Ind. Eng. Chem. Res. 1992,31,2232-2237
2232
Computation of the Incipient Equilibrium Carbon Dioxide Hydrate Formation Conditions in Aqueous Electrolyte Solutions Peter Englezos Department of Chemical Engineering, University of British Columbia, 2216 Main Mall, Vancouver, B.C. V6T 124, Canada
The existing thermodynamics-based method for calculating gas hydrate equilibria in aqueous electrolyte solutions cannot be used to predict accurately the incipient gas hydrate formation pressures in systems containing carbon dioxide. This is because the solubility of carbon dioxide in salt solutions cannot be computed accurately using rigorous thermodynamic models. In this paper, a recently proposed theory in conjunction with an equation of state is used to describe the liquid phase containing water, electrolytes, and dissolved gases. The theory is suitable for calculating the high-pressure solubility of gases in aqueous salt solutions and was utilized in this work to develop a predictive method for gas hydrate equilibria. The method employs the van der Waals-Platteeuw model for the hydrate-phase fugacities and the TrebbleBishnoi equation of state for the vapor-phase fugacities. The new liquid-phase model also uses this equation of state. The method successfully predicted the incipient carbon dioxide hydrate formation pressures in aqueous NaCl solutions. The average deviation between the predicted and the experimental values was found to be 7.2%.
Introduction Carbon dioxide has been known since 1882 to be among a number of molecules that can physically combine with water under suitable pressure and temperature conditions to form inclusion compounds. Thermodynamically, these compounds are solid solutions known as gas hydrates (Byk and Fomina, 1968; Davidmn, 1973; Makogon, 1981; Berecz and Balla-Achs, 1983; Jeffrey, 1984, Sloan, 199Oa). Carbon dioxide and water are frequently part of natural gas streams and they are found in oil reservoirs during enhanced oil recovery. Hydrate formation in oil and natural gas systems may cause problems during production and processing (Barker and Gomez; 1989; Sloan, 1990a). In other cases, however, gas hydrate formation may be desirable because it can facilitate separation processes (Nguyen et al., 1989; Willson et al., 1990). It can also replace the crystallization step in a freeze concentration process for seawater desalination, wastewater treatment, or fruit juice concentration (Knox et al., 1961; Werezak, 1969; Bozzo et al., 1973; Tech. Commentary, 1988). Carbon dioxide is a suitable substance for the hydrate freeze concentration process. These technological interests necessitate the need for phase equilibrium data and predictive methods for hydrate formation in pure water as well as in solutions containing inhibiting substances like electrolytes and alcohols. Incipient equilibrium data on carbon dioxide (alone or with other gases) hydrate formation in pure liquid water are available (Deaton and Frost, 1946; Unruh and Katz, 1949; Larson, 1955; Vlahakis et al., 1972; Robinson and Mehta, 1971; Ng and Robinson, 1985). Vlahakis et al. (1972) and Larson (1955) also studied carbon dioxide hydrate formation in aqueous sodium chloride solutions. Ng and Robinson studied extensively the effect of methanol on carbon dioxide containing hydrate forming systems (Ng and Robinson, 1985; Ng and Robinson, 1983; Ng et al., 1985; Robinson and Ng, 1986; Ng et al., 1987). In systems containing carbon dioxide, the incipient equilibrium hydrate formation conditions in water and in aqueous solutions containing organic substances (e.g., alcohols) can be computed by thermodynamics-based predictive methods. The results are accurate enough for process design calculations. Anderson and Prausnitz (19861, Munck et al. (19881, and Du and Guo (1990) have employed the UNIQUAC activity coefficient model in conjunction with empirical Henry’s law correlations for the
noncondensable gases. A thermodynamically consistent and simple approach is to use an equation of state. Englezos et d. (1991) used the Trebble-Bishnoi equation of state (Trebble and Bishnoi, 1988) and found the predictions to agree well with the experimental data. In aqueous electrolyte solutions, however, the absence of a rigorous thermodynamic model to describe the solubility of carbon dioxide has prevented the formulation of a thermodynamics-based method for calculating hydrate-phase equilibria. Menten et al. (1981) were the first to present an empirical method, based on freezing point depression data, for computing light hydrocarbon hydrate formation conditions in single salt solutions. Englezos and Bishnoi (1988) presented a rigorous method with no adjustable parameters that computes hydrate formation in aqueous solutions of single or mixed electrolytes. This method produced excellent results for systems with substances sparingly soluble in water (e.g., light hydrocarbons, nitrogen). However, it is not suitable for carbon dioxide hydrate formation in aqueous electrolyte solutions because the solubility of carbon dioxide in water is significant. The objective of the work undertaken in this study was to develop a thermodynamics-basedmethod which can be used to compute the incipient equilibrium carbon dioxide hydrate formation conditions in aqueous electrolyte solutions. Such a method was developed and is presented here. It utilizes the van der Waals-Platteeuw model for the hydrate phase (van der Waals and Platteeuw, 1959), the Trebble-Bishnoi equation of state (Trebble and Bishnoi, 1988) for the vapor phase, and a recently proposed theory (model) that describes high-pressure solubility in aqueous electrolyte solutions for the aqueous phase (AasbergPetersen et al., 1991). The proposed hydrate prediction method does not have any adjustable parameters. Computations were performed for carbon dioxide hydrate formation, and the results were found to agree well with all the available experimental data.
