Temperature and Pressure Dependence of the Diffusion Coefficients and NMR Relaxation Times of Mixtures of Alkanes

Abstract

Recently, it was shown (1, 2) that the diffusion coefficient and nuclear magnetic resonance (NMR) relaxation times of a molecule in a mixture of alkanes follow scaling laws in the chain length of the molecule and the mean chain length of the mixture. These relations can be used to determine the chain length distribution of crude oils from diffusion and relaxation measurements. Oil reservoirs are usually at elevated temperatures and pressures, so it is important to know how these scaling relations depend on temperature and pressure. In this paper, we obtain the relation between the molecular composition of mixtures of alkanes at elevated pressures and temperatures and their diffusion coefficients D(i) and relaxation times T(1i) and T(2i). Using properties of free volume theory and the behavior of the density of alkanes, we show that, for a large range of pressures, the diffusion coefficients and relaxation times depend on pressure and mean chain length of the mixture only through its density. We further show that the pressure effect can be taken into account in the power laws of refs 1 and 2 by a multiplicative prefactor that depends only on temperature and the free volumes of pure alkanes at the pressure of interest and a reference pressure. We also combine the scaling laws for D(i), T(1i), and T(2i) and the Arrhenius dependence on temperature to obtain the temperature dependence of the diffusion coefficients and relaxation times. We obtain good fits between the scaling relations and literature data. These scaling relations can be used to determine the composition of a mixture of alkanes from measurements of diffusion coefficients or relaxation times at elevated pressures and temperatures.

Rotational relaxation times of individual compounds within simulations of molecular asphalt models

“…The results are of more broad interest in terms of how relaxations of different molecules in a mixture respond to changes in temperature. Similar questions motivated by petroleum-derived systems were pursued by Freed, [4][5][6] who investigated how the diffusion coefficients of n-alkanes in an n-alkane mixture depend on the distribution of chain lengths found in the mixture. Decoupling between translation and rotation was described by Lombardo et al 7 in a single-component glass-forming system.…”

Temperature-Dependent Oxygen Effect on NMR D-$$T_2$$ Relaxation-Diffusion Correlation of n-Alkanes

“…The correlation of fluids’ viscosity to diffusion coefficients is relatively straightforward and can be described either with Stokes-Einstein or Bloembergen’s approach [20], while the connection between NMR relaxation time and diffusion may be less obvious. A number of comprehensive discussions have been published, e.g., see Lo et al [3], Winkler et al  [15], Chen et al [21] and Freed [18]. We tested some of these correlations experimentally and present the results below.…”

“…However, in later years Mutina and Hürlimann [16] and Benamsili et al [17] attributed that effect rather to high-molecular components of crudes (specifically asphaltenes). Freed [18] introduced scaling law of diffusion and relaxation for alkanes mixtures at elevated pressures and temperatures (in oxygen free state).…”

Fluorine tracers for the identification of molecular interaction with porous asphaltene aggregates in crude oil

“…on the composition of the crude oil. A detailed investigation of the dependence of 1 H relaxation and diffusion properties on molecular sizes has been discussed for linear alkanes [4,5]. In the more complicated situation of most crude oils, with many thousands of components, two-dimensional techniques that correlate two of the mentioned three parameters were employed as a means to assess oil composition [6].…”