2232 Ind. Eng. Chem. Res. 1992,31,2232-2237 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 zyxwv 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 zyxwvut 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 en- hanced 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 de- sirable 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. In- cipient 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 for- mation 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., zyxwvu al- cohols) can be computed by thermodynamics-based pre- dictive 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 correlationsfor the oass-~aa~/92/2~3i-2232$03.00/o noncondensable gases. A thermodynamically consistent and simple approach is to use an equation of state. En- glezos et d. (1991) used the Trebble-Bishnoi equation of state (Trebble and Bishnoi, 1988) and found the predic- tions to zyxwv 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 thermody- namics-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, ni- trogen). 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 zy can be used to compute the incipient equilibrium carbon dioxide hydrate formation conditions in aqueous electrolyte solu- tions. 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 (Aasberg- Petersen et al., 1991). The proposed hydrate prediction method does not have any adjustable parameters. Com- putations 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 The 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 0 1992 American Chemical Society