2180
Znd. Eng. Chem. Res. 1991,30, 2180-2185
Heat Mass Transfer 1968,11, 1087-1104. Schmidt, R. R.; Sparrow, E. M.Turbulent Flow of Water in a Tube with Circumferentially Nonuniform Heating, With or Without Buoyancy. J. Heat Transfer 1978,100,403. Shoham, 0.;Dukler, A. E.; Taitel, Y. Heat Transfer During Intermittent/Slug Flow in Horizontal Tubes. Znd. Eng. Chem. Fundam. 1982,21,312-318. Taitel, Y.; Dukler, A. E. A Model for Slug Frequency During Gas-
Liquid Flow in Horizontal and Near Horizontal Pipee. Znt. J. Multiphase Flow 1977,3,585-596. Tronconi, E. Prediction of Slug Frequency in Horizontal Two-Phase Slug Flow. AZChE J. 1990,36(5), 701-709.
Received for review October 12, 1990 Revised manuscript received January 14, 1991 Accepted February 27,1991
Prediction of High-pressure Gas Solubilities in Aqueous Mixtures of Electrolytes Kim Aasberg-Petersen, Erling Stenby,* and Aage Fredenslund Engineering Research Center IVC-SEP, Imtitut for Kemiteknik, The Technical University of Denmark, DK 2800 Lyngby, Denmark
This work presents a new model for prediction of the solubilities of gases in aqueous electrolyte solutions at high pressures. The model combines an equation of state (EOS)with a modified
Debye-Huckel electrostatic contribution. The EOS used in this work is the ALS equation with a volume-dependent mixing rule for determination of the mixture a parameter. A single temperatureand composition-independent parameter is used to take into account gas-salt interactions. This parameter may be obtained by using readily available low pressure experimental data. Predicted solubilities of N2, CHI, and C02 in aqueous solutions of NaCl and CaC12agree well with experimental data at almost all pressures and salt concentrations up to 4 mol/kg. T h e new model is compared with and found to be superior to an earlier model of Harvey and Prausnitz. Finally, the solubility of a natural gas in a reservoir brine has been calculated. The predicted solubilities are in good agreement with experimental data.
Introduction The purpose of this work was to develop a model for predicting the high-pressure solubility of natural gases in brine or formation water. The mixtures of interest contain various light hydrocarbons, Nz, COP,and water with dissolved salts, often at high temperatures and pressures. Many models have been developed that are able to predict phase equilibria of mixtures that contain both polar and nonpolar compounds. This is usually done either by introducing a volume-dependent a parameter mixing rule into a conventional cubic equation of state (EOS) or by coupling the EOS with an activity coefficient model (e.g., Huron and Vidal, 1979; Mathias and Copeman, 1983; Mollerup, 1985; Gani et al., 1989; Michelsen, 1989). However, none of these models can take into account the presence of ions. Numerous models have also been developed for predicting vapor-liquid equilibria in mixtures containing electrolytes (e.g., Sander et al., 1986; Macedo et al., 1990) but do not in general include noncondensable gases. In addition, these models are usually limited to low pressures. It is the purpose of this paper to describe a new model for predicting the high-pressure gas solubilities in aqueous electrolyte solutions. It was our objective to develop a simple method for which the necessary interaction parameters for high-pressure predictions can be obtained by using easily available low-pressure experimental data. The Model The model described in this paper is based on the assumption that no ions are present in the gas phase. It is therefore necessary only to develop expressions for calculation of the fugacities of the nonionic components in the mixture. The following equation has proven to be a successful1 basis for predicting vapor-liquid equilibria for mixtures