Phase Equilibrium and Thermodynamic Models T h e phase equilibrium problem was formulated and the thermodynamic models required for the solution are presented here. The rationale for using these models and the conditions under which each model was applied are explained. Carbon dioxide forms structure I hydrate. This phase is denoted by H. In a system with N substances from which only Nh are present in the hydrate crystal
oass-~aa~/92/2~3i-2232$03.00/o 0 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31, No. 9,1992 2233 lattice, equilibrium among the gas (V), the liquid (L), and the hydrate (H) phases is represented, using fugacities, by
= i = 1, ..., N for all the N components, and by fl = ff j = 1, ..., Nh
fl
(1) (2)
f!=k
(3) Equations 1 and 3 together with the mass balance equations can be solved to calculate the incipient hydrate formation conditions provided that suitable thermodynamic models for the description of the phases are available. Vapor Phase. An equation of state can be used to compute the fugacities which are given by
i = 1, ..., N
(4)
where yi and r#~~denote the mole fraction and the fugacity coefficient for component i at a pressure P. The fugacity coefficient is computed from an expression based on the equation of state. In the present work, the TrebbleBishnoi equation of state with quadratic mixing rules and binary interaction parameters independent of temperature was used (Trebble and Bishnoi, 1988). The binary interaction parameter values for the carbon dioxide-water system are all zero except for kd, which has a value of -0.2523. This value was obtained from the regression of the solubility data of Stewart and Munjal (1970). Hydrate Phase. The fugacity of water in the hydrate is given by
(
fi = fZTexp -A:,)
where
eT
In the above equation, is the fugacity of water in the empty hydrate lattice, Cp, are the Langmuir constants,,Y are the number of cavities of type m per water molecule in the hydrate lattice (vl = 1/23and v2 = 3/23),and fj are the component fugacities in the vapor phase which are calculated b usin the equation of state. The quantity Apr-" = p b denotes the difference between the chemical potential of water in the empty hydrate lattice (MT) and that in the hydrate phase (H). The fugacity of water in the empty hydrate lattice, f r , is given by
2
f y = fL," exp
-
B G
for the Nhhydrate-forming components including water. Electrolytes are known to be excluded from the hydrate crystal lattice and the vapor phase. Hence, the van der Waals-Platteeuw statistical thermodynamics model can be used to describe the hydrate phase. An important idiosyncrasy of this model is that it implicitly incorporates vapor-hydrate equilibria. As a result, the Nhequations (2)are replaced by the following single equation
fl = y&P
Table I. Physical and Thermodynamic Reference Properties for Gas Hydrates property value (structure I)
(7)
where the quantity inside the parentheses is given by a correlation proposed by Holder et al. (1980). This correlation is
0.141 J/(mol K2) -38.13 J/(mol K) -4860.0 J/mol 1264.0 J/mol 4.6 X lo4 m3/mol
W
Ah: A& *,VMT-L' W
In eq 7, denotes the fugacity of pure liquid water and it is calculated by using the equation of state. This is used even when the temperature is below the normal freezing point of water and pure liquid water is a hypothetical state. In eq 8, the quantity A&.is an experimentally determined quantity which denotes the difference between the chemical potential of the empty hydrate lattice and the pure liquid water at TO = 273.15 K and zero absolute pressure. Similarly, the quantities Ahy-" and denote differences in enthalpy and volume, respectively. A correlation for the enthalpy difference has also been given by Holder et al. (1980): T
Ah$T-L" = Aha + IF(ACiw + B(T - TO)) dT (9)
Several values for the parameters A&, Aha, A C L , and have been reported in the literature. A summary of these values is available (Englezos et al., 1991). In this work, the values reported by Parrish and Prausnitz (1972)were used and are shown in Table I. These values are consistent with the Langmuir constant calculation procedure of P d h and Prausnitz which was also adopted here. The Langmuir constants account for the gas-water, van der Waals type interactions in the hydrate lattice. They can be rigorously computed if a potential function for the interaction between a guest molecule and a water molecule in a cavity is available (van der Waals and Platteeuw, 1959; McKoy and Sinanoglu, 1963;John and Holder, 1982). Parrish and Prausnitz (1972)using the Kihara potential