Random Walk simulation of Nuclear Magnetic Resonance for characterization of reservoir rocks using micro-CT data

Resumo

Random walk algorithms have been used to simulate nuclear magnetic resonance (NMR) transverse
relaxation (T2) decay in porous media since the early 1990’s. Since the time of their first implementation, they
have been primarily based on geometric models of pores and grains such as the grain consolidation model. These
models have been useful for examining mismatches between the actual T2 distributions and the pore size

distributions from mercury injection capillary pressure (MICP) and those from X-ray microtomography (micro-
CT) images. Noticeable success has been achieved, particularly in complex carbonate rock samples where the T2

distributions may represent an average pore size between the macro-pores and the micro-pores due to diffusive
coupling. In typical random walk simulations, the position of the walker is calculated geometrically in terms of
the radius of the macro-pore to determine if it has arrived at the grain surface. This approach is useful for
geometric models with Euclidean geometry pores. Currently, micro-CT images would require an intermediate
step, where the image is converted and approximated to Euclidean geometries such as spheres and prisms to
represent the macro-porosity. An alternative approach would be to construct a binary cube for 3D simulations (or
square for 2D). In this approach, the position of the walkers is linked to the binary cube index where 0 would
represent macro- pores and 1 would represent the micro-porous grains. Comparison between the results of these
two approaches shows similar computational times and the indexed method is more suitable for binary images
from micro-CT.