Parameters Kihara

Oa and ob are the polarizability of species A and B and I and /b are the corresponding ionization potentials. The values of 7 and p arc determined from the molecular volumes and acentric foctors of the individual species. The values for the molecular diameter of species i, / , and its Kihara parameters and at are given by... 

The evaluation of the Langmuir constant may then be determined from a minimum of experimentally fitted Kihara parameters via an integration over the cavity radius. Equation 5.27a shows the Langmuir constant to be only a function of temperature for a given component within a given cavity. 

The experimentally fitted hydrate guest Kihara parameters in the cavity potential uj (r) of Equation 5.25 are not the same as those found from second virial coefficients or viscosity data for several reasons, two of which are listed here. First, the Kihara potential itself does not adequately fit pure water virials over a wide range of temperature and pressure, and thus will not be adequate for water-hydrocarbon mixtures. Second, with the spherical Lennard-Jones-Devonshire theory the point-wise potential of water molecules is smeared to yield an averaged spherical shell potential, which causes the water parameters to become indistinct. As a result, the Kihara parameters for the guest within the cavity are fitted to hydrate formation properties for each component. 

In order to examine the effect of the Kihara parameters on the predicted hydrate equilibrium pressures, a sensitivity analysis was carried out (see also Cao et al. ). In this study we report results for methane (si hydrate former) and propane (sll hydrate former). The Kihara parameter values, as well as the thermodynamic property values, reported by Sloan were taken as the base-reference case and hydrate equilibrium pressures were calculated by perturbing the reference values in the range +(1%-10%). On the other hand, the reported thermodynamic parameters zl// and Ah have a wider range, but as it is going to be discussed later, have a less significant effect on the predictions. 

Figure 1 Sensitivity analysis of the Kihara parameters and the thermodynamic properties for methane. Effect on the predicted equilibrium pressure of (a) energy parameter, e/k, (b) distance parameter, a, and (c) reference chemical potential difference, Ap ...

A sensitivity analysis was performed to examine the effect of the thermodynamic properties and the Kihara parameters on the hydrate equilibrium calculations. It was demonstrated that the Kihara parameters (s/k and a) had a more significant effect on hydrate equilibrium predictions than the thermodynamic properties (Ap and Ah ) for the cases of methane and propane that were examined in this work. It was observed that parameters obtained from one set of experiments could not always be used in correlating successfully other hydrate experimental data sets. This problem was more pronounced in cases that the fitted parameters were to be used for other properties such as virial coefficients or viscosities. Finally, issues such as satisfactory predictions at very high pressures and multiple cage occupancy need to be considered. 

Arithmetic mean values of the diameter, R, Kihara diametisr, and and 9 are used in the evaluation of the interaction between two o lecules A and B. These values, and an associated parameter t, are defined as... 

McKoy and Sinanoglu (1963) and Child (1964) refined the van der Waals and Platteeuw method using different intermolecular potentials such as the Kihara potential. Workers at Rice University, such as Marshall et al. (1964) and Nagata and Kobayashi (1966a,b), first fit simple hydrate parameters to experimental data for methane, nitrogen, and argon. Parrish and Prausnitz (1972) showed in detail how this method could be extended to all natural gases and mixed hydrates. 

The original work by van de Waals and Platteeuw (1959) used the Lennard-Jones 6-12 pair potential. McKoy and Sinanoglu (1963) suggested that the Kihara (1951) core potential was better for both larger and nonspherical molecules. The Kihara potential is the potential currently used, with parameters fitted to experimental hydrate dissociation data. However, it should be noted that the equations presented below are for a spherical core, and while nonspherical core work is possible, it has not been done for hydrates. 

Regressed Kihara Potential Parameters ("a" as in Original Reference)... 

Potential parameters (such as the Kihara core or Lennard-Jones potentials of the previous sections) can be calculated from a small set of fundamental, ab initio intermolecular energies, rather than fits of the potentials to phase equilibria and spectroscopic data. 