and experimental data on hydrate formation developed a correlation which can also be used for the calculation of the Langmuir constants at temperatures above 260 K. This correlation is accurate within 0.2%. Liquid Phase. Because of physical as well as chemical interactions with water molecules C02has a relatively high solubility in water. This may explain the fact that the hydrate is formed rapidly and in the form of flakes (Berecz and Balla-Achs, 1983). In the presence of electrolytes the solubility decreases because the interactions between the water molecules and the ions are stronger than the interactions between the water and the dissolved COz (salting out). However, even though the solubility decreases it does not become negligible and the activity of water will not only depend on the dissolved electrolytes but also on COP Computation of the solubility of COz requires a model which in addition to the C02-water and electrolyte-water interactions will also account for the C02-electrolyte interactions. Aasberg-Petersen et al. (1991)presented a model which can be used to calculate the solubility of solutes like carbon dioxide in aqueous electrolyte solutions. The liquid phase is treated as a salt-free mixture and the equation of state (EOS) approach is used to describe it. However, the fugacity coefficient which is computed by the EOS is corrected with the Debye-Huckel electrostatic term. This term depends on the ionic strength of the solution and hence, on the electrolyte concentration. It also depends on the type of the electrolyte through an adjustable parameter which is independent of temperature and composition.
2234 Ind. Eng. Chem. Res., Vol. 31, No. 9, 1992
The fugacities in the aqueous liquid phase that contains the electrolytes are calculated from the equation = X ~ ~ $ ? -i ~=P1, ...,N
(10)
where the fugacity coefficient, r$?-', is given by the model of Aasberg-Petersen et al. (1991) as follows: In +?-' = In #os In rHL i = 1, ..., N (11)
+
In an aqueous liquid phase that does not contain any electrolytes, the fugacity coefficient is that given by an equation of state. In a system that also contains electrolytes a correction is added to account for the electrostatic interactions. The second term accounts for the effect of the electrolytes. The electrolytes are not among the N components. In the above equation, the Trebble-Bishnoi equation of state is used to compute the first term on the right-hand side. In fact, any equation of state can be used. In eq 11,the salt-free mole fractions are utilized. These mole fractions are defined as follows: N,
i = 1, ..., N
= &/(l- Ctj) j=l
(12)
where N , is the number of salts and ti are the true mole fractions. The second term in eq 11 is given by
In the above equation, pis is an interaction coefficient between the dissolved salt and a nonelectrolytic component. This coefficient is independent of temperature, composition, and ionic strength. The ionic strength is denoted by I whereas M, is the salt-free mixture molecular weight determined as a molar average. The parameters A and B and the function F are given by the following equations: dC5 A 1.327757 X lo5( 14) (€*T)1.5
B
6.359696
dm0.5
X
(6mT)0'5
F(BP.5)
1
+ BP.' - 1 + 1BP.5 - 2 In (1 + BF5)
(16)
In eqs 14 and 15, d, is the density of the salt-free mixture and it is asaumed to be equal to the density of water. The quantity em is the salt-free mixture dielectric constant which for a mixture of gases and water is given by t, = XN€N (17) where xN and tN are salt-free mole fraction and the dielectric constant of water. Aasberg-Petersen et al. (1991) computed the dielectric constant of water using data from the CRC Handbook of Chemistry and Physics, but in the present work the following correlation from Zemaitis et al. (1986) was used: 305.7 exp(-exp(-12.741 + 0.018752') - T/219) 4N (18)
where the temperature T is in K. The interaction coefficients pis have been calculated by Aasberg-Petersen et al. (1991) for a number of water-electrolyte and gaselectrolyte systems. The value for the pair carbon dioxide-sodium chloride was not reported; however, in this work it was determined by regression of vapor-liquid equilibrium data for the carbon dioxide-water-sodium
0 Start
Given Temperature and Overall Feed Composition Assume a Value for the Pressure
F Perform Isothermal-Isobaric Flash Calculations
t T
Compute a New Pressure
4 Compute the Fugacity of Water in the Hydrate
1
fl Check for H-V-L Equilibria
YES
The Assumed Pressure is the Incipient Hydrate Formation Pressure
Figure 1. Computational flow diagram.
