zhang yi

Thermodynamic Modeling of Gas Hydrates : 

Thermodynamic Modeling of Gas Hydrates ChEM 2440 Mini Term Project Yi Zhang April 20, 2003

Introduction: 

Introduction Gas hydrates are crystalline molecular complexes formed from mixtures of water and low molecular weight gases. The water molecules that form the lattice are strong hydrogen bonded with each other. The gas molecules interact with the water molecules through van der Waals type dispersion forces. There is no chemical association between gas and water molecules. [1] http://www.sns.gov/acns/presentations/chakoumakos.pdf

Introduction (Cont.): 

Introduction (Cont.) Hydrate formation has long been a problem in natural gas production, processing and transportation. The prediction of equilibrium conditions for hydrates has received greatly increased interest in the past decade, because of the discovery of large hydrate deposits which could be a potential energy source in the future, and its close relationship to world environmental protection. [2]

Thermodynamic model of Hydrate Formation: 

Thermodynamic model of Hydrate Formation The well known van der Waals-Platteeuw (VDW-P) model was proposed in 1959, which is based on classical statistical thermodynamics and has the following assumptions:[3] Each cavity can contain at most one gas molecule. The interaction between a gas and water molecule can be described by a pair potential function, and the cavity can be treated as perfectly spherical. The gas molecule can freely rotate within the cavity. There is no interaction between the gas molecules in different cavities, and the gas molecules interact only with the nearest neighbor water molecules. The free energy contribution of the water molecules is independent of the mode of dissolved gases (the gas does not distort the hydrate lattice).

The method of Predicting Equilibrium: 

The method of Predicting Equilibrium At equilibrium, Where, is the chemical potential of water in the hydrate phase; is the chemical potential of water in the water rich or ice phase. The condition for equilibrium can be rewritten as Where, is the chemical potential of an unoccupied hydrate lattice, used as the reference state. [3]

Calculation of : 

Calculation of Assuming an ideal solution relationship for the water and dissolved gas phase. [3] Where, experimentally determined reference chemical potential; is an experimentally determined reference enthalpy difference between the empty hydrate lattice and pure water phase at the reference temperature; is an experimentally determined reference enthalpy difference; is the mole fraction of water in the water-rich phase.

Calculation of : 

Calculation of is the ratio of j-type cavities present to the number of water molecules present in the hydrate phase; is the Langmuir constant for species i in cavity j. is the gas phase (and hydrate phase) fugacity of the i type hydrate forming species which can be calculated by the Peng-Robinson equation of state. is the fraction of j-type cavities, which are occupied by i-type gas molecules. [3]

Calculation of Langmuir Constants: 

Calculation of Langmuir Constants Langmuir constants for spherical molecules is determined by integrating the gas-water potential function over the volume of the cavity. [4] Assuming a Kihara type interaction between the gas molecule and the nearest water molecules, and that the cavity is perfectly spherical and the water molecules which form the cavity are smeared evenly over the surface of this sphere. The cell potential obtained is Where,

Modification of the model: 

Modification of the model John and Holder determined the contribution of more distant water molecules by assigning “second” and “third” water shells and developed a generalized model that could use the Kihara parameters obtained from virial coefficient data. [5] and are smooth cell contributions of the first, second, and third shells, respectively to the Kihara potential function.

Improvement to the model: 

Improvement to the model The effect of lattice stretching due to gas molecule size on the reference chemical potential difference between the empty lattice and water is calculated by Holder et al.. [6] A new concept, which included local stability, linked cavity, basic hydrate, and basic hydrate component, was proposed in the late 90’s. [7] In 2001, Trout developed a method to extract potentials from the temperature dependence of Langmuir constants for clathrate-hydrates by using an analytical “inversion” method based on the standard statistical model of vdW-P. [8] Sloan proposed a method in 2002, which optimized the model by direct incorporation of spectroscopic data. [9]

References: 

References [1] G. D. Holder, S.P. Zetts and N. Pradhan, Phase Behavior in Systems Containing Clathrate Hydrates: A Review, Reviews In Chemical Engineering, Vol. 5, No. 1-4, 1988. [2] S.-Y. Lee and G.D.Holder, A Generalized Model for Calculating Equilibrium States of Gas Hydrates: Part II, Volume 912 of the Annals of the New York Academy of Sciences, 1999. [3] van del Waals, J.H. and J. C. Platteeuw, Clathrate Solutions, Adv. In Chem.Phys., 2, 1-57, 1959. [4] V. McKoy and O. Sinanoglu, Journal of Chemical Physics, 38 (No. 12), 2946-2955, 1963. [5] V. T. John and G. D. Holder, Journal of Physical Chemistry, 86 (No.4), 455-459, 1982. [6] Ming-Jing Hwang, G. D. Holder and S. R. Zele, Lattice Distortion by Guest Molecules in Gas-Hydrates, Fluid Phase Equilibria, 83, 437-444, 1993.

Reference (Cont.): 

Reference (Cont.) [7] Guang-Jin Chen and Tian-Min Guo, Thermodynamic Modeling of Hydrate Formation Based on New Concepts, Fluid Phase Equilibria, 122, 43-65, 1996. [8] Martin Z. Bazant and B. L. Trout, A method to extract potentials from the temperature dependence of Langmuir constants for clathrate-hydrates, Physica A, 300, 139-173, 2001. [9] A.L. Ballard and E. D. Sloan Jr., The next generation of hydrate prediction I. Hydrate standard states and incorporation of spectroscopy, Fluid Phase Equilibria, 194-197, 371-383, 2002.