  The diffusion/relaxation behavior of polarized spins of pore filling fluid,
as often probed by NMR relaxometry, is widely used to extract information on
the pore-geometry. Such information is further interpreted as an indicator of
the key transport property of the formation in the oil industry. As the
importance of reservoirs with complex pore geometry grows, so does the need for
deeper understanding of how these properties are inter-related. Numerical
modeling of relevant physical processes using a known pore geometry promises to
be an effective tool in such endeavor. Using a suite of numerical techniques
based on random-walk (RW) and Lattice-Boltzmann (LB) algorithms, we compare
sandstone and carbonate pore geometries in their impact on NMR and flow
properties. For NMR relaxometry, both laboratory measurement and simulation
were done on the same source to address some of the long-standing issues in its
borehole applications. Through a series of "numerical experiments" in which the
interfacial relaxation properties of the pore matrix is varied systematically,
we study the effect of a variable surface relaxivity while fully incorporating
the complexity of the pore geometry. From combined RW and LB simulations, we
also obtain diffusion-convection propagator and compare the result with
experimental and network-simulation counterparts.
