Investigating NMR-based absolute and relative permeability models of sandstone using digital rock techniques

Absolute permeability determines fluid production capacity, and relative permeability determines the produced fluid types, and their accurate calculations are critical for evaluating hydrocarbon-bearing formations. In oil/gas fields, the nuclear magnetic resonance (NMR) logging tool has been widely used due to its unique advantage of directly detecting the rock pores. However, this tool cannot measure absolute permeability or relative permeability directly. There exist many approaches for estimating NMR-based permeabilities, but most of them lack the basic understandings of fluid flow characteristics in micro-pores. To investigate NMR-based absolute and relative permeability models of sandstone, we suggest three types of pores, i.e., non-flowing bound water pores, slowflowing free water pores, and fast-flowing free water pores, and incorporate them into the permeability calculations. The digital rock technique was utilized to study fluid flow mechanisms. Lattice Boltzmann method (LBM) was applied on two constructed three-dimensional digital rocks to calculate fluid flow velocity field distributions and absolute permeabilities. From the fluid flow simulation results, it was found that bound water exists not only in small pores but also in medium-sized pores and big pores. By comparing the permeability values of digital rocks with various porosities, we demonstrated that fast-flowing free water pores have the highest contribution to absolute permeability. Five relative permeability calculation models were investigated, where we found that the best link between the T2 spectrum and relative permeability curve was the pore size distribution index. The obtained results indicated that the traditional Coates model combined with the spectral bulk volume irreducible method and the Brooks-Corey model are high-precision models for calculating the NMR-based absolute and relative permeabilities in sandstone reservoirs.