with electrolytes at low pressures (Sander et al., 1986; Macedo et al., 1990): In yi = In y:CT + In yiEL (1) yiACTis evaluated by using a conventional activity coefficient model (e.g., UNIQUAC),and rimis an electrostatic contribution. It is not possible to use activity coefficient models for mixtures with noncondensable gases at high pressures. The following expression analogous to eq 1 is therefore suggested as basis for the new model: In di = In diEoS+ In 4iEL i = 1, ...,N (2)
N is the number of nonelectrolytic components (gases or solvents) in the mixture. Equation 2 states that the fugacity coefficient may be calculated as a product of a contribution from an EOS and a contribution from an electrostatic term. The second term on the right-hand side of eq 2 is equal to zero if the mixture is free of electrolytes. Since di = di0yi,eq 2 may be rewritten as In 4i = In 4io+ In yiEoS+ In yPL i = 1, ...,N (3) di0 is the pure component fugacity coefficient at the same temperature and pressure as the mixture. Since $iois independent of composition, dio is equal to 4j0ms.Equation 3 then becomes In di = In dims + In yiEL i = 1, ...,N (4) Any model suitable for correlation of gas-water equilibria may be used to calculate the first term on the right-hand side of eq 4. In this work the ALS EOS (Adachi et al., 1983) as modified by Jensen (1987) is employed. The ALS EOS is a(T) p = - RT (5) u - bl ( u - b&(U + b,)
0888-5885f 91f 2630-218O$02.50f 0 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 9,1991 2181 Table 1. Values of Parameters C,-C, (&e Eq 8) component water methane ethane propane
n-butane
co NZ
co2
C1
CZ
c,
0.8742 0.4497 0.6300 0.8007 0.6622 0.4739 0.4617 0.6934
-0.1988 -0.2536 O.oo00 O.oo00 O.oo00
0.1170 0.4945 O.oo00
O.oo00 O.oo00
O.oo00 O.oo00
-0.0334
0.6860
(16)
O.oo00 O.oo00
For pure componenta the four parameters are obtained as follows: a(T) = 4T)ac (6) ac = Qa(RTc)'/Pc (7) 4T) = [ l + C1(1 - TR'/') + Cz(1 - TR1/')' + C3(l - TR'/')']~ (8) b k = Qb@T,./P, k = 1, 2, 3 (9) In eq 8 TR is the reduced temperature. Expressions for calculation of 0, and Qb& are given in the Appendix. The equation for determination of a(T) was suggested by Mathias and Copeman (1983) for obtaining accurate correlations of pure component vapor pressures for polar substances. Equation 8 has also been used for CHI and COz. For all other gases parameters Czand C3have been set equal to 0, and C1has been calculatedfrom the acentric factor correlation suggested by Adachi et al. (1983): C1 = 0.4070 + 1 . 3 7 8 7 ~- 0.2933~' (10) Table I gives values of parameters C1-C3 for some substances. The conventional linear mixing rule is used for determination of the mixture b parameters: N
bk = &bk,i
k = 1, 2, 3
i
(11)
The following volume-dependent a parameter mixing rule is employed: .-.?IC
The parameters a" and ancare determined from N N
N
N
a" = Cx?a?Cxjtji i
I
tii = tjj = 0
(14)
The mixing rule defined by eqs 12-14 was derived by Mathias and Copeman (1983) using the Peng-Robinson equation of state. In the derivation Mathias and Copeman suggested to use uci instead of ai in eq 14. In our experience, however, correlation of gas solubilities has been considerably improved by using the temperature-dependent am (Aasberg-Petersen, 1991). Useful insight into the nature of the mixing rule may be gained by writing the expression for a" for a mixture of water (component N ) and N - 1 gases:
In the liquid phase all gas mole fractions are close to zero. Setting X N = 1 - zxi (i = 1, 2, ...,N - 1) and discarding all terms involving a product of two or more gas mole fractions, the following is obtained from eq 15:
The above derivation shows that in the liquid phase ,t has little importance compared to -t* In the vapor phase the parameter am has little or no influence since the molar volumes are large compared to bz and b3 (see eq 12). It should be noted that in all preceding equations the parameters are evaluated by using the salt-free mole fractions defined by
