1. Introduction

This chapter deals with one of the key aspects of hydrocarbon production from the oil and gas reservoirs, known as the thermal diffusion process. This process plays an important role to separate isotopic mixtures and isobaric mixtures, analyze hydrodynamic instability in mixtures, transport mass in living matters, migrate minerals, separate and characterize polymers and colloidal particles by thermal field flow fractionation. In the case of hydrocarbon productions, the thermal diffusion process is generally used to study the compositional variation and segregation in hydrocarbon oil and gas reservoirs [1, 2].

In some hydrocarbon reservoirs, very large compositional variations can be observed in horizontal and vertical directions. There is a large temperature gradient in the vertical direction, and a small temperature gradient in the horizontal direction. The horizontal temperature gradient always induces both thermal convection and thermal diffusion, while the vertical temperature gradient causes thermal diffusion but may or may not induce thermal convection. The temperature gradient develops a concentration gradient of the mixture constituents. A thermal diffusion process takes place when the convection free gas and liquid mixture tend to separate under a temperature gradient. This phenomenon is known as the "Soret Effect." This effect can be measured by means of thermal diffusion factor (αT).

A significant progress has been made in recent past to measure thermal diffusion factors in liquid mixtures [3, 4].

The available experimental data have indicated that in low pressure gaseous mixtures and ideal liquid mixtures, α<sup>T</sup> is small, and molecular size and mass govern its magnitude [5]. On the other hand, α<sup>T</sup> may be large in non-ideal liquid mixtures where energy interactions, size and shape of the molecules, and thermodynamic conditions govern the magnitude of α<sup>T</sup> [6]. Also, the thermal diffusion can enhance composition gradient in vertical direction in hydrocarbon reservoirs [7], and it can enhance or weaken compositional variation in vertical direction as thermal diffusion is usually opposite in sign to the gravitational segregation in hydrocarbons reservoirs [8, 9].

Therefore, a reliable theoretical model of thermal diffusion factors in hydrocarbon mixtures is require to accurately predict the compositional variations in reservoirs and evaluate the formation fluid.

There has been a continued interest in the thermodynamic modeling and the measurement of thermal diffusion factors in multicomponent mixtures (e.g., [10–16]). Numerous classical thermodynamic approaches have been utilized to describe the thermal diffusion factors in binary hydrocarbon mixtures only qualitatively [10–13]. A more successful thermodynamic model of thermal diffusion factors of non-ideal mixtures was presented by Shukla and Firoozabadi [2, 14]. The model was based on the thermodynamics of irreversible processes and kinetic theory, combining both the equilibrium and non-equilibrium properties. In this model, the equilibrium properties were determined from the equation of state while the non-equilibrium properties were obtained from the fluid viscosity. The model predictions of thermal diffusion factors in several binary mixtures were found to represent the experimental data very well. However, the signs of thermal diffusion factors of components could not establish uniquely the direction of warmer and colder region of fluids, especially in multicomponent mixtures. Furthermore, these models provide little or no information about the intermolecular forces in the system, and cannot describe adequately the thermal diffusion factors close to the critical point of the fluids.

Several attempts were made in the past to better describe thermal diffusion factors of gaseous hydrocarbon mixtures using statistical thermodynamics and molecular simulations depending on the intermolecular interactions [17–19]. A review of the developments in the theory and experiment of thermodiffusion has been presented recently by Kohler and Morozov [20]. However, the statistical theory of thermal diffusion was not applied to the liquid hydrocarbon mixtures of industrial interest. Moreover, the rigorous theories were not available to express the volumetric and heat flow properties accurately.

Recently, Shukla [21] proposed a model of thermal diffusion factors in hydrocarbon mixtures using the statistical thermodynamics of intermolecular interactions [22]. The model was able to describe the thermal diffusion factors of several binary hydrocarbon and non-hydrocarbon mixtures. The objective of this paper is to examine the accuracy of the proposed model in describing thermal diffusion factors of binary hydrocarbon mixtures.

Section 2 describes briefly the relation between the mass flux and thermal diffusion coefficient of a binary fluid mixture. Section 3 establishes the relation between statistical thermodynamics of thermal diffusion factors and how to account for the intermolecular interactions of the molecular constituents. Section 4 compares theoretical results with experimental data and examines the reliability of the theory for the selected binary hydrocarbon mixtures. Section 5 presents the conclusion of this study.
