Quantitative evaluation of the heterogeneity for tight sand based on the nuclear magnetic resonance imaging

Tight sand exhibits high degree of heterogeneity due to the complex pore structure. It is vital to evaluate the heterogeneity since it controls the fluid storage and transportation mechanisms, as well as geophysical responses. A novel method is put forward to quantify the heterogeneity based on the magnetic resonance imaging (MRI) experiments and the variogram analysis. Images of weight transversal relaxation times of fully water saturated core samples are acquired based on the spin echo sequence, slice-selecting pulse, frequency-coding pulse and phase-coding pulse and two dimensional discrete fast Fourier transform (2D-FFT). In addition, variogram function of the first order spherical model and the genetic algorithm are implemented to characterize the heterogeneity of pore distributions along vertical and horizontal directions. Furthermore, relationships between the average heterogeneity index and the tortuosity, and the mercury withdrawal efficiency, are also investigated to reveal the physical meaning of the heterogeneity index we presented. The result shows that the average heterogeneity index is positively correlated with the tortuosity index and negatively correlated with the mercury withdrawal efficiency. Our study provides an effective way to investigate the spatial heterogeneity of pore space, which serves as an important source of information for core analysis and formation evaluation.