Pore-scale petrophysical models for the simulation and combined interpretation of nuclear magnetic resonance and wide-band electromagnetic measurements of saturated rocks
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The interpretation of well logs in terms of hydraulic permeability, irreducible and free fluid saturations, hydrocarbon grades, and wettability is currently approached with oversimplified models of electrical resistivity and nuclear magnetic resonance (NMR). Inconsistent interpretations arise in the presence of clay, complex rock morphologies, and mixed wettabilities. Wide-band electromagnetic (WBEM) measurements in the kHz-GHz range are sensitive to all these petrophysical attributes but cannot be interpreted in an independent fashion. New interpretation methods are necessary that can effectively combine the resolving capabilities of NMR and WBEM measurements performed under complex petrophysical conditions. This dissertation develops numerical models to simulate NMR and WBEM measurements in saturated rocks using explicit pore-scale spatial distributions of grains and saturating fluids. The purpose of such models is three-fold: (1) to describe the fundamental properties of NMR and electromagnetic measurements using pore-scale physics; (2) to benchmark the accuracy and reliability of standard macroscopic models used for the interpretation of NMR and WBEM measurements; and (3) to show the complementary nature of NMR and WBEM measurements for the petrophysical evaluation of complex petrophysical conditions. Two geometrical models are developed to simulate electrical conductivity, NMR, and WBEM measurements in saturated rocks. The first model consists of continuous 3-dimensional dense packs of grains. Immiscible fluids are distributed in the ensuing pore-space with adherence to capillary and saturation history. Random walkers diffusing throughout these pore geometries accurately reproduce DC conductivity and NMR magnetization decay as functions of porosity, rock morphology, saturation history, fluid types, wettability, rock surface relaxation, and NMR pulse sequences. The second model is constructed with 2-dimensional digital pore maps, where pixels are assigned contrasting electrical properties for grain, clay and fluids. KHz-GHz dispersions of effective conductivity and dielectric permittivity are computed for each pore map. These wide-band dispersions exhibit measurable sensitivity to brine salinity, grain/pore eccentricity, fluid saturation, and wettability. The 3D model accurately reproduces resistivity index hystereses in mixed-oil wet rocks and incorporates the combined effects of saturation history, microporosity and clay-exchange cations on rock conductivity. In the case of NMR measurements, unaccounted saturation history leads to erroneous petrophysical interpretations in addition to known adverse effects due to grain morphology and paramagnetic clays. Rock morphologies and fluid configurations where NMR measurements do not lend themselves to accurate petrophysical interpretation are shown to exhibit characteristic dielectric dispersions. This result suggests a practical procedure to quantitatively integrate both NMR and WBEM techniques to improve the assessment of permeability, wettability, and fluid content.