Freed Denise E
Schlumberger Doll Research, Cambridge, Massachusetts 02139, USA.
J Phys Chem B. 2009 Apr 2;113(13):4293-302. doi: 10.1021/jp810145m.
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.
最近有研究表明（1, 2），烷烃混合物中分子的扩散系数和核磁共振（NMR）弛豫时间随分子链长和混合物平均链长遵循标度律。这些关系可用于通过扩散和弛豫测量来确定原油的链长分布。油藏通常处于高温高压环境，因此了解这些标度关系如何依赖于温度和压力很重要。在本文中，我们得到了高温高压下烷烃混合物的分子组成与其扩散系数D(i)、弛豫时间T(1i)和T(2i)之间的关系。利用自由体积理论的性质和烷烃密度的行为，我们表明，在很大的压力范围内，扩散系数和弛豫时间仅通过混合物的密度依赖于压力和平均链长。我们进一步表明，压力效应可以通过一个仅依赖于温度以及在感兴趣压力和参考压力下纯烷烃自由体积的乘性前置因子，纳入参考文献1和2的幂律中。我们还结合了D(i)、T(1i)和T(2i)的标度律以及对温度的阿伦尼乌斯依赖关系，以得到扩散系数和弛豫时间的温度依赖性。我们发现标度关系与文献数据吻合良好。这些标度关系可用于通过在高温高压下测量扩散系数或弛豫时间来确定烷烃混合物组成。
