier or branched alkanes, as well as with other classes of hydrocarbons.
6. List of symbols A, B, C CN cp h hi h Ei P R T Tmin
parameters of Eqs. Ž4. and Ž6. number of carbon atoms heat capacity enthalpy Žheat. partial molar enthalpy partial molar excess enthalpy pressure gas constant absolute temperature temperature of minimum hydrocarbon solubility
x
liquid mole fraction
Greek letters D cp
heat capacity of solution
Dh
enthalpy Žheat. of solution
Subscripts hc w
property of hydrocarbon property of water
Acknowledgements The author is grateful to Exxon Research and Engineering, for permission to publish this paper, and to John L. Heidman, for suggesting Eq. Ž5. and other helpful comments.
References w1x w2x w3x w4x w5x w6x w7x w8x
C. Tsonopoulos, G.M. Wilson, AIChE J. 29 Ž1983. 990–999. J.L. Heidman, C. Tsonopoulos, C.J. Brady, G.M. Wilson, AIChE J. 31 Ž1985. 376–384. I.G. Economou, J.L. Heidman, C. Tsonopoulos, G.M. Wilson, AIChE J. 43 Ž1997. 535–546. D.G. Shaw ŽEd.., Hydrocarbons with Water and Seawater: Part I. Hydrocarbons C 5 to C 7 ; Part II. Hydrocarbons C 8 to C 36 , Vol. 37 and 38, IUPAC Solubility Data Series, Pergamon Press, Oxford, 1989. E.G. Baker, Science 129 Ž1959. 871–874. F. Franks, Nature 210 Ž1966. 87–88. C. Sutton, J.A. Calder, Environ. Sci. Technol. 8 Ž1974. 654–657. F. Yoshida, T. Yamane, Biotechnol. Bioeng. 13 Ž1971. 691–696.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
w9x w10x w11x w12x w13x w14x w15x w16x w17x w18x w19x w20x w21x w22x w23x w24x w25x w26x w27x w28x w29x w30x w31x w32x w33x
33
E. Peake, G.W. Hodgson, J. Am. Oil Chem. Soc. 43 Ž1966. 215–222. E. Peake, G.W. Hodgson, J. Am. Oil Chem. Soc. 44 Ž1967. 696–702. I. Szleifer, E.M. O’Toole, A.Z. Panagiotopoulos, J. Chem. Phys. 97 Ž1992. 6802–6808. S.J. Gill, N.F. Nichols, I. Wadso, ¨ J. Chem. Thermodyn. 7 Ž1975. 175–183. S.J. Gill, N.F. Nichols, I. Wadso, ¨ J. Chem. Thermodyn. 8 Ž1976. 445–452. J.A. Jonsson, J. Vejrosta, J. Novak, ¨ ´ Fluid Phase Equilibria 9 Ž1982. 279–286. R.L. Bohon, W.F. Claussen, J. Am. Chem. Soc. 73 Ž1951. 1571–1578. P.C. Gillespie, G.M. Wilson, Gas Processors Association Research Report 48, Tulsa, OK, 1982. C. McAuliffe, Nature 200 Ž1963. 1092–1093. C. McAuliffe, J. Phys. Chem. 70 Ž1966. 1267–1275. C. McAuliffe, Science 163 Ž1969. 478–479. L.C. Price, Am. Assoc. Petrol. Geol. Bull. 60 Ž1976. 213–244. W.R. Parrish, A.G. Pollin, T.W. Schidt, Proceedings of the 61st Gas Process, Assoc. Annual Convention, 1982, pp. 164–170. J. Polak, B.C.-Y. Lu, Can. J. Chem. 51 Ž1973. 4018–4023. J.W. Roddy, C.F. Coleman, Talanta 15 Ž1968. 1281–1286. P. Schatzberg, J. Phys. Chem. 67 Ž1963. 776–779. S.-O. Nilsson, J. Chem. Thermodyn. 18 Ž1986. 877–884. J.R. Atwood, F. Hamada, K.D. Robinson, G.W. Orr, R.L. Vincent, Nature 349 Ž1991. 683–684. C. Black, G.G. Joris, H.S. Taylor, J. Chem. Phys. 16 Ž1948. 537–543. L.S. Budantseva, T.M. Lesteva, N.M. Nemtsov, Russ. J. Phys. Chem. 50 Ž1976. 814. B.A. Englin, A.F. Plate, V.M. Tugolukov, M.A. Pryanishnikova, Chem. Technol. Fuel Oil 10 Ž1965. 722–726. R.G. Sultanov, V.G. Skripka, Russ. J. Phys. Chem. 46 Ž1972. 1245, VINITI Document No. 4386-72. H.-J. Bittrich, H. Gedan, G. Feix, Z. Phys. Chem. ŽLeipzig. 260 Ž1979. 1009–1013. N.A. Ghanem, M. Marek, J. Exner Ž1970.. Ya.D. Zel’venskii, A.A. Efremov, G.M. Larin, Chem. Technol. Fuel Oil 10 Ž1965. 506–510.