chloride system. The data were obtained from Malinin and Savelyeva (1972). The estimated value for the interaction coefficient was found to be 92.5.
Computational Method In order to compute the incipient equilibrium hydrate formation pressure at a given temperature for a gas hydrate forming mixture of known overall composition, eqs 1and 3 together with the mass balance equations for an isothermal-isobaric vapor-liquid equilibrium flash calculation must be solved simultaneously. The computational flow diagram is shown in Figure 1. The first step is to assume a pressure and perform the flash calculations which ensure vapor-liquid equilibrium. Subsequently,one has to check if the fluid phases are in equlibrium with the hydrate phase. This is accomplished by checking if eq 3 is satisified within some tolerance. If it is satisfied, then the assumed pressure is the hydrate formation pressure. Otherwise, a new pressure is computed by either the secant or the Newton-Raphson method and the flash calculations are repeated at that new pressure. The check for the threephase equilibria is l1n E/klIZ5 6 (19) where the tolerance 6 has a value of lo-'*. The fugacities for the vapor and liquid phases are calculated from eqs 4 and 10, respectively. Equation 5 is used for the fugacity of water in the hydrate phase. Results, Comparison with Experimental Data, and Discussion The accuracy of the hydrate phase equilibrium calculations will depend on the ability of the thermodynamic models to describe accurately the phases. Since the van der Waals-Platteeuw model has been successfully used in hydrate equilibria calculations, the accuracy of the computations in this work depend primarily on the ability of the newly proposed model in conjunction with the Trebble-Bishnoi equation of state to describe the aqueous
Ind. Eng. Chem. Res., Vol. 31, No. 9,1992 223s Table 11. Solubility of C 0 2 in Aqueous Solutions COz mole fraction exptla calcd temp (K) press. (MPa) 0.0126 0.0095 273.15 1.013 25
278.15 283.15
a
2.533 13 3.03975 1.01325 2.026 5 3.85035 1.013 25 2.026 50 3.85035
0.0239 0.0263 0.0105 0.0180 0.0253 0.0085 0.0153 0.0218
0.0210 0.0242
-
O.Oo90
0.0167 0.0273 0.0085 0.0159 0.0264
1.0 273 275 277
Stewart and Munjal, 1970.
279 2 8 1 2 8 3
Temperature
Table 111. Solubility of COSin Aqueous NaCl Solutions at 298 E and 4.792 MPa cO, mole fraction NaCl (M) exptP calcd ~~
0 0.905 1.793 2.597
0.0212 0.0173 0.0136 0.0109
0.0246 0.0192 0.0133 0.0096
Table IV. Incipient Equilibrium COz Hydrate Formation Conditions in Aqueous NaCl Solutions incipient COPhydrate formation press. (MPa) temp (K) NaCl (wt %) exDtl" calcd
Malinin and Savelyeva, 1972.