NIS is the total number of ionic species and ti are the true mole fractions. The basis for determination of the term In yin. in eq 4 is the following Debye-Huckel activity coefficient expression (Macedo et al., 1990):
Mi is the pure component molecular weight (kg/mol), di and d, are the pure-component and salt-free mixture densities (kg/m3), and I is the ionic strength based on molality. Equation 18 was chosen because of its success in phase equilibrium calculations for mixtures with electrolytes (Macedo et al., 1990). Since the gas solubility is quite low, it has in this work been assumed that d, may be set equal to the density of pure water (dN). dN is obtained as function of temperature by using the DIPPR tables (1985). The function f ( z ) is obtained from f ( z ) = 1 + z - 1/(1 + z ) - 2 In (1 + z ) (19) The parameters A and B are given by A = 1.327757 X 106d,1/2/(t,T)3/2
(20)
B = 6.359696 X dm1/2/(tmT)'/2 (21) e, is the salt-free mixture dielectric constant. For a mixture of gases and water, t, is evaluated from (AasbergPetersen, 1991) ,6 = X N ~ N (22) xNand tN are the salt-free mole fraction and the dielectric constant of water. eN is calculated by using data from the CRC Handbook of Chemistry and Physics (1987). When supercritical gases are present in the mixture, it is impoaible to work with pure-component liquid densities. The following empirical expression is therefore suggested for the ratio d,/di in eq 18: d,/di = hisM,/Mi i = 1, ..., N (23) M, is the salt-free mixture molecular weight determined as a molar average and hi, may be interpreted as an interaction coefficient between the dissolved salt and a nonelectrolytic component. In this work hi, is assumed independent of temperature, composition, and ionic strength. On the basis of the above considerations, the following expression is obtained for determination of In yiEL:
Parameter Evaluation and Results The optimal values of the three binary nonelectrolytic interaction coefficients (k12, t12, t z l ) were determined by regression using experimental salt-free gas-liquid equi-
2182 Ind. Eng. Chem. Res., Vol. 30,No. 9, 1991 Table 11. Binary Gas (1)-Water (2) Interaction Coefficients (N, Number of Experimental Points; T and P, Experimental Temwrature and Pressure Ranges) CHI C2H6 C3H8 n-C4H10 N2 co COZ k i_i 0.062 0.313 0.253 0.172 0.278 0.173 0.101 -0.055 -22.56 33.18 0.073 0.020 0.004 -5.933 t21 0.135 0.175 0.193 0.098 0.093 0.067 t12 0.065 311-422 311-424 325-398 311-589 374-393 325-398 311-41 1 T,K 27-136 7-190 1-41 P, atm 100-608 100-608 3-136 23-694 N 18 24 17 21 18 15 26 C b b a d source a e 400'Sullivanand Smith (1970). *Kohayashi and Katz (1953). 'Reamer et al. (1952).dGillespie and Wilson (1980). ePrutton and Savage (1945). Table 111. Water-Salt Interaction Coefficients salt hN. NaCl -7.85 CaCl, -4.30
Table IV. Gas-Salt Interaction Coefficients Determined from High-pressure Data (N, T,and P, See Table 11; m , Exwrimental Molality Range (mol/kg)) CH4-CaC12 C02-CaC12 N2-NaCl CHI-NaCI h 41.97 36.29 64.30 65.50 374-394 325-398 325-398 !fK 298-398 P, atm 100-600 17-703 100-608 100-608 m 1 1-4 1-4 1-4 N 30 89 33 32 source b e a a
1 .oo
*
See Table 11. Blanco and Smith (1978).
g 0.80 0
f
Table V. Gas-Salt Interaction Coefficients Determined from Low-Pressure Salting Out Constants (T, Temperature at Which k. Was Measured) h, T,,K source CHI-CaCli 53.55 298 a CO&aCli 41.00 298 b N2-NaC1 64.50 323 C CH,-NaCl 66.10 323 C C2&-NaC1 86.30 323 C C3H8-NaC1 105.60 323 C n-C4Hlo-NaCl 115.20 323 C
B 3
.8 0.60 C
5
P
e
LL 0)
2 0.40 00000 T=366K AAAAA T=477K
Pawlikowski and Prausnitz (1983)from correlation.
- Model
0.20 0
I
I
I
0.5
1 .o
1.5
10'
x
al. (1970). cLandolt-Bornstein (1962).
