Restricted Diffusion Effects in Saturation Estimates from 2D Diffusion-Relaxation NMR Maps

Abstract

A new model is proposed for interpreting two-dimensional diffusion-relaxation nuclear magnetic resonance (2D NMR) maps by including the effects of restriction on the diffusion of water in a connected porous medium. The model's theoretical underpinnings are reviewed and a correlation derived between the diffusion and relaxation of restricted water molecules, i.e., the expected 'water line' where the water signal should appear on 2D NMR maps. The main application discussed in this paper is to improve the quantitative separation of different fluids in the formation, leading to better prediction of water and hydrocarbon saturations. In many carbonate formations, the effects of restriction may be quite pronounced making the standard fluid characterization with diffusion-relaxation maps questionable. The restricted-diffusion model is applied to laboratory measurements on carbonate core plugs and to an example log from a Middle East carbonate well where the saturations obtained with the new model are compared against other measures of saturation available in the dataset.

Robust determination of surface relaxivity from nuclear magnetic resonance DT2 measurements

“…In particular, their use of fixed L T (L M in their model), the length scale characterizing the transition from the short-time behavior to the long-time behavior of the restricted diffusion, for heterogeneous materials is supported by the observation that it enables reasonable fits to the data. However, this is inconsistent with experimental observations targeting this question [23] which shows that L T ( 0 D  in Latour et al paper) scales with the pore size and is generally a fraction of the pore size [23], rather than the "heterogeneity length scale of the media" [25] which is usually much larger. Because the extracted surface relaxivity depends sensitively on L T when fitting the signal model, it is critical to use the correct L T for a robust surface relaxivity determination.…”

“…To construct a restricted diffusion model that covers all diffusion observation times, a Padé approximation is used to connect the expressions for the short and long diffusion observation times [23,25,28]. [21,23] and that in general it scales with the pore size [23].…”

“…Otherwise, Eq. 8 reverts to the signal model employed by Zielinski et al [25] (where the two 22 s kT  terms in Eq. 8 are replaced by L T ), and in the limit of large pores ( approaches infinity), Eq.…”

“…Recently, an improved in situ NMR approach based on the two-dimensional (2D) NMR DT 2 measurement was proposed by Zielinski et al [25,26] to extract surface relaxivity and estimate saturation. The diffusion dimension on the DT 2 map is utilized to extract the local surface-to-volume ratio for different pore sizes whereas the different pore sizes are distinguished by their T 2 relaxation times.…”

The Observation of Residual Oil Evolution During Waterflooding Using NMR D–T 2 Maps

“…With this technique, NMR results can be displayed as a two-dimensional map known as a Diffusion-T 2 map. The diffusion differences between oil and water enable the separation of the oil and water signals without using replacing fluids [10][11][12].…”