Thermodynamic analysis of the mutual solubilities of normal alkanes and water Constantine Tsonopoulos
)
Exxon Research and Engineering, Florham Park, NJ 07932, USA
Abstract Mutual solubility data for C 5 –C 16 alkanes and water close to 298 K are investigated, along with calorimetric heats of solution, as a function of the carbon number. The solubility of alkanes in water at 298 K drops steeply with increasing CN Žcarbon number., but the rate of decrease becomes significantly smaller for CN ) 11, possibly suggesting a transition to a ‘collapsed’ conformation that reduces contact of the alkane with water. Calorimetric data for the heat of solution of normal alkanes Žand normal alkylbenzenes. in water strongly suggest that the heat of solution is a linear function of temperature, in excellent agreement with solubility data, and both calorimetric and solubility data indicate a minimum in solubility Žheat of solutions 0. at around 303 K Žvs. 290 K for the alkylbenzenes.. The solubility of water in alkanes presents a much different picture from that of alkanes in water. First, the solubility of water in alkanes at 298 K is fairly insensitive to CN, rising slightly with increasing CN, while calorimetric measurements give a heat of solution that is nearly independent of temperature and CN. Its magnitude, 35 kJ moly1 Ž8.4 kcal moly1 ., is that of a normal hydrogen-bond energy, suggesting that the dissolution of n water molecules leads to the breaking of n hydrogen bonds. The temperature dependence of the solubility data is well represented by an equation that assumes a temperature-independent heat of solution that decreases slightly with increasing CN. q 1999 Elsevier Science B.V. All rights reserved. Keywords: Alkane solubility; Water solubility; Carbon number effect; Heat of solution
1. Introduction Knowledge of the hydrocarbonrwater mutual solubilities is frequently important in the design and operation of process equipment in refineries and petrochemical plants. Hydrocarbons, like other pollutants, must be removed from refinery and petrochemical plant wastewater streams. Accordingly,
)
Tel.: q1-973-765-1380; fax: q1-973-765-1189; e-mail: [email protected]
0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 0 2 1 - 7
22
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
the solubility and volatility of the hydrocarbons are needed to trace their phase distribution through the entire process sequence and to design separation equipment Ž such as sour water strippers. for their removal. If the water present in a hydrocarbon mixture exceeds its solubility limit, a second liquid phase will form, the ‘free’ water phase, that can affect product specifications and equipment operation. Perhaps the most common adverse process effect is corrosion. Even when a free-water phase does not form, the solubility of water in hydrocarbons at 470 K and above is so high that the phase distribution of water can affect both the operation of the equipment, say, a distillation tower, and the product quality. Sometimes, however, a water-rich phase is formed intentionally, for example, to remove salts that would otherwise deposit out. This case also requires the accurate prediction of the solubility limits. The maximum temperature of interest in water pollution abatement is about 420 K, or even 470 K in certain cases, which can be reached in sour water strippers. On the hydrocarbon-rich side, the maximum temperature of interest is the three-phase critical end point temperature, the maximum temperature at which the hydrocarbon-rich liquid phase can exist. As shown in Fig. 1, this is below the critical temperature of the hydrocarbon. In a series of publications w1–3x, we presented new mutual solubility data on C 6 –C 12 hydrocarbons and water, where we emphasized the high-temperature range. Here, we focus on temperatures closer
Fig. 1. P – T diagram of n-decanerwater Žfrom Ref. w1x..
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
23
to 298 K Žgenerally, below 400 K. and examine both the mutual solubilities and the heats of solution as a function of the carbon number. As a first step, we consider the C 5 –C 16 normal alkanes Ž along with solubility of water in liquid ethane and propane. .
2. Mutual solubilities of alkanes and water An example of the phase behavior of alkanerwater binaries is given in Fig. 1 for n-decanerwater w3x. A point below the three-phase equilibrium curve represents equilibrium between one liquid phase and the vapor, while a point above the line represents equilibrium between the hydrocarbon-rich and water-rich liquid phases. All three phases are at equilibrium at P3 , the three-phase equilibrium pressure. Because the mutual solubilities are only weakly pressure-dependent w1x, the mutual solubilities are generally measured at P slightly above P3 Žif the vapor phase is of no interest.. As it will be shown later, the two mutual solubilities have a significantly different dependence on carbon number, as well as on temperature; that is, the two heats of solution are drastically different. The solubility of alkanes in water goes through a minimum Ž where the heat of solution is zero. , while that of water in alkanes increases monotonically with increasing temperature w1–3x. We will examine the solubility and heat of solution separately for alkanes in water and water in alkanes. First we will consider the solubility at 298 K, and then the heat of solution.
