Mixing Rules and Correlations of NMR Relaxation Time With Viscosity, Diffusivity, and Gas/Oil Ratio of Methane/Hydrocarbon Mixtures

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Abstract
Summary: Viscosity, diffusivity, relaxation time, and gas/oil ratio are important properties in the characterization of reservoirs by nuclear magnetic resonance (NMR) well logging and in prediction of production performance. For the past few years, NMR well logging has been used to estimate formation properties and hydrocarbon liquid/ vapor characterization. Previous work has shown that pure al-kanes, alkane mixtures, viscosity standards, and stock tank crude oils have NMR relaxation times that vary linearly with viscosity/ temperature and diffusivity on a log-log scale. However, pure methane at some temperatures and pressures does not follow the same trend. Thus, the linear correlation may not be valid for live crude oils that contain a significant amount of methane. Therefore, the study of methane-hydrocarbon mixtures is of interest. An NMR spectrometer equipped with a high-pressure probe was used to study the relationship between NMR T1 relaxation time and viscosity/temperature, diffusivity, and gas/oil ratio of methane-hydrocarbon mixtures. Relaxation time and diffusivity measurements of three mixtures were made: methane-n-hexane, methane-n-decane, and methane-n-hexadecane. It was found that unlike stock tank oil, relaxation times do not depend linearly on viscosity/temperature on a log-log scale. Each of the mixtures forms a different curve. Generalized correlations between viscosity, diffusivity, gas/oil ratio, and NMR relaxation times were developed. First, the relaxation time mixing rule was developed by studying the theory of NMR relaxation mechanism. From the mixing rule, it was found that departure of relaxation times of methane-n-alkane mixtures from linear correlations on a log-log scale can be correlated with the proton fraction of methane, expressed as gas/oil ratio. Thus, correlations between relaxation time, viscosity/temperature, and gas/oil ratio were developed. Correlations between relaxation time, diffusivity, and gas/oil ratio were also developed. There is a linear relation between diffusivity and viscosity/temperature that is independent of composition. From these correlations, viscosity and gas/oil ratio can be estimated from NMR T1 relaxation time and diffusivity.