The knowledge of horizontal compositional variation is of prime importance in hydrocarbon reservoir delineation. However, the effect of natural convection on this variation is largely unknown. The behavior is investigated using a method of successive approximations, which iterates on solution of Poisson's equation.
An alternative scenario is that the gradient asymptotes to a value where the horizontal density derivative approaches zero.
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Thermodynamics of Hydrocarbon Reservoirs
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Citing Literature. 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. We consider a binary fluid mixture. The total diffusive mass flux of component 1 of the mixture is given by [ 21 , 23 ].
The first, second and third parts of Eq. For a binary mixture, the thermal diffusion factor of component 2 has the opposite sign. Here we consider a one dimension case in steady state, and assume that there are no convection and gravity segregation. Therefore, the mass flux can be assumed to be zero. Under these conditions, the composition and the temperature gradients are related through the following equation [ 2 ]:. Here we present the thermodynamic theory based on the modified form of Chapman and Cowling [ 22 ] and Kihara [ 24 ] as applied to binary hydrocarbon mixtures.
This approach involves the calculation of collision integrals of the fluid mixture for a well-defined potential function.
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The calculation of the transport property collision integrals for gases, whose molecules obey a simple intermolecular potential, enables to explain the transport properties of slightly non-ideal gas mixtures following the isotropic intermolecular interactions. For non-ideal mixtures, in which molecules interact with strongly anisotropic intermolecular interactions, additional contributions are assumed arising from the expansion of non-equilibrium distributions.
These anisotropic interactions could affect the thermal diffusion factors significantly [ 25 ]. We consider a binary mixture of components i and j. In this mixture the molecules are assumed to interact with an effective pair-wise additive intermolecular potential function Exp-6 , given by. M 1 and M 2 are the molecular weights of the mixture components 1 and 2.
The minor of A m obtained by striking out the row and column containing A ij is denoted by the symbol A ij m. Similarly, the i and jth minor of A 00 m is denoted by the symbol A ij00 m. The elements A ij are functions of the mole fractions, molecular weights and collision integrals, which are functions of temperature, molecular size and energy parameters. From Eqs. The dimensionless collision integrals of the above equations can be expressed as follows:. Using the first-order approximation, Eq. The details on the various parameters are given elsewhere [ 21 ].
To consider the effects of pressure and unlike interaction parameters, Eq. The following van der Waals mixing rules were applied to determine the mixture properties:.produbupin.tk
Thermodynamics of Hydrocarbon Reservoirs
Since the properties of the reservoir fluids depend on the fluid compositions, temperature and pressure, and since the collision integrals do not account for the pressure effects of the liquid mixtures, the empirical Eq. In this section, the performance of the thermodynamic theory is examined to represent the thermal diffusion factors in a few selected binary gas and liquid mixtures. The intermolecular potential parameters along with molecular weight of the pure fluids involved in binary mixtures studied in this work are given in Table 1. The pressure and potential parameters dependences of the unlike collision integrals are expressed in terms of a simple polynomial as given in Eq.
The polynomial parameters p i for the specific mixtures are given in Table 2. The model is seen to compare well with both simulation and measured results within their data uncertainties. When several data points of thermal diffusion factor were available in different non-ideal conditions of temperature, pressure and concentration, we re-evaluated the single point parameters by incorporating several data points in parameters regression. Also, in most of the cases the three parameters p 1 , p 2 and p 3 can describe well the diffusion factors and can depend on the temperature, pressure, concentration and interaction parameters.
Figure 2 presents results for the collision integrals independent of pressure.
The calculated collision integral results are physically consistent and agree with the literature data very well [ 25 ]. In both cases the theoretical results are in agreement with the measured data well within the experimental uncertainty.
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The variations of thermal diffusion coefficients with pressure are investigated. The comparison between theory and experiment is very good for all the tested conditions. In this paper the statistical thermodynamics has been applied to predict the thermal diffusion factors of binary hydrocarbon systems using the thermodynamic model based on the statistical thermodynamics and the Exp-6 potential function of two-body molecular interactions.
The collision integrals were redefined to account for the energy and size parameters of the molecules in addition to their pressure and temperature dependency. Theoretical results are tested against the molecular simulation results and experimental data for a few selected binary hydrocarbon gas and liquid mixtures. The model can successfully describe the simulation results of the binary hydrocarbon mixture investigate her.
In general, the comparisons of theoretical results with experimental data for the thermal diffusion coefficients show a very good performance of the theory in different non-ideal reservoir conditions over a range of temperature, pressure and concentration.
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The unlike interaction parameters are seen to be important for accounting the non-ideal effects in collision integrals, and for improving the correlation and prediction of thermal diffusion factors in non-ideal hydrocarbon liquid mixtures. Licensee IntechOpen.
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