Numerical simulation of multi-dimensional NMR response in tight sandstone

Conventional logging methods have limitations in the evaluation of tight sandstone reservoirs. The multi-dimensional nuclear magnetic resonance (NMR) logging method has the advantage that it can simultaneously measure transverse relaxation time (T-2), longitudinal relaxation time (T-1) and diffusion coefficient (D). In this paper, we simulate NMR measurements of tight sandstone with different wettability and saturations by the random walk method and obtain the magnetization decays of Carr-Purcell-Meiboom-Gill pulse sequences with different wait times (TW) and echo spacings (TE) under a magnetic field gradient, resulting in D-T-2-T-1 maps by the multiple echo trains joint inversion method. We also study the effects of wettability, saturation, signal-to-noise ratio (SNR) of data and restricted diffusion on the D-T-2-T-1 maps in tight sandstone. The results show that with decreasing wetting fluid saturation, the surface relaxation rate of the wetting fluid gradually increases and the restricted diffusion phenomenon becomes more and more obvious, which leads to the wetting fluid signal moving along the direction of short relaxation and the direction of the diffusion coefficient decreasing in D-T-2-T-1 maps. Meanwhile, the non-wetting fluid position in D-T-2-T-1 maps does not change with saturation variation. With decreasing SNR, the ability to identify water and oil signals based on NMR maps gradually decreases. The wetting fluid D-T-1 and D-T-2 correlations in NMR diffusion-relaxation maps of tight sandstone are obtained through expanding the wetting fluid restricted diffusion models, and are further applied to recognize the wetting fluid in simulated D-T-2 maps and D-T-1 maps.