Simulation of NMR responses in sandstone and restricted diffusion

Nuclear magnetic resonance (NMR) responses and restricted diffusion phenomenon of the fluids in sandstone were simulated by the Random-Walk method. Sandstone of different pore sizes was generated by changing digital cores' resolution, permitting to study how the fluid diffusion coefficient changes with time when the sandstone of different pore sizes were saturated with water, and to simulate the NMR responses of the either single or two phase fluids in the sandstone. Then the relationship between the fluid restricted diffusion coefficient and the T-2 relaxation time was researched, and the influence on restricted diffusion phenomenon of wetting phase fluid posed by the surface relaxivity and cementation index of the sandstone was analyzed. Finally the analysis results were used to interpret the D-T-2 distributions of the sandstone. It was concluded that the diffusion coefficient of fluid gradually decreases and tends to be constant with increase of diffusion time. The smaller pore size of the rock, the restricted diffusion phenomenon is more obvious, and the restricted diffusion has a greater influence on NMR responses. The position of the restricted diffusion coefficient line of wetting phase fluid is affected by the rock cementation index and surface relaxivity. The wetting phase fluid signal in the D-T-2 distributions deviates from the unrestricted diffusion coefficient line due to the decreasing diffusion coefficient of the wetting phase fluid, hence the restricted diffusion coefficient line of fluid should be used to recognize the wetting phase fluid in D-T-2 distributions.