Emmanuel Toumelin

Comparison of NMR simulations of porous media derived from analytical and voxelized representations

We develop and compare two formulations of the random-walk method, grain-based and voxel-based, to simulate the nuclear-magnetic-resonance (NMR) response of fluids contained in various models of porous media. The grain-based approach uses a spherical grain pack as input, where the solid surface is analytically defined without an approximation. In the voxel-based approach, the input is a computer-tomography or computer-generated image of reconstructed porous media. Implementation of the two approaches is largely the same, except for the representation of porous media. For comparison, both approaches are applied to various analytical and digitized models of porous media: isolated spherical pore, simple cubic packing of spheres, and random packings of monodisperse and polydisperse spheres. We find that spin magnetization decays much faster in the digitized models than in their analytical counterparts. The difference in decay rate relates to the overestimation of surface area due to the discretization of the sample; it cannot be eliminated even if the voxel size decreases. However, once considering the effect of surface-area increase in the simulation of surface relaxation, good quantitative agreement is found between the two approaches. Different grain or pore shapes entail different rates of increase of surface area, whereupon we emphasize that the value of the surface-area-corrected coefficient may not be universal. Using an example of X-ray-CT image of Fontainebleau rock sample, we show that voxel size has a significant effect on the calculated surface area and, therefore, on the numerically simulated magnetization response.

Limits of 2D NMR Interpretation Techniques to Quantify Pore Size, Wettability, and Fluid Type: A Numerical Sensitivity Study

Two-dimensional (2D) NMR techniques have been proposed as efficient methods to infer a variety of petrophysical parameters, including mixed fluid saturation, in-situ oil viscosity, wettability, and pore structure. However, no study has been presented to quantify the petrophysical limitations of such methods. We address this problem by introducing a pore-scale framework to accurately simulate suites of NMR measurements acquired in complex rock/ fluid models. The general pore-scale framework considered in this paper is based on NMR random walks for multiphase fluid diffusion and relaxations, combined with Kovscek’s pore-scale model for two-phase fluid saturation and wettability alteration. We use standard 2D NMR methods to interpret synthetic data sets for diverse petrophysical configurations, including two-phase saturations with different oil grades, mixed wettability, or carbonate pore heterogeneity. Results from our study indicate that for both water-wet and mixed-wet rocks, T2 (transverse relaxation)/D (diffusion) maps are reliable for fluid typing without the need for independently determined cutoffs. However, significant uncertainty exists in the estimation of fluid type, wettability, and pore structure with 2D NMR methods in cases of mixed-wettability states. Only light oil wettability can be reliably detected with 2D NMR interpretation methods. Diffusion coupling in carbonate rocks introduces additional problems that cannot be circumvented with current 2D NMR techniques.

Improving Petrophysical Interpretation With Wide-Band Electromagnetic Measurements

Because of their sensitivity to ionic content and surface texture, wide-band electromagnetic (WBEM) measurements of saturated rocks exhibit frequency dispersions of electrical conductivity and dielectric constant that are influenced by a variety of petrophysical properties. Factors as diverse as fluid saturation, porosity, pore morphology, thin wetting films, and electrically charged clays affect the WBEM response of rocks. Traditional dielectric mixing laws fail to quantitatively and practically integrate these factors to quantify petrophysical information from WBEM measurements. This paper advances a numerical proof of concept for useful petrophysical WBEM measurements. A comprehensive pore-scale numerical framework is introduced that incorporates explicit geometrical distributions of grains, fluids and clays constructed from core pictures, and that reproduces the WBEM saturated-rock response on the entire kHz-GHz frequency range. WBEM measurements are verified to be primarily sensitive (a) in the kHz range to clay amounts and wettability; (b) in the MHz range to pore morphology (i.e., connectivity and eccentricity), fluid distribution, salinity, and clay presence; and (c) in the GHz range to porosity, pore morphology and fluid saturation. Our simulations emphasize the need to measure dielectric dispersion in the entire frequency spectrum to capture the complexity of the different polarization effects. In particular, it is crucial to accurately quantify the phenomena occurring in the MHz range where pore connectivity effects are confounded with clay polarization and pore/grain shape effects usually considered in dielectric phenomena. These different sensitivities suggest a strong complementarity between WBEM and NMR measurements for improved assessments of pore-size distribution, hydraulic permeability, wettability, and fluid saturation.