I
2.0
* Onda et
700 I
1
I
Mole Fraction CO i n Liquid Phose
Figure 1. Experimental and predicted vapor-phase mole fractions
600.
of CO in the CO/H20 mixture at two temperatures.
librium data. The resulting values are given in Table I1 along with the references to the experimental data used. Figure 1 shows the calculated and experimental xy diagrams for the CO-H20 mixture at two temperatures. The correlated results are in good agreement with the observed values. The electrolytic interaction coefficients between salt and water (hNJ have in this work been determined by matching the model to the experimental vapor pressure lowering of a 1 m salt solution at T = 373.15 K. The resulting hNs values are given in Table 111. T w o approaches have been tried for evaluation of the gas-salt interaction coefficients (h,). In the first approach h, has been obtained by correlation using high-pressure ternary gas-water-salt solubility data. Table IV shows the h, parameters obtained by using this procedure. In the second approach h, was determined by matching the model to low-pressure salting out constants defined by Landolt-BBmstein (1962) as k, = 1/c, log ( S , / S ) (25) k, is the salting out constant, C, is the salt concentration, and Soand S are the gas solubilities per mass unit of water in pure water and in the salt solution, respectively. Values of h, obtained from low-pressure data are given in Table V.
500. T
400. v
g,
8 300 L
200
00000 No Salt 00000 1M NaCl
AAAAA4M NaCl
- Correlated predicted
1 .o
6.0 10'
x
2.0
3.0
and
4.0
Salt Free Mole Fraction N2 in Liquid Phase
Figure 2. Experimental and calculated pressures versus salt free mole fractione of N2 in water and aqueous mixtures of NaCI; T = 398 K.
Figures 2-5 show experimental and calculated pressures versus gas solubilities for four ternary gas-water-salt systems using both of the approaches for obtaining hw For the N2-NaC1-water and CH,-NaC1-water mixtures, the results obtained by using the low- and high-pressure ap-
Ind. Eng. Chem. Res., Vol. 30, No. 9, 1991 2183 8oo
1 .o
6.0 10'
x
2.0
3.0
4.0
9
5.0 Salt Free Mole Fraction COz in Liquid Phase
Salt Free Mole Fraction CHI in Liquid Phase
Figure 3. Experimental and calculated pressures versus salt free mole fractions of CH, in water and aqueous mixtures of NaCl using the HP EOS and the model presented in this work; T = 375 K.
Figure 5. Experimental and calculated pressures versus salt free mole fractions of C02 in water and aqueous mixtures of CaCI,; T = 394 K.
r .-3 n
-u 0
3
.-c s 2
L3
c
.-" 0
t -00 '1
?! LL
Experiment:
Y
00000Water
In
00000 Brine
X
n
1 .o
8.0 10'
x
2.0
3.0
4.0
5.0
Salt Free Mole Fraction C H I in Liquid Phase
Figure 4. Experimental and calculated pressures versus salt free mole fractions of CHI in water and in a 1 M CaC4 solution; T = 375
K.
proaches are almost identical. The pressures calculated by using the HP EOS of Harvey and Prausnitz (1989) are also shown for the CH4-NaC1-water system. For all the mixtures the agreement between the experimental and correlated resulta by using the new model is very good at all salt concentrations. When the low-pressure approach is used for determination of h,, the gas solubilities in the NaCl solutions are predicted with good accuracy. The solubility of CHI in both 1and 4 m solutions of NaCl are predicted better with the new model than with the HP EOS,which like the present model uses a single gas-salt interaction coefficient determined from lowpressure data. The new model predicts the solubility of C02in a 10 wt % CaC12 solution well, whereas the salting out effect is somewhat overestimated if the salt concentration is as much as 30 wt 90. The same is the case for the the salting out of CHI from a 1 m CaC12 solution.
