Abstract
NMR is typically used in the petroleum industry to characterize pore size and identify fluids in fully and partially saturated reservoir samples. While the NMR relaxation response can be used to estimate the permeability of the rock, it may also provide information about fluid distribution for multi-phase systems which would lead to the estimation of effective permeability of fluids at partial saturations and derivation of relative permeability to assess hydrocarbon recovery. Using a random walk method, we simulate the NMR response as function of saturation on tomographic images of Bentheimer and Berea sandstone as well as a Ferroan Dolomite samples. Fluid distributions are simulated using the capillary pressure curves of these samples via capillary drainage transform (CDT) allowing the calculations of the saturations directly on the images. The magnetic susceptibility of minerals and fluids is used to calculate the internal magnetic fields from the material distributions of solids and fluids. We show that the logarithmic mean of the NMR T2 distribution is a robust measure of permeability and results in strong correlations between NMR response and relative permeability of both fluids. The observed relative permeability from NMR in our work is in excellent agreement with relative permeability calculations on direct image based using the lattice Boltzmann method (LBM). We have also compared our NMR results for the wetting phase to published experimental results on Bentheimer and Berea sandstone samples and observed strong agreement. Using NMR numerical calculations, we demonstrate that internal gradients aid the establishment of relative permeability correlations for the non-wetting phase.
