Special Session Title: High Pressure Gas-Liquid Separation; paper proposal title: Theoretical Prediction of Interfacial Tensions for Hydrocarbon mixtures with Gradient Theory in Combination with Peng-Robinson Equation of State
Authors: Nilssen Hui , Fredheim Arne , Solbraa Even , Kvamme Bjørn 
Published: July 2010

Abstract
In this paper the Gradient Theory of inhomogeneous fluids interface will be discussed and applied to compute the interfacial tension of hydrocarbon mixtures. The two inputs of the Gradient Theory model are the Helmholtz free energy densities of homogeneous bulk phases and the influence parameters of inhomogeneous interface. The bulk phase properties are calculated by the Peng-Robinson Equation of State. The pure component influence parameters are obtained from a correlation based on pure component experimental surface tension data, and the mixture influence parameters are determined from the geometric mixing rule. Experimental interfacial tension data for binary hydrocarbon mixtures and real petroleum fluids from two gas condensate reservoirs are collected and used to evaluate the Gradient Theory and Parachor Method. It is found that the accuracy of the Gradient Theory is superior to the Parachor Method which is traditionally used in the oil industry for interfacial tension predictions.

1 Introduction
It is well known that the interfacial tension is regarded as one of important thermophysical parameters in many industrial processes. For example, in gas liquid separation process, there are strong dependencies between liquid interfacial tensions and gas-liquid separation performance, because both droplet size distribution and re-entrainment are sensitive to interfacial tension in the scrubber. In addition surface tension also plays important role in oil recovery process, extraction process, refinery process, etc. In spite of the importance of interfacial tension in petroleum industry, there is still a considerable lack of reliable experimental data in the open literature, especially near the critical conditions. Therefore, the theoretical and semi empirical prediction of interfacial tensions are of particular significance.
There are several approaches which have been proposed for the estimation of interfacial tensions. These approaches can be divided into two categories: empirical correlations and statistical thermodynamics-based method which takes into account the density gradient between the bulk phase interfaces. The simple estimation method includes the Parachor Method [1-2], the Corresponding State Correlation [3] and the Perturbation Theory [4], which are not satisfactory for estimating interfacial tension of mixtures that exhibit strong hydrogen bonding. The statistical thermodynamics based methods include the Density Function Theory [5-6] and the Gradient Theory [7-8].
The Gradient Theory is of particular importance for practical computations of surface and interfacial tensions. It was originated by Rayleigh and Van der Waals [7] and rediscovered by Cahn and Hilliard in 1958 [8]. In this work the Gradient Theory of inhomogeneous fluid interface will be applied to obtain the interfacial tension of the hydrocarbon mixtures. The short descriptions of the Gradient Theory can be found in section 2. The Peng-Robinson Equation of State will be recalled in the section 3 and is utilized to compute some thermodynamic properties of the vapor/liquid phases and the interface. Finally the predicted interfacial tensions will be compared to experimental tensions. The superiority of the Gradient Theory is that it simultaneously can simulate mixture compound density profiles over the interfaces which are hardly accessible in experimental observation and measurement. The density profiles are very useful for theoretical studies and characterization of the interfacial behaviors of the hydrocarbon mixtures.