(667a) Effect of Langmuir Constants On Hydrate Equilibrium Calculations

Under appropriate conditions of pressure and temperature water molecules can self-assemble to form cavities that are stabilized by the presence of guest molecules that can fit within the cavities. These non-stoichiometric, solid (ice-like), inclusion materials are known as clathrate hydrates and have significant applications in science and engineering. Hydrate equilibrium at the continuum (i.e., macroscopic) level is described by a theory based on statistical mechanics that has been developed, initially by van der Waals and Platteuw [1], and subsequently modified by others (e.g., see the extended review by Sloan and Koh [2]). In this type of theory the cavity occupancies (i.e., the fraction of cavities occupied by the guest molecules) are described by Langmuir-type functions of the gas fugacity. The Langmuir constants that appear in these functions are temperature, guest, as well as, cavity-type-dependent, and affect the accuracy of the calculations. Therefore, it is essential to develop dependable and accurate methods for the calculation of the Langmuir constants. Traditionally, two approaches are followed in order to calculate the Langmuir constants:

(i) An intermolecular potential is chosen to describe the water-guest interactions (e.g., the Lennard-Jones, the square-well, or the Kihara potential), and the potential parameters are obtained by a fitting procedure using available experimental hydrate equilibrium data. Following this approach results in very good agreement with hydrate equilibrium predictions (within the range of development of the method), however, the values for the potential parameters are significantly different than those calculated when using experimental data of second virial coefficients or transport properties to obtain the potential parameters. Therefore, extrapolation to hydrate equilibrium predictions outside the range of development becomes highly problematic.

(ii) The interaction energies between the guest molecules and the water molecules that form the hydrate cavities are calculated using ab initio methods [3]. The ab initio calculation results, subsequently, are fitted to an empirical formula (e.g., the Lennard-Jones plus a Coulombic charge-charge formula) in order to obtain the potential parameters [4]. The accuracy of calculations of ab initio potential energy surfaces depends on the level (e.g., HF, MP2, MP3, MP4, etc.) of the simulations, and the basis sets used. Increasing the complexity of the calculation, results in increasing significantly the computational cost.

Alternatively, the following approach could be used. Hydrate formation can be simulated as a special case of a process of gas adsorption in a solid matrix. Such processes have been simulated with Monte Carlo techniques with great success. The hydrate cavity occupancies, thus, could be calculated from the Monte Carlo simulations at various temperatures and pressures, and the results can be fitted to Langmuir-type functions [5]. Such temperature and pressure-dependent functions, once they are obtained, can be introduced to models that use the van der Waals and Platteuw theory for hydrate equilibrium predictions. However, the hydrate equilibrium predictions of such macroscopic models seem to be very sensitive to the values of the Langmuir constants used. As a result of such sensitivity, other constants of the macroscopic thermodynamic models need to be re-adjusted in order to increase the accuracy of the calculations. In the current study we perform a detailed analysis of the sensitivity of the hydrate equilibrium calculations on the values used for the Langmuir constants. We attempt to delineate the boundaries of the values of the Langmuir constants obtained from Monte Carlo simulations that can be used by van der Waals–Platteuw–type models without having to re-adjust any other of the model parameters.

References

[1]    van der Waals, J. H.; Platteeuw, J. C. Adv. Chem. Phys. 1959, 2, 1-57.

[2]    Sloan, E. D.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3^rdedition, Taylor & Francis. CRC Press, 2008.

[3]    Klauda, J. B.; Sandler, S. I.  J. Phys. Chem. B 2002, 106, 5722-5732.

[4]    Sun, R.; Duan, Z. Geochim. Cosmochim. Acta 2005, 69, 4411-4424.

[5]    Papadimitriou, N. I.; Tsimpanogiannis, I. N.; Papaioannou, A. Th.; Stubos, A. K. J. Phys. Chem. B 2008, 112, 10294-10302.