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We develop a numerical algorithm to simulate nuclear magnetic resonance (NMR) measurements in the presence of constant magnetic field gradients. The algorithm is based on Monte Carlo conditional random walks in restricted and unrestricted space. Simulations can be performed of 3D porous media that include both arbitrary bimodal pore distributions and multiphase fluid saturations. The ability to account for the presence of a constant external magnetic field gradient allows us to replicate actual well-logging conditions that include the effect of Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences at a microscopic level. This is accomplished by simulating ideal pulse-acquisition techniques that include multiple interecho times (TE) similar to those currently used by the well-logging industry. Benchmark examples are presented to validate the accuracy and internal consistency of our algorithm against previously published results for the case of a null magnetic field gradient. Validation examples also are presented against actual NMR measurements performed on core samples of carbