## Determining equation of state binary interaction parameters using K- and L-points

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##### Date

2004-10-07##### Author

Mushrif, Samir Hemant

##### Type

Thesis##### Degree Level

Masters##### Abstract

The knowledge of the phase behaviour of heavy oils and bitumen is important in order to understand the phenomenon of coke formation. Computation of their phase behaviour, using an equation of state, faces problems due to their complex composition. Hence n-alkane binaries of polyaromatic hydrocarbons are used to approximate the phase behaviour of heavy oils and bitumen. Appropriate values of binary interaction parameters are required for an equation of state to predict the correct phase behaviour of these model binary fluids.
This thesis deals with fitting of the binary interaction parameter for the Peng-Robinson equation of state using landmarks in the binary phase space such as K- and L-points. A K- or an L-point is a point in the phase space where two phases become critical in the presence of another phase in equilibrium. An algorithm to calculate K- and L-points using an equation of state was developed. The variation of calculated K- and L-points with respect to the binary interaction parameter was studied and the results were compared with the experimental data in the literature. The interaction parameter was then fitted using the best match of experimental results with the computed ones. The binary interaction parameter fitted using a K- or an L-point was then used to predict the P-T projection of the binary system in phase space. Also, the qualitative effect of the binary interaction parameter on the P-T projection was studied.
A numerical and thermodynamic study of the algorithm was done. Numerical issues like the initial guesses, convergence criterion and numerical techniques were studied and the thermodynamic constraints in the generalization of the algorithm are discussed. It was observed that the binary interaction parameter not only affects the location of K- and L-points in the phase space but also affects the calculation procedure of K- and L-points.
Along with the propane binaries of polyaromatic hydrocarbons, K- and L-points were also calculated for systems like methane binaries of higher n-alkanes and the ethane + ethanol binary. In the case of the ethane + ethanol system, K- and L-points, matching the experimental results were calculated with different values of the binary interaction parameter. But the Peng-Robinson equation of state was unable to predict the correct type of phase behaviour using any value of the binary interaction parameter.
The Peng-Robinson equation of state was able to predict the correct type of phase behaviour with the binary interaction parameter, fitted using K- and/or L-points for methane + n-alkane systems. The systems studied were the methane binaries of n-pentane, n-hexane and n-heptane.
For the propane binaries of polyaromatic hydrocarbons, no value of the binary interaction parameter was able to predict the K-point with a good accuracy. The binary interaction parameter which gave the best possible results for a K-point failed to predict the correct type of phase behaviour. The binary interaction parameter fitted using the P-T projection enabled the Peng-Robinson equation of state to give a qualitative match for the high pressure complex phase behaviour of these systems. Solid phase equilibria were not taken into consideration.

##### Degree

Master of Science (M.Sc.)##### Department

Chemical Engineering##### Program

Chemical Engineering##### Supervisor

Phoenix, Aaron##### Copyright Date

October 2004##### Subject

equation of state

phase equilibrium

K- and L-points

critical point

tangent plane criterion

binary interaction parameter