n -0
200 300 400 Pressure ( a h . ) Figure 6. Experimental and predicted natural gas solubilities in water and in a reeervoir brine (m y 0.6 M) using the H P EOS and the model presented in this work; T = 366 K. The gas composition is given in Table VI. 100
Table VI. Composition of Natural Gas (Dodson and Standing, 1944) component mol % methane 88.51 ethane 6.02 propane 3.18 isobutane 0.46 n-butane 0.85 isopentane and heavier 0.98
Figure 6 shows observed and predicted natural gas solubilities in water and in a reservoir brine by using both the HP EOS and the model presented in this work. The composition of the natural gas is given in Table VI. The C4+fraction of the gas was treated as n-C4Hlo,and since more than 95% of the salt content consisted of NaCl, the
2184 Ind. Eng. Chem. Res., Vol. 30, No. 9, 1991
calculations were performed with a concentration of NaCl corresponding to the ionic strength of the brine. All gas-gas interaction coefficients were set equal to 0, and all gas-NaC1 and the water-NaC1 interaction coefficients were taken from Tables III-V. For the interaction between CHI and NaCl the high-pressure value was used. Agreement between the experimental and predicted gas solubilities is very good and somewhat better than when the H P EOS is used. Discussion The main objective of this work was to develop a model that, based on easily available experimental data, is able to predict the solubility of a gas in aqueous electrolyte solutions at high temperatures and pressures. Apart from an accurate EOS for predicting gas-water equilibria the only additional information needed is a salting out constant for the gas at low pressure. Salting out constants are relative easy to measure and are available for many systems in the literature (e.g., Landolt-Borstein, 1962; Onda et al., 1970). When the salting out constants are used to determine the gas-salt interaction coefficients, predicted gas solubilities are in very good agreement with the experimental data for the NaCl mixtures. For the CaC12 solution the deviations are somewhat larger. The likely explanation for the better agreement for the NaCl mixtures is to be found in the low-pressurek, values (see eq 25). For the CH4-CaCl2-water mixture no experimental value could be found in the literature, and it was therefore necessary to use a correlation developed by Pawlikowski and Prausnitz (1983) to predict k, for this mixture. While this correlation is often quite accurate, the deviation between calculated and experimental values may in certain cases be 10-1570. This could explain that the salting out effect is overpredicted for this system. For the C02-CaC1,-water mixture it should be noted that the used k, value was measured at 298 K (see Table V). For the N2-NaC1-water and the CH4-NaC1-water mixtures the k, values used to evaluate h, were measured at 323 K. To test whether this had any influence on the results, calculations were performed for both the NaCl mixtures using k, values obtained at 303 K. For both systems this resulted in a larger h, value, corresponding to an increased salting out effect. This may therefore to a certain extent explain the deviations observed in the C02-CaC12-water system. More experimental data are needed to explore this point further. It is shown in Figure 3 that the solubility of CH4in both 1 and 4 m aqueous solutions of NaCl are predicted better with the new model than with the H P EOS. The better predictions are partly caused by using an improved model for calculating the solubility of CHI in pure water. The salting out effect from the 1 m solution is predicted with reasonable accuracy by using the H P model, whereas it is considerably underpredicted from the 4 m solution. A problem arises if the new model is to be used for predicting the solubility of a gas in a solution containing two or more dissolved salts. To solve this problem, it would be necessary to develop a suitable mixing rule for determination of the gas-salt and water-salt interaction coefficients. However, if most of the dissolved solids come from one salt, it may be safely assumed that the mixture contains only this salt at a concentration corresponding to the ionic strength of the solution. This procedure is illustrated in Figure 6, where the predicted natural gas solubilities in the reservoir brine were obtained by assuming that NaCl was the only salt present in the mixture. The concentration of the brine was slightly greater than 0.6 m. The results predicted by using the new model are
