Viscosity of heavy n-alkanes and diffusion of gases therein based on molecular dynamics simulations and empirical correlations

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Highlights

Abstract

The viscosity of pure n-alkanes and n-alkane mixtures was studied by molecular dynamics (MD) simulations using the Green–Kubo method. n-Alkane molecules were modeled based on the Transferable Potential for Phase Equilibria (TraPPE) united atom force field. MD simulations at constant number of molecules or particles, volume and temperature (NVT) were performed for n-C8 up to n-C96 at different temperatures as well as for binary and six-component n-alkane mixtures which are considered as prototypes for the hydrocarbon wax produced during the Gas-To-Liquid (GTL) Fischer–Tropsch process. For the pure n-alkanes, good agreement between our simulated viscosities and existing experimental data was observed. In the case of the n-alkane mixtures, the composition dependence of viscosity was examined. The simulated viscosity results were compared with literature empirical correlations. Moreover, a new macroscopic empirical correlation for the calculation of self-diffusion coefficients of hydrogen, carbon monoxide, and water in n-alkanes and mixtures of n-alkanes was developed by combining viscosity and self-diffusion coefficient values in n-alkanes. The correlation was compared with the simulation data and an average absolute deviation (AAD) of 11.3% for pure n-alkanes and 14.3% for n-alkane mixtures was obtained.

Introduction

The study of transport properties in alkanes is of considerable practical and theoretical interest. In the petrochemical industry, the ability to predict and control the viscosity, and thus the diffusion in systems of alkanes and their mixtures is crucial for product design and process optimization. An immediate example refers to the Gas-To-Liquid (GTL) synthesis of high value hydrocarbons which is a classical Fischer–Tropsch catalytic process. Here, accurate knowledge on solubility, and self-diffusivity of hydrogen (H2), carbon monoxide (CO), and water (H2O) in hydrocarbon wax both in bulk and the catalytic nanopores as well as of the corresponding mixture viscosities of such systems at high temperature and pressure is necessary.

Although there is a large amount of experimental data available for the viscosity of n-alkanes and the self-diffusivity of solutes in n-alkanes [1], [2], [3], [4], [5], not all information relevant for processes design can be gathered by experiments. Consequently, suitable theoretical models or accurate computational approaches provide an appealing alternative with respect to time and cost. Based on the work of Vesovic and Wakeham [6], Assael et al. [7] proposed a model for the viscosity of liquid mixtures according to the hard-sphere theory of Assael et al. [8]. This approach requires a number of adjustable parameters and was used to predict the viscosity of liquids and liquid mixtures up to high pressures for a wide range of different chemical systems, such as hydrocarbons, alcohols, and halogenated refrigerants. Moreover, Queimada et al. [9] provided experimental measurements of viscosity, liquid density and surface tension of several mixtures of a heavy n-alkane (n-C20H42, n-C22H46 or n-C24H50) with a smaller one (n-C7H16, n-C10H22 or n-C16H34). They also used the friction theory, proposed by Quiñones-Cisneros et al. [10], to model the viscosity of the n-alkane mixtures and good agreement with experimental data was achieved. Motahhari et al. [11] used the Expanded Fluid (EF) viscosity correlation to predict the viscosity of asymmetric hydrocarbon mixtures. They concluded that EF correlation is accurate, simple and robust and well suited for use with process and reservoir simulators.

