Pore-scale modelling of NMR relaxation for the characterization of wettability

Several research groups are currently investigating the determination of wettability using NMR relaxation times. Although correlations with traditional wettability indices have been presented with some success, further effort is needed to relate the wettability at pore-scale to a core-scale measurement of NMR response. For example, a qualitative method using the arithmetic mean of relaxation times at various saturations has been presented [Guan, H., Brougham, D., Sorbie, K.S., Packer, K.J., 2002. Wettability effects in a sandstone reservoir and outcrop cores from NMR relaxation time distributions. J. Petroleum Sci. and Eng. 34, 35–54] and a wettability index that quantifies the amount of surface area that is wetted either by oil or by water, by using the T2 peak at four different saturations has been proposed [Fleury, M., Deflandre, F., 2003. Quantitative evaluation of porous media wettability using NMR relaxometry. Mag. Reson. Imaging 21, 385–387]. Our group at the Imperial College have previously shown experimentally that the T2 distribution provides valuable information about wettability and overall fluid distribution within the pore-space, which is lost if only a single value from the T2 distribution is considered [Al-Mahrooqi, S.H., Grattoni, C.A., Moss, A.K., Jing, X.D., 2003. An investigation of the effect of wettability on NMR characteristics of sandstone rock and fluid systems. J. Petroleum Sci. and Eng. 39, 389–398].In this paper we use a simple pore-scale model to understand the effect of wetting and its relationship with NMR relaxation times. The model uses triangular capillary pores with a given pore size distribution. The oil/water distribution within the pores is obtained as a function of capillary pressure and wettability. At a given capillary pressure, the volumes and surface areas of water and oil are calculated for each individual pore. This allows us to calculate the theoretical T2 distribution for that pore size distribution as a function of wettability and saturation.We have used the model to study the T2 distribution for a range of wettabilities and saturations. Results from the model confirmed previous observations from experiments regarding the effect of wettability on NMR T2 distributions. Based on these qualitative results, an improved index for characterising wettability from the T2 distribution has been proposed. We tested the proposed index using NMR T2 data from synthetic and real sandstone core plugs with different wettabilities, ranging from strongly water-wet to strongly oil-wet. Comparison between the proposed index and wettability for the synthetic samples and Amott–Harvey index for core plugs show good correlation.