in good agreement with the experimental data, although the gas solubilitiesare slightly overpredicted at the highest pressures. The new model performs better than the H P EOS. Also in this case this may be partly ascribed to a superior model for predicting the phase equilibria of the salt-free mixture. Note that the same good predictions using the new model would have been obtained had the low-pressure value of the interaction coefficient between CH4-NaC1 been used, since the high- and low-pressure values differ only slightly (see Tables I11 and IV). Conclusions In this work a new model for prediction of gas solubilities in aqueous mixtures of electrolytes has been presented. The model combines an equation of state with a modified Debye-Huckel electrostatic contribution to obtain the fugacity coefficientsof the nonionic species present in the mixture. The EOS used in this work is the ALS equation with the density-dependent mixing rule of Mathias and Copeman (1983), but in principle any equation suitable for accurate correlations of gas-water equilibria could be used. The main purpose of this work has been to provide a means for predicting high-pressure gas solubilities based on low-pressure experimental information for the gassalt-water system. In the new model g a s d t interactions are taken into account by a single temperature- and composition-independent parameter. This parameter is determined from low-pressure salting out constants. This approach results in fine predictions of high-pressure gas solubilities, although the salting out effect may be slightly overpredicted at high salt concentrations. Predicted CH4 solubilities in NaCl solutions have been considerably improved compared to the H P EOS of Harvey and Prausnitz (1989). The two models have also been compared for their ability to predict natural gas solubilities in a reservoir brine. The solubilities calculated by using the present model are in good agreement with experimental data and are somewhat more accurate than the results obtained with the H P EOS. Acknowledgment K.Aa.-P. is grateful to the Norwegian oil company Norsk Hydro for financial support of this project. Appendix The following expressions for calculation of Q, and Qbl were obtained by Adachi et al. (1983) by fitting to pure component properties along the critical isotherm 52, = 0.44869 + 0.04024~+ 0.011110~- 0 . 0 0 5 7 6 ~ (Al) ~
+
= 0.08974 - 0.03452~ 0 . 0 0 3 3 ~ ~ (A2)
Using the experimentally observed critical point criteria (dP/dv), = (d2P/dV2), = 0
(A3)
Jensen (1987) derived the following expressions for Qb2 and Qb3;
52b2
Qb3
= 0.5[2(1 + nbl) - 3(Q,)'/3 + (4Q0- 3(QJ2/3)'/2] (A4) = 0.5[-2(1
+ Qb1) + 3(Qa)'/3+ (40, - 3(Qa)2/3)1/2] (445)
Literature Cited Aasberg-Petersen,K. Prediction of Phase Equilibria and Physical Properties for Mixtures with Oils, Gases, and Water. Ph.D Thesis, Department of Chemical Engineering,The Technical Univ-
Znd. Eng. Chem. Res. 1991,30,2185-2191
2186
Aggregatzusthden, 2. Teil, Bandteil b. Lbsungsgleichgewichte I; Springer Verlag: Berlin, 1962. Macedo, E. A.; Skovborg, P.; Rasmwen, P.Calculation of phase equilibria for solutions of strong electrolytes in solvent/water mixtures. Chem. Eng. Sci. 1990,45, 875. Mathias, P. M.; Copeman, T. W. Extension of the Peng-Robinson equation of state to complex mixtures: Evaluation of the various forms of the local composition concept. Fluid Phase Equilib.
ersity of Denmark, Denmark, 1991. Adachi, Y.; Lu, B. C.-Y.; Sugie, H. A four-parameter equation of state. Fluid Phase Equilib. 1983,11,29. Blanco, L. H. C.; Smith, N. 0. The high pressure solubility of methane in aqueous calcium chloride and aqueous tetraethylammonium bromide. Partial molar properties of dissolved methane and nitrogen in relation to water structure. J. Phys. Chem. 1978,82, 186. CRC Handbook of Chemistry and Physics; CRC Press Inc.: Boca Raton, FL, 1987. DIPPR tables. DIPPR data compilation project, Department of Chemical Engineering, 167 Fenske Laboratory, The Pennsylvania State University, 1985. Dodson, C. R.; Standing, M. B. Pressure-volume-temperature and solubility relations for natural gas-water mixtures. In: Drilling and Production Practice; American Petroleum Institute: 1944; p 173. Gani, R.; Tzouvaras, N.; Rasmuasen, P.; Fredenslund, Aa. Prediction of gas solubility and vapor-liquid equilibria by group-contribution. Fluid Phase Equilib. 1989, 47, 133. Gillespie, P. C.; Wilson, G. M. Vapor-liquid equilibrium data on water-substitute gas components: Nz-HzO, H2-H20, CO-HzO, H2-CO-Hz0, and H2S-Hz0. Gas Processors Association Research Report 41, 1980. Harvey, A. H.; Prausnitz, J. M. Thermodynamics of high pressure aqueous systems containing gases and salts. MChE J . 1989,35,
1983, 13, 91.