liquid phase. Therefore, the solubility of carbon dioxide in water and in aqueous electrolyte solutions was calculated first and the results were compared with experimental data. Only the solubility in aqueous NaCl solutions was examined because the only hydrate formation data available are those from Vlahakis et al. (1972)and they concern carbon dioxide hydrate formation in aqueous NaCl solutions. Those solubility data that have been taken at conditions close to the hydrating region were used. Subsequently, the incipient eqdibrium carbon dioxide hydrate formation conditions in pure water and in aqueous NaCl solutions were computed and compared with all the available experimental data. Solubility of COP Using the Trebble-Bishnoi equation of state, the solubility of carbon dioxide in water is computed. The results are reasonably good as seen in Table 11, where the experimental data of Stewart and Munjal (1970)are also shown. The experimentally determined mole fractions of carbon dioxide were close to the calculated ones, and the average per cent deviation between them was found to be 11.0. Furthermore, the trends of the solubility to increase with pressure and decrease with temperature were also predicted. It was noted, however, that the values of the calculated mole fractions were not consistently smaller or larger than the experimental values. Subsequently, the theory of Aasberg-Petersen for the liquid phase was employed in order to compute the solubility of C02in an aqueous NaCl solution. The reaulta are shown in Table III together with experimental data from Malinii and Savelyeva (1972). The average percent deviation of the computed mole fractions from the experimental values was found to be 10.3. As it is seen from these calculations, the calculated solubility was close to the experimental value and the trend of the solubility to decrease with increasing salt content was predicted. In spite of this, the calculated mole fractions were not consistently smaller or larger than the experimental values. This was also found to be the case for the solubility in pure water and is an indication of the difficulties in modeling these systems. However, the liquid model of Aasberg-Petersen represents the state of the art in aqueous electrolyte liquid phase phenomenological modeling and was therefore, employed in the hydrate equilibria calculations. C 0 2Hydrate Phase Equilibria. In Figure 2 the experimental data from Larson (1955)on C02hydrate for-
(K)
Figure 2. Incipient equilibrium carbon dioxide hydrate formation pressures.
276.12 277.17 279.15 279.57 279.99 275.87 276.38 277.0 277.5 277.93 278.63 279.33 279.7 271.60 272.09 272.59 273.13 273.65 274.06 274.65 275.28 280.36 a
5.42 5.28 5.30 4.865 5.37 5.27 5.72 5.76 5.80 5.545 5.445 5.45 5.53 4.79 5.215 5.375 5.26 5.385 4.665 5.715 4.81 5.875
2.297 2.596 3.371 3.468 3.877 2.158 2.333 2.534 2.795 2.886 3.231 3.530 3.727 1.319 1.398 1.502 1.589 1.709 1.737 1.927 2.018 4.227
2.204 2.484 3.208 3.328 3.622 2.126 2.303 2.485 2.649 2.765 3.013 3.311 3.501 1.291 1.384 1.471 1.555 1.656 1.684 1.880 1.946 3.927
Vlahakis et al.. 1972.
mation in aqueous NaCl solutions are shown together with the data from Vlahakis et al. (1972)for hydrate formation in pure water. The inhibiting effect of the salt is evident. In addition, the computed incipient hydrate formation pressures at the experimental temperatures are shown. The average percent deviation of the computed and the experimental pressures was found to be 2.1. The maximum deviation found was 4.5%. It was observed at 273.65 K and zero molarity. Additional experimental data were measured by Vlahakis et al. (1972). A total of 57 experiments at various concentrations of NaCl were performed. These data together with the predicted hydrate formation pressures are shown in Tables IV-VI. The average deviation between the vlahakis experimental values and the ones predicted by the proposed method was found to be 7.2%. The maximum deviation was 14.8%. It was observed at 277.2 K and 10.2 wt % NaC1. These results indicate a close agreement between the predicted hydrate formation pressures and the experimentally determined ones. It is also noted that convergence of the computational procedure was easily accomplished. From the point of view of hydrate phase equilibrium calculations,the new aspects are (a) the use of a new theory (model) for the aqueous liquid phase and (b) the development of the computational methodology. A secondary
2236 Ind. Eng. Chem. Res., Vol. 31, No. 9, 1992 Table V. Incipient Equilibrium C 0 2 Hydrate Formation Conditions in Aqueous NaCl Solutions incipient COPhydrate formation press. (MPa) exptl' calcd NaCl (wt W ) temp (K) 1.653 1.603 273.18 5.871 1.865 1.798 274.18 5.917 2.056 1.983 275.07 5.834 2.251 2.355 276.17 5.764 2.555 2.408 276.60 6.132 2.675 2.529 277.15 5.733 2.734 2.899 277.73 5.860 3.072 2.920 278.21 5.949 3.222 3.060 278.68 5.632 3.254 5.568 3.438 279.16 1.614 10.17 1.735 271.61 2.024 1.818 10.33 272.62 2.095 1.930 10.30 273.16 2.168 10.31 2.384 274.16 2.327 2.651 274.69 10.50 2.442 2.786 10.30 275.17 3.040 2.619 10.46 275.68 2.750 10.26 3.185 276.15 3.434 2.969 276.71 10.37 3.138 277.18 10.27 3.619 3.213 277.38 10.21 3.767 1.189 1.130 268.15 10.59 1.339 1.252 269.13 10.55 "Vlahakiset al., 1972. Table VI. Incipient Equilibrium C 0 2 Hydrate Formation Conditions in Aqueous NaCl Solutions incipient C02 hydrate formation Dress. (MPa) exptl' calcd temp (K) NaCl (wt 9%) 1.488 1.383 270.12 10.38 1.522 271.06 10.22 1.648 1.725 272.18 10.25 1.919 2.039 10.22 2.261 273.67 2.250 2.488 274.52 10.20 2.483 2.892 10.32 275.30 2.502 10.30 275.37 2.878 2.797 276.31 10.19 3.233 2.876 10.29 276.49 3.333 3.020 3.454 276.93 10.16 276.95 10.41 3.066 3.567 277.20 10.20 3.136 3.681 'Vlahakis et al., 1972.