3. Solubility of alkanes in water 3.1. Solubility at 298 K The solubility of liquid normal alkanes in water at 298 K drops steeply with increasing molar volume, which is proportional to the carbon number. As shown in Fig. 2, the solubility goes from about 10 parts per million by mole for pentane to less than 10 parts per billion by mole for decane Žwhere the data w4x scatter between 1 and 7 mppb. . This steep drop in solubility with increasing carbon number is approximately given by the equation ln x hc s y3.9069 y 1.51894CN
Ž1.
which was obtained by regressing the solubility data for 5 F CN F 9 by Shaw w4x. Although the solubility continues to decrease with increasing carbon number for CN) 10, the data plotted in Fig. 2 1 w5–8x suggest, the scatter notwithstanding, a significantly weaker CN dependence for CN ) 11. This change has been attributed to the formation of micelles. The formation of such colloidal suspensions can indeed raise significantly the apparent Ž non-equilibrium. solubility w9,10x, 1
See additional information in Ref. w4x.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
24
Fig. 2. Solubility of normal alkanes in water at 298.15 K. Line calculated with Eq. Ž1..
but this could also result from a transition of the C 11 q normal alkanes to a ‘collapsed’ conformation, which would reduce contact of the alkane with water, and would thus make their solubility in water higher than that predicted by Eq. Ž 1.. Such a transition has been discussed for polymers in poor solvents w11x, and Fig. 2 raises the speculation that it may start for alkanes in water at around CN s 11. 3.2. Heat of solution Generally, it is accepted that the heat of solution includes two effects: a positive heat of cavitation and a negative heat of hydrophobic interaction between the alkane and water. These two effects cancel each other at Tmin , the temperature at which the alkane solubility goes through a minimum, with the heat of cavitation becoming the dominant effect at T ) Tmin .
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
25
The relationship between solubility and heat of solution is given by
ž
E ln x i ET
/
( P
Dhi
Ž2.
RT 2
D h i , the heat of solution, is the difference between the enthalpy of the hydrocarbon i in solution and the enthalpy of the pure hydrocarbon: D h i s h i Ž in solution. y h i Ž pure hc .
Ž3.
Thus, D h i s h Ei , the partial molar excess enthalpy of component i. Gill et al. w12,13x have measured the heat of solution of C 6 –C 9 normal alkylbenzenes and cyclohexane in water from 288.15 to 308.15 K, using a flow-microcalorimetric technique. Gill’s measurements have established that the heat of solution is a linear function of temperature; therefore, the heat capacity of solution Ž or the partial molar excess heat capacity. is constant. Such a linear dependence is also assumed for the normal alkanes, although Gill et al. w13x only measured the heat of solution at 288.15 and 298.15 K for n-pentane and n-hexane. Integration of Eq. Ž2., where D h i is expressed as a linear function of temperature, leads to Eq. Ž4. ln x hc s A q BrT q C lnT
Ž4.
where D c p s RC s 8.31451C J Ky1 moly1. The predicted minima in the solubility Ž where D h s 0. and the values of D c p from the data of Gill et al. for pentane and hexane are compared in Table 1 with the results obtained from the analysis of the solubility data of Jonsson et al. w14x for C 5 –C 8 ¨ normal alkanes in water, which confirm the linear dependence of D h on temperature. The agreement is better than what would normally be expected, because only the highly precise solubility data of Jonsson et al. were used in the comparison. Heats of solution measured calorimetrically and derived ¨ from solubility data are compared in Fig. 3 Žfrom Ref. w2x.. The minimum in the solubility of C 5 –C 8 alkanes in water is at around 303 K, with perhaps a slight decrease in Tmin with increasing carbon number. The more extensive calorimetric data of Gill et al. w12,13x for C 6 –C 9 normal alkylbenzenes give a minimum at 291 K Ž with a slight increase in Tmin with increasing CN. , which is confirmed by the solubility data of Bohon and Claussen w15x, which give Tmin s 290 " 1 K. Thus, the minimum in the liquid hydrocarbon solubility in water is very Table 1 Comparison of calorimetric and solubility data D c p ŽJ Ky1 moly1 . Pentane Hexane Heptane Octane Nonane a
Calorimetric
Solubility
Calorimetric
Solubility
400"70 440"45
399 448 474 495 515a
303 298
303.0 302.9 302.5 301.8 303b
Extrapolated value. Assumed average for alkanes.