Michelsen, M. L. A modified Huron-Vidal mixing rule for cubic equations of state. SEP publication 8921, Department of Chemical Engineering, The Technical University of Denmark, Denmark. Submitted to Fluid Phase Equilib. Mollerup, J. Correlation of gas solubilities in water and methanol at high pressure. Fluid Phase Equilib. 1985,22, 139. Onda, K.; Sada, E.; Kobayashi, T.; Koto, S.; Ito, K. Salting-out parameters of gas solubility in aqueous salt solutions. J. Chem. Eng. Jpn. 1970, 3, 18. OSullivan, T. D.; Smith N. 0. The solubility and partial molar volume of nitrogen and methane in aqueous sodium chloride from 50 to 125 OC and 100 to 600 atm. J. Phys. Chem. 1970,74,1460. Pawlikowski, E. M.; Prausnitz, J. M. Estimation of Setchenow constants for nonpolar gases in common salts at moderate temperatures. Ind. Eng. Chem. Fundam. 1983,22,86. Prutton, C. F.; Savage, R. L. The solubility of carbon dioxide in calcium chloride-water solutions at 75, 100, 120 "C and high pressures. J . Am. Chem. SOC.1945, 67, 1550. Reamer, H. H.; Sage, B. H.; Lacey, W. N. Phase equilibria in hydrocarbon systems. n-Butanewater in the twophase region. Znd. Eng. Chem. 1952,44,609. Sander, B.; Fredenslund, Aa.; Rasmussen, P. Calculation of vaporliquid equilibria in mixed solvent/salt systems using as extended UNIQUAC equation. Chem. Eng. Sci. 1986,41,1171.
635.
Huron, M. J.; Vidal, J. New mixing rules in simple equations of state for representing vapor-liquid equilibria of strongly non-ideal mixtures. Fluid Phase Equilib. 1979, 3, 255. Jensen, B. H. Densities, viscosities and phase equilibria in enhanced oil recovery. Ph.D Thesis, Department of Chemical Engineering, The Technical University of Denmark, Denmark, 1987. Kobayashi, R.; Katz, D. L. Vapor-liquid equilibria for binary hydrocarbon-water systems. Ind. Eng. Chem. 1953,45,440. Landolt-Bbmstein tables, 1962. Eigenschaften der Materie in Ihren
Received for review November 13, 1990 Accepted March 8, 1991
Reaction Pathways in Lubricant Degradation. 2. n -Hexadecane Autoxidation Steven Blaine and Phillip E. Savage* Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136
We oxidized n-hexadecane in an isothermal batch reactor a t temperatures ranging from 140 to 180 "C for times ranging from 10 min to 24 h. The viscosity of the n-hexadecane oxidate was measured, and the average molecular weight of the oxidate was determined with the use of gel permeation chromatography. The oxidate viscosity and the average molecular weights increased with both reaction time and temperature, but the viscosity increase was much more dramatic. The maximum viscosity measured was 219 cP, which resulted from oxidation a t 180 "C for 11 h. This high viscosity constituted a 6500% increase. By comparison, the increase in the average molecular weights of the oxidate never exceeded 50%. Analyses using 'H and 13C NMR spectroscopies, acid-base and iodometric titrations, and gas chromatography provided the total concentrations of hydroperoxides, carboxylic acids, ketones, aldehydes, alcohols, and esters present in the reaction mixture. Monitoring the temporal variations of the concentrations of these different functional groups facilitated resolution of the autoxidation pathways for paraffin oxidation under relatively severe conditions. These reaction pathways provide insight into the chemical transformations that occur during the degradation of a lubricating oil under service conditions.
Introduction The degradation of lubricating oils under service conditions is a problem that carries significant economic penalties. Indeed, lubricant replacement constitutes a major portion of the $6 billion annual market for lubricants (Hydrocarbon Promsing, 1989). Oxidation is the primary agent of degradation (Fenske et al., 1941;Korcek et al., 1986,Guneel et al., 1988,Naidu et al., 1984,1986),and this observaion has motivated substantial research into lubricant oxidation. Many groups have examined the oxidation of fully formulated lubricants and base oils (Colclough, 1987;Jette and Shaffer, 1988; Tseregounis et al., 0888-5885/91/2630-2185$02.50/0
1987;Naidu et al., 1984,1986;Willermet et al., 1979;Diamond et al., 1952;Spearot, 1974; Hsu et al., 1986), but the physical and chemical complexity of these systems haa frustrated resolution of the controlling reaction pathways, kinetica, and mechanisms. Thii complexity has motivated much experimental work with model reactants such as paraffins because they provide simpler systems to study. These studies of paraffin oxidation (e.g., Emanuel, 1966; Brown and Fish, 1969;Boss and Hazlett, 1969;Benson, 1981;Jensen et al., 1979;Denisov et al., 1977;Van Sickle et al., 1973;Mill et al., 1972;Van Sickle, 1972;Boss and Hazlett, 1975)have provided substantial insight into the 0 1991 American Chemical Society
