Pore-scale network modelling of flow propagators derived from pulsed magnetic field gradient spin echo NMR measurements in porous media

Pulsed magnetic field gradient spin echo (PGSE) NMR experiments carried out on porous media where fluid flow is occurring, may be analyzed to give the propagator, P(ξ,t), This quantity is the ensemble density distribution of particle (nuclei) displacements in a chosen direction, ξ, in a given time interval, t. These displacements arise as a result of both the convection and diffusion of molecules in the flowing fluid. The propagator can be derived for various displacement times, t, and hence these gradually probe a wider domain of the pore-scale velocity field within the porous medium. Such measurements can be performed separately on the oil and water phases in a two-phase flowing system. The interpretation and modelling of these single- and two-phase propagators in terms of the pore-scale flow field within the porous medium presents a difficult and interesting scientific challenge. In this paper, we model the main qualitative features of the experimentally measured propagators for both single- and two-phase flow using connected 3D pore network models of porous media. The calculated flow field within such models shows some non-trivial and qualitatively correct predictions about real flow fields in porous media. The propagator is modelled directly by incorporating transport due to both convection and diffusion for large numbers of marker particles (the nuclei) for both single- and two-phase flow. In the latter case, the transport within each of the two immiscible phases (oil and water) has been modelled in their separate pore occupancy networks. The network model captures most of the qualitative features for both single- and two-phase propagators thus giving us the capability to clearly interpret the respective flowing and non-flowing fractions of the oil (non-wetting) and water (wetting) phases in two-phase experiments. Therefore, our findings offer a powerful approach - PGSE NMR experiments and associated pore-scale modelling - for understanding and characterizing two-phase flow through porous media.