Effect of Internal Magnetic-Field Gradients on Nuclear-Magnetic-Resonance Measurements and Nuclear-Magnetic-Resonance-Based Pore-Network Characterization

Abstract

Summary Nuclear-magnetic-resonance (NMR) measurements have been extensively used for determining porosity, pore-size distribution, and fluid saturation in porous media. However, internal gradients of the magnetic field generated by the presence of paramagnetic or diamagnetic centers such as shale or clay particles can significantly affect NMR response. Consequently, the resulting interpretation for pore-size distribution and porosity is also affected. In this paper, we quantify the effect of internal magnetic-field gradients and spatial distribution of matrix components such as clay minerals on NMR response using pore-scale NMR numerical simulations. We also quantify the influence of the aforementioned parameters on the NMR-based evaluation of porous media. We used the finite-volume method to numerically solve the Bloch (1946) equations and simulated magnetization decay in porous media. We cross validated the reliability of numerical simulations using analytical solutions given for spherical pores in different diffusion regimes. The model was then used for simulation of NMR response in the pore-scale images of sandstone and carbonate rocks. We used Larmor frequency of 2 MHz, external magnetic-field gradient of 0.10 T/m, and half-echo spacing time of 0.5 ms for simulating NMR response in pore-scale images of sandstones and carbonates. We then developed synthetic cases using actual rock images covering a wide range of spatial distribution of clay minerals (i.e., paramagnetic centers) to quantify the sensitivity of NMR decay to internal magnetic-field gradients. We quantified the sensitivity of NMR response for distribution of clays as thin laminae in the rock and as thin layers on the surface of the grains. The results showed that at low concentration (0.3 to 0.7%) of dispersed clay, there is a negligible effect of internal magnetic-field gradients on magnetization decay. At higher concentration of dispersed clay (5.1 to 7.3%), we observed a significant effect of internal magnetic-field gradients on magnetization decay. The presence of shale minerals can cause 53% variation in the location of the transverse-relaxation-time constant (T2) and up to 67% relative error in the assessment of dominant pore sizes. Shale laminations containing clay were found to produce an effect of up to 31.8% on T2 relaxation-time constant, which could cause a relative error of 50.0% in estimates of dominant pore size in the rock. The outcomes of this paper demonstrated the effect of heterogeneous rock mineralogy on NMR response. The effect of internal magnetic-field gradients generated by shale and clay on NMR becomes relevant when shale and clay particles are close to the pore fluid and their magnetic field starts to affect the distribution of magnetic field in the pore space. The results reveal the importance of characterizing the distribution of shale and clay minerals before interpreting NMR response and can potentially improve conventional techniques of pore-network characterization (pore-size distribution and pore volume) in the presence of clay minerals where internal magnetic-field gradients are not negligible.