aspect is the a priori calculation of several parameters which were required. The new model for the liquid phase was successfully utilized for the development of the predictive method for gas hydrate equilbria. The agreement between experimental and predicted values, as c8n be seen in Figure 2 and in Tables IV-VI, is very good. It should be noted that the solubilityin aqueous solutionscontaining more than one electrolyte can also be computed with the same liquid-phase model without any additional parameters (Aasberg-Petersen et al., 1991). Consequently, the proposed hydrate equilibria predictive method is applicable. For the purposes of designing processes to either prevent hydrate formation or use the formation as a step in a separation process, the proposed predictive method will be useful. As the hydrates research focuses more and more on the equilibriumhydrate formation in the presence of substances like electrolytesand polymers (Sloan, 199Ob; Englezos, 1992) and on the kinetics of gas hydrate formation (Englezos et al., 1990; Sloan, 1990b; Sloan and Fleyfel, 19911, the proposed method is expected to be useful for the interpretation of these phenomena. Another potential use is in fluid inclusion studies (Thomas and Spooner, 1988).
Conclusions The incipient equilibrium hydrate formation conditions for gas mixtures containing components that are considerably soluble in water can now be computed rigorously by a predictive method that is presented in this work. The method is based on a new model which was used in conjunction with the Trebble-Bishnoi equation of state for the computation of high-pressure solubility of gases in aqueous electrolyte soutions. The van der Waals-Platteeuw model was used for the description of the hydrate phase. The incipient carbon dioxide hydrate formation pressures in aqueous NaCl solutions were computed, and the results were compared with the experimental data. The average deviation between the predicted values and those experimentally determined was found to be 7.2%. Acknowledgment
I acknowledge the financial assistance provided by the Natural Sciences and Engineering Research Council of Canada (NSERC). Nomenclature C = Langmuir constant, 1/MPa C p = heat capacity, J/(mol K) d, = density of the salt-free mixture, kg/m3 f = fugacity, MPa h = enthalpy, J/mol Z = ionic strength k d = binary interaction parameter for the Trebble-Bishnoi equation of state Lo = pure liquid water M, = salt-free mixture molecular weight, kg/mol N = number of components N h = number of hydrate-formingsubstances N , = number of electrolytes P = Pressure, MPa R = universal gas constant, J/mol T = temperature, K V = volume, m3 z = liquid-phase salt-free mole fraction X N = salt-free dielectric constant of water Greek Letters y = activity coefficient 6 = tolerance e, = salt-free mixture dielectric constant t N = dielectric constant of water p = chemical potential, J/mol v, = number of cavities of type m = liquid-phase true mole fraction pia = interaction coefficient between the dissolved salt and a nonelectrolytic component 4 = fugacity coefficient Subscripts i = component i j = component j w = water Superscripts
= reference conditions of 273.15 K and zero absolute pressure A-P = Aasberg-Petersen EL = electrolyte EOS = equation of state H = hydrate L = liquid MT = empty V = vapor Registry No. COz, 124-38-9; NaCl, 7647-14-5.
