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Abstract
This thesis considers the relationship between NMR relaxation-diffusion responses and permeability for partially saturated rock samples on the basis of Xray-CT images.
The NMR relaxation response is often used in petroleum engineering applications to estimate a pore size distribution, providing a length scale for the estimation of permeability downhole, where direct measurements of permeability via well logging are not available. This application generally relies on the introduction of a constant surface relaxivity, and assumes that the dominant relaxation mechanism is surface relaxation. Extending this concept to partial saturations, e.g. rocks saturated with two immiscible fluids, this thesis analyses the relationship between relative permeability and the NMR relaxation response of the fluids saturating the pore space directly on tomographic images of the rock samples.
Segmented tomographic images of Berea and Bentheimer Sandstone and a Ferroan-Dolomite are used to calculate the permeability and relative permeability at various saturations. Here the fluid saturations are derived by simulating the drainage of these samples assuming strongly water-wet conditions. The NMR responses are calculated using a random walk method which takes account of internal gradient effects on the basis of mineralogy, which was derived by a combination of Xray-CT imaging and XRD analysis. Literature values for the susceptibility of the minerals present were used.
To test the correlations between NMR relaxation response and relative permeability for the individual fluids, we set the hydrogen index of one of the fluids to zero, allowing a numerical partition of the two fluids, while calculating the correct internal magnetic field distributions. There is excellent agreement between relative permeability predictions from NMR and lattice Boltzmann calculations for all three samples. Remarkably, this includes the relative permeability prediction for the oil phase with a zero surface relaxivity between oil and all other phases, implying that the correlation is based on internal gradient effects and saturation alone. We finally extend the analysis to NMR relaxation-diffusion responses and show that a partition of the response into the different fluids like in conventional NMR fluid typing allows the prediction of relative permeability.