b
T ŽK. at minimum solubility
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
26
Fig. 3. Heat of solution of hydrocarbons in water Žfrom Ref. w3x..
definite, but the different affinity that alkanes and alkylbenzenes have for water possibly leads to a different Tmin . In view of the high precision of Jonsson’s solubility data Ž and their agreement with calorimetric ¨ data., an extrapolation was made to nonane on the basis of the following assumptions: D h s 0 at 303 K D c p s 515 J Ky1 moly1 The value of A in Eq. Ž4. was determined with the solubility value calculated with Eq. Ž1.. Selected data for the solubility of C 5 –C 9 normal alkanes w1,2,14,16–20x and the values calculated with Eq. Ž 4. Žwith the parameters given in Table 2. are compared in Fig. 4. Although there is
Table 2 Solubility of normal alkanes in water with Eq. Ž4. Alkane
A
B
C
Pentane Hexane Heptane Octane Nonanea
y333.59719 y374.90804 y396.93979 y415.7563 y433.434
14 537.472 16 327.128 17 232.298 17 975.386 18 767.82
47.97436 53.89582 56.95927 59.55451 61.940
a
Extrapolated; see text and Table 1.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
27
Fig. 4. Solubility of C 5 –C 9 normal alkanes in water from 273 to 413 K. Lines calculated with Eq. Ž4. and the parameters in Table 2.
considerable scatter in the data, Eq. Ž4. with parameters based only on the data of Jonsson et al. w14x ¨ for C 5 –C 8 Žand extrapolated for C 9 . , does reasonably well up to around 400 K.
4. Solubility of water in alkanes 4.1. Solubility at 298 K The solubility of water in liquid alkanes at 298 K presents a much different picture from that of alkanes in water. Unlike the sharp drop in solubility with increasing CN shown in Fig. 2, the solubility of water in normal alkanes is fairly insensitive to CN, rising slightly with increasing CN.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
28
Fig. 5 includes data for water in liquid ethane and propane from Parrish et al. w21x, in C 5 –C 8 from Polak and Lu w22x, in C 6 from Roddy and Coleman w23x, and in C 7 –C 16 from Schatzberg w24x. The dependence of the solubility of water on CN is given by ln x w s
y79.6677 y 6.6547CN
Ž5. 9.5470 q CN The solubility of water in n-hexadecane is only 60% greater than that in n-pentane, unlike the larger than four orders of magnitude difference between the solubility of these hydrocarbons in water Ž Fig. 2.. 4.2. Heat of solution The relationship between solubility and heat of solution is given by Eqs. Ž 2. and Ž 3.. However, here h i is the enthalpy of water in solution and h i is the enthalpy of pure liquid water. An important
Fig. 5. Solubility of water in normal alkanes at 298.15 K. Line calculated with Eq. Ž5..
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
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Table 3 Solubility of water in normal alkanes with Eq. Ž6. Alkane
A
B
D h w ŽkJ moly1 .
Pentane Hexane Heptane Octane Decane Hexadecane
6.951930 6.698073 6.76126 a 6.839365 6.476563 6.418156
y4381.365 y4291.186 Žy4290.7. b y4290.165 y4179.296 y4089.393
36.4 35.7 Ž35.7. b 35.7 34.7 34.0
a b
Determined with the solubility of water at 298.15 K from Eq. Ž5. and the interpolated value for B. Interpolated values.
difference is that the heat of solution for water in alkanes is always positive and is nearly the same for all alkanes.
Fig. 6. Solubility of water in n-octane. Line calculated with Eq. Ž6. and the parameters in Table 3.
30
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
Nilsson w25x measured the heat of solution for water in C 7 –C 12 normal alkanes at 298 K and concluded that, within experimental uncertainty, it is independent of CN and equal to Ž34.9 " 1.1. kJ moly1. What is striking about this large value for the heat of solution is that its magnitude is close to that of the hydrogen-bond energy. Typical values for the energy of a ‘normal’ hydrogen bond range between 20 and 40 kJ moly1 Ž5 to 10 kcal moly1 .. Thus, not surprisingly, the magnitude of the heat of solution suggests that dissolution of n water molecules leads to the breaking of n hydrogen bonds, which to a good approximation is independent of both carbon number and temperature. As a result, the solubility and the heat of solution of water in alkanes have only a weak dependence on carbon number and temperature. Among hydrocarbons, alkanes have the least affinity for water. That is, they must have the smallest Žin absolute sense. heat of hydrophobic interaction. Since this makes a negative contribution to the heat of solution, the heat of solution of water in other hydrocarbons should be less than that in alkanes. Indeed, Nilsson’s w25x calorimetric measurements in benzene give D h s 24.4 kJ moly1. This difference of ; 10 kJ moly1 between benzene and alkanes is a measure of the difference in the
Fig. 7. Solubility of water in n-heptane. Line calculated with Eq. Ž6. and the parameters in Table 3.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
31
respective heats of hydrophobic interaction with water. Ž X-ray diffraction data suggest that water forms weak hydrogen bonds to the aromatic p electrons of an aromatic compound in the solid state w26x.. If we assume that D h is constant, then D c p s 0 and integration of Eq. Ž2. gives ln x w s A q BrT
Ž6.