Ind. Eng. Chem. Res., Vol. 31,No.9,1992 2237
Literature Cited Aasberg-Petersen K.; Stenby, E.; Fredenslund, A. Prediction of High-pressure Gas Solubilities in Aqueous Mixtures of Electrolytes: Znd. Eng. Chem. Res. 1991,30,2180-2185. Anderson, F. E.; Prausnitz, J. M. Inhibition of Gas Hydrates by Methanol. EZChE J. 1986, 32 (8),1321-1333. Barker, J. W.; Gomez, R. K. Formation of Hydrates During Deepwater Drilling Operators. J. Pet. Technol. 1989,297-301. Beren, E.; Baa-Achs, M. Studies in Inorganic Chemistry 4: Gas Hydrates; Elsevier: Amsterdam, 1983; pp 184-188. Bozzo,A. T.; Chen. HA.; Kass, J. R.;Barduhn, A. J. The Properties of the Hydrates of Chlorine and Carbon Dioxide. Roc. Znt. Symp. Fresh Water Sea 1973,3,437-451. Byk, S. S.; Fomina, V. J. Gas Hydrates. Russ. Chem. Rev. 1968,37 (6), 469-491. Davidson, D. W. Gas Hydrates. In Water: A Comprehensive Treatise; Frank, F., Ed.; Plenum Press: New York, 1973; Vol. 2, Chapter 3. Deaton, W. M.; Frost, E. M., Jr. U.S.Bur. Mines Monogr. 1946,B (cited by Sloan, 1989). Du, Y.; Guo, T.-M. Prediction of Hydrate Formation for Systems Containing Methanol. Chem. Eng. Sci. 1990, 45 (4), 893-900. Englezos, P. Incipient Equilibrium Hydrate Formation Conditions in Aqueous Polymer Solutions. Chem. Eng. Res. Des. 1992, 70, 43-47. Englezoe, P.; Bishnoi, P. R. Prediction of Gas Hydrate Formation Conditions in Aqueous Electrolyte Solutions. AZChE J. 1988,34 (lo), 1718-1721. Englezos, P.; Kalogerakis, N. E.; Bishnoi, P. R.Formation and Decomposition of Gas Hydrates of Natural Gas Components. J. Inclusion Phenom. Mol. Recognit. Chem. 1990,8,89-101. Englezos, P.; Huang, Z.;Bishnoi, P. R. Prediction of Natural Gas Hydrate Formation Conditions in the Preaence of Methanol Using the Trebble-Bishnoi Equation of State. J. Can. Pet. Technol. 1991, 30 (2), 148-155. Holder, G. D.; Gorbin, G.; Papadopoulos, K. D. Thermodynamic and Molecular Properties of Gas Hydrates from Mixtures Containing Methane, Argon, and Krypton. Znd. Eng. Chem. Fundam. 1980, 19,282-286. Jeffrey, G. A. Hydrate Inclusion Compounds. J. Inclusion Phenom. Mol. Recognit. Chem. 1984,1,211-222. John, V. T.; Holder, G. D. Contribution of Second and Subsequent Water Shells to the Potential Energy of Guest-Host Interactions in Clathrate Hydrates. J. Chem. Phys. 1982,86,455-459. Knox, W. G.; Hess, M.; Jones, G. E.; Smith, H. B. The Hydrate Process. Chem. Eng. Rog. 1961,57,66-71. Larson, S. D. Phase Studies of the Two-Component Carbon Dioxide-Water System Involving the Carbon Dioxide Hydrate. Ph.D. Dissertation, University of Illinois, 1955. Makogon, Y. F. Hydrates of Natural Gas; Cieelewin, W. J., Transl.; Penn Well Publiihing Co.: Tulsa, OK, 1981. Malinin, S. D.; Savelyeva, N. I. The Solubility of C02 in NaCl and CaCl2 Solutions at 25,50, and 75O Under Elevated C02 Preaaurea. Geochem. Znt. 1972,410-418. Translated from Geokhimiya 1972, 6, 643-653. McKoy, V.; Sinanoglu, 0. Theory of Dissociation Pressures of Some Gas Hydrates. J. Chem. Phys. 1963,38 (3), 2946-2956. Menten, P. D.; Parrish, W. R.;Sloan, E. D., Jr. Effect of Inhibitors on Hydrate Formation. Znd. Eng. Chem. Process Des. Deu. 1981, 20 (2), 399-401. Munck, J.; Jorgensen, S. S.; Raamussen, P. Computations of the Formation of Gas Hvdrates. Chem. En#. - Sci. 1988, 43 (lo), 2661-2672. Ng, H.-J.; Robinson, D. B. ’Equilibrium Phase Compositions and Hydrating Conditions in Systems Containing Methanol, Light