The reciprocal of the square root of the chemiluminescence intensity versus time gives a linear relationship as published by Kihara and Hosoda [26]. In the region where the plot gives a straight line, the slope is the value of fkhfj. This parameter is named CL-decay rate and may be used to evaluate the thermal history of different polymers. 

The column headed HSE uses an approximation made originally by Mansoori and Leland (3) that the diameter used in the hard sphere equations of state is c0o-, the LJ a parameter for each molecule multiplied by a universal constant for conformal fluids. This approximation then requires that be replaced by equations defining the HSE pseudo parameters, Equations 10 and 11. The results in the HSE column use c0 = 0.98, the value for LJ fluids obtained empirically by Mansoori and Leland. This procedure is correct only for a Kihara-type potential and it is not consistent with the LJ fluids in Table I. Furthermore, this causes only the high temperature limit of the repulsion effects to be included in the hard-sphere calculation. Soft repulsions are predicted by the reference fluid. 

Although certain of the above-mentioned theories are moderately successful in representing the experimental data of CF4 -t- CH and other fluorocarbon + hydrocarbon mixtures, experimental values of and x are required. At present there is no satisfactory method of obtaining these parameters a priori. Scott, in his 1958 review, considered the various possible factors that could lead to a weakening of the unlike interactions in such mixtures. He concluded that the three most significant were the presence of non-central forces, differences in ionization potential, and differences in size of the two component molecules. The use of the Kihara potential together with the Hudson and McCoubrey rule takes account of all these effects and thus the undoubted success of the Knobler treatment is not surprising. Criticisms could be levelled at his use of a spherically symmetric potential for substances such as n-hexane but the use of a more realistic potential such as the Kihara line-core potential is hardly justified until reliable experimental values for the ionization potentials of the fluorocarbons become available. 

Non-central Potential Functions.—Non-central interactions can also be handled in terms of specific multi-parameter potential functions such as the Stockmayer and Kihara potentials. Although there is an extensive literature on the subject of such potentials, it is only rarely that virial coefficients are sufficiently precise or extensive to warrant their use. For this reason we will deal only briefly with the subject. 

When multi-parameter potentials are applied to mixtures, the combination rules for parameters other than e and a often follow from the model underlying the potential. For example, the Kihara spherical-core potential is based on a model in which each molecule has a molecular core of characteristic radius an. The combination rules an = (an + jj)/2 follows directly from the hard-core assumption. ... 

The Kihara potential function [12] is used as described in McKoy and Sinanoglu [13]. The Kihara potential parameters, a (the radius of the spherical molecular core), a (the collision diameter), and e (the characteristic energy) are taken from Tohidi-Kalorazi [14], The fugacity of water in the empty hydrate lattice, // in Equation , can be calculated by ... 

The values of the rate constants and their respective activation parameters are given in Table 14. Kihara et al. discuss their rate constants in the light of previous work. 

It was easy to show that the intermolecular potential curves for spherical molecules would yield a single family of reduced equations of state. If one takes the Kihara model with spherical cores, then the relative core size can be taken as the third parameter in addition to the energy and distance scale factors in the theoretical equation of state. 

The most important test of our bimolecular potential is its use in statistical thermodynamic models for the prediction of phase equilibria. Monovariant, three-phase pressure-temperature measurements and invariant point determinations of various gas hydrates are available and are typically used to fit parameters in molecular computations. The key component needed for phase equilibrium calculations is a model of the intermolecular potential between guest and host molecules for use in the configurational integral. Lennard-Jones and Kihara potentials are usually selected to fit the experimental dissociation pressure-temperature data using the LJD approximation (2,4,6), Although this approach is able to reproduce the experimental data well, the fitted parameters do not have any physical connection to the properties of the molecules involved. 

In Approach 1, experimental equilibrium three-phase dissociation pressure data compiled by Sloan (57), consisting of 97 points for the methane-water system from 148.8 to 320.1 K, were used in the parameter optimization. Although the fits were satisfactory, the intermolecular parameters fitted from the experimental data did not have much physical meaning (9). We also found that none of the simple potentials, including Lennard-Jones 12-6, Kihara, and optimized potential from liquid simulation (OPLS), were able to predict both... 

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