This simple equation, with the parameters in Table 3, fits the data remarkably well to within ; 30 K of the three-phase critical temperature, as can be seen in Fig. 6 for water in n-octane w2,22,27–30x. 2 ŽTo fit x w up to the three-phase critical temperature, 539 K, it is necessary to use the more complex equation derived in ŽRef. w2x; Eq. Ž 6. .. In agreement with the calorimetric data, the parameters B Žs 8.31451D h. are very slightly dependent on CN and give an average D h s 35.3 " 0.8 kJ moly1. However, the solubility data Ž which are not as smooth as those of Jonsson et al. w14x for alkanes in ¨ water. suggest that D h decreases slightly with increasing CN. Finally, Fig. 7 shows that the interpolated parameters for water in n-heptane Žsee Table 3. fit reasonably well the widely scattered solubility data 2 w22,24,27–29,31–33x, especially considering that the data of Black et al. w27x and Englin et al. w29x for water solubility in other hydrocarbons have always been found to be too high Ž see also Fig. 6. . Essentially no information is available for water in C 9 and C 11 –C 15 alkanes, except for the data of Schatzberg at 298 and 313 K w24x. 5. Conclusions and recommendations There is good agreement between solubility and calorimetric measurements, for both the solubility of alkanes in water and of water in alkanes. At 298 K, Fig. 2 clearly demonstrates that the solubility of alkanes in water decreases steeply with increasing carbon number, although around CN s 11 there appears to be a transition to a much slower solubility decrease with CN, possibly due to folding of the C 11 q alkanes. On the other hand, the solubility of water in alkanes at 298 K increases only slightly with CN ŽFig. 5.. There are two contributions to the heat of solution: a positive heat of cavitation and a negative heat of hydrophobic interaction. On the water-rich side, there is a definite minimum in the solubility around 303 K ŽFig. 4. , where the two contributions cancel each other. The heat of solution Ž either measured calorimetrically or derived from solubility data. is a linear function of temperature Ž Fig. 3. , thus, giving a constant heat capacity of solution. The solubility of water in alkanes increases monotonically with temperature ŽFigs. 6 and 7.. To an excellent approximation, the heat of solution of water in alkanes is a constant that changes only slightly with CN, because it is primarily influenced by the breaking of hydrogen bonds in water. The resulting two-parameter equation for the solubility of water in alkanes is very satisfactory to within about 30 K of the three-phase critical end point temperature ŽFig. 6.. It is hoped that the recommendations reached here on the mutual solubilities of alkanes and water ŽEqs. Ž1., Ž4. – Ž 6. ; Tables 2 and 3. will be useful both in engineering application and theoretical investigations. In the latter case, having a relatively clear picture on how the mutual solubilities depend on carbon number and temperature may facilitate the development of molecular models and 2
Data and later references are given in Ref. w4x.
C. Tsonopoulosr Fluid Phase Equilibria 156 (1999) 21–33
32
simulations that will explain at least some of the observations summarized in the previous paragraphs. It may then be possible to predict with some confidence the mutual solubilities of water with heavier or branched alkanes, as well as with other classes of hydrocarbons.
6. List of symbols A, B, C CN cp h hi h Ei P R T Tmin
parameters of Eqs. Ž4. and Ž6. number of carbon atoms heat capacity enthalpy Žheat. partial molar enthalpy partial molar excess enthalpy pressure gas constant absolute temperature temperature of minimum hydrocarbon solubility
x
liquid mole fraction
Greek letters D cp
heat capacity of solution
Dh
enthalpy Žheat. of solution
Subscripts hc w
property of hydrocarbon property of water
Acknowledgements The author is grateful to Exxon Research and Engineering, for permission to publish this paper, and to John L. Heidman, for suggesting Eq. Ž5. and other helpful comments.
References w1x w2x w3x w4x w5x w6x w7x w8x
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