A powerful computational approach refers to the molecular dynamics (MD) simulation. By taking advantage of the tremendous increase of computing power and the development of accurate MD models, transport properties of fluids can be reliably estimated. Two widely used MD methods for the calculation of the viscosity of fluids are the non-equilibrium molecular dynamics (NEMD) method and the Green–Kubo method using equilibrium molecular dynamics (EMD) [12]. The former provides the zero shear rate viscosity by studying the shear rate dependent viscosity of the liquid, while the latter yields the viscosity as the time integral of the correlation function of the elements of the pressure tensor. Significant research has been devoted for the estimation of the viscosity of alkanes using NEMD [13], [14], [15], [16], [17], [18], [19] or the Green–Kubo method [20], [21], [22], [23], [24]. These simulations cover linear and branched n-alkanes with a chain length ranging between n-C10 up to n-C40. Galliéro et al. [25] developed a correlation for the viscosity of the Lennard–Jones fluid based on MD simulations. By comparing to literature empirical models and experimental measurements, they showed that the proposed model works well for simple molecules, while for larger molecules, in highly dense conditions, the model can be improved by a fitting procedure on the atomic diameter. Some limitations were identified when the model was applied to asymmetric mixtures of methane with toluene. Aquing et al. [26] have performed composition analysis and viscosity predictions of complex fuel mixtures using an anisotropic united atom force-field approach. Recently, coarse-grained molecular models have been used successfully to predict the viscosity of medium size n-alkanes [27], [28].

In two recent publications [29], [30], the thermodynamic and structural properties of several pure n-alkanes and n-alkane mixtures as well as the self-diffusion coefficients of H2, CO, and H2O in them at various conditions were investigated by EMD simulations. The results were found to be in good agreement with literature experimental data. Moreover, a macroscopic correlation for predicting the diffusion coefficient of solutes in n-alkanes and n-alkane mixtures was developed based on the rough hard sphere (RHS) theory proposed by Matthews et al. [2], [31] and Erkey et al. [32]. For all the studied pure n-alkanes, the average absolute deviation (AAD) of the self-diffusion coefficient between simulation and correlation calculations was between (4.4 and 6.5)%. In the case of n-alkane mixtures, the AAD was even lower, ranging between (3.1 and 3.8)%.

In this work, the Green–Kubo method is used for the viscosity calculations which are extended to high molecular weight n-alkanes, such as n-C96, binary and six-component n-alkane mixtures over a wide range of temperatures. The viscosity results obtained from long MD simulations are used subsequently to develop a new correlation for the prediction of the self-diffusivity of gases dissolved in the corresponding mixtures. The correlation is developed in terms of the solvent viscosity, the solute molar volume at its normal boiling point, and the temperature. The new correlation reproduces satisfactorily the self-diffusivity of solutes in the n-alkanes and their mixtures.

Section snippets

Atomistic force field and simulation details

A united-atom (UA) representation was used to model the n-alkane molecules. In particular, the Transferable Potential for Phase Equilibria (TraPPE) [33] was employed. TraPPE has been shown to be very accurate for the thermodynamic properties of pure n-alkanes and their mixtures over a wide range of temperatures and pressures, including the critical point. Details on the functional form of the force field and the parameters for the various terms can be found in previous work [29]. For H2 and CO,

Viscosity calculations

For the calculation of viscosity of the pure n-alkanes and their mixtures, NVT MD simulations were performed at a pressure of 3.4 MPa. For this pressure, experimental density data are available in literature [43], [44], [45]. In table 2, the experimental literature densities and our MD viscosity results for pure n-C8, n-C12, n-C16, n-C20, n-C64, and n-C96 are reported.

In figure 2, the computed viscosities are compared to experimental data and previous simulation studies. In all cases, simulation

Conclusions

In this work, the viscosity of pure n-alkanes from n-C8 up to n-C96 as well as of binary and GTL model six-component n-alkane mixtures were examined using long MD simulations. Accurate atomistic force fields were used to model n-alkane chains and viscosities were determined using the equilibrium fluctuations of the off-diagonal components of pressure according to the Green–Kubo formula.

The viscosities of the pure n-alkanes were compared with available experimental data and a good agreement was

Acknowledgments

Financial support from Shell Global Solutions International BV through a contracted research agreement is gratefully acknowledged. We are thankful to the High Performance Computing Center of Texas A&M University at Qatar for generous resource allocation.

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