Hydrocarbons, Carbon Dioxide and Hydrogen Sulfide”; Research Report RR-66; Gas Processors Association: Tulsa, OK, 1983. Ng, H.-J.; Robinson, D. B. Hydrate Formation Conditions in Systems Containing Methane, Ethane, Propane, Carbon Dioxide or Hydrogen Sulfide in the Presence of Methanol. Fluid Phase Equilib. 1985,21, 145-155. Ng, H.-J.; Chen, C.-J.; Robinson, D. B. “Hydrate Formation and Equilibrium Phase Compositions in the Presence of Methanol: Selected Systems Containing Hydrogen Sulfide, Carbon Dioxide, Ethane or Methane”; Research Report RR-66; Gas Processors Association: Tulsa, OK, 1985. Ng, H.-J.; Chen, C. J.; Saeterstad, T. Hydrate Formation and Inhibition in Gas Condensate and Hydrocarbon Liquid Systems. Fluid Phase Equilib. 1987,36,99-106. Nguyen, H.; Phillip, J. B.; John, V. T. Clathrate Hydrate Formation in Reversed Micellar Solutions. J. Phys. Chem. 1989, 93 (25), 8123-8126. Parrish, W. R.;Prausnitz, J. M. Dissociation Pressures of Gas Hydrates Formed by Gas Mixtures. Znd. Eng. Chem. Process Des. Deu. 1972,11,26-34. Robinson, D. B.; Mehta, B. R. Hydrates in the Propane-Carbon Dioxide-Water System. J. Can. Pet. Technol. 1971,lO (1).33-35. Robinson, D. B.; Ng, H.-J. Hydrate Formation and Inhibition in Gas or Gas Condensate Streams. J. Can. Pet. Technol. 1986,26 (3), 26-30. Sloan, E. D., Jr. Clathrate Hydrates of Natural Gases; Marcel Dekker: New York, NY,1990a. Sloan, E. D., Jr. Natural Gas Phase Equilibria and Kinetics: Understanding the State-of-theArt. Rev. Znst. Fr. Pet. 1990b,45 (2), 245-266. Sloan, E. D.; Fleyfel,’F. A Molecular Mechanism for Gas Hydrate Nucleation from Ice. AIChE J. 1991,37 (9), 1281-1292. Stewart, P. B.; Munjal, P. Solubility of Carbon Dioxide in Pure Water, Synthetic Sea Water, and Synthetic Sea Water Concentrates at -5O to 25O C and 10-to 45 Atm. Preasure. J. Chem. Eng. Data 1970,15 (l), 67-71. Tech. Commentary 1988,l (l), 1-4 (Freeze Concentration). Thomas, A. V.; Spooner, E. T. C. Fluid Inclusions in the Systems H2O-CH4-NaCl-CO2from Metasomatic Tourmaline Within the Border Unit of the Tanco Zoned Granitic Pegmatite, S.E. Manitoba. Geochim. Cosmochim. Acta 1988,52, 1065-1075. Trebble, M. A.; Bishnoi, P. R. Extension of the Trebble-Bishnoi Equation of State to Fluid Mixtures. Fluid Phase Equilib. 1988, 40, 1-21. Unruh, C. H.; Katz, D. L. Gas Hydratea of Carbon Dioxide-Methane Mixtures. Pet. Trans. AZME 1949, April, 83-86. van der Waals, J. H.; Platteeuw, J. C. Clathrate Solutions: Adu. Chem. Phys. 1959,2, 1-57. Vlahaki, J. G.; Chen, HA.; Suwandi, M. S.; Barduhn, A. J. ‘The Growth Rate of Ice Crystals: Properties of Carbon Dioxide Hydrate, A Review of Properties of 51 Gas Hydrates”. Syracuse University Research and Development Report No 830 prepared for the Office of Saline Water, U.S. Department of the Interior, November 1972. Werezak, G. N. Unusual methode of separation. AZChE Symp. Ser. 1969,65, (91), 6-18. Willson, R.C.; Bulot, E., Cooney, C. L. Clathrate Hydrate Formation Enhances Near-critical and Supercritical Extraction Equilibria. Chem. Eng. Commun. 1990,47-55. Zemaitis, J. F.; Clark, D. M.; Rafal, M.; Scriven, N. C. Handbook of Aqueous Electrolyte Thermodynamics; DIPR/AIChE: New York, 1986. Received for review December 23, 1991 Revised manuscript received April 23, 1992 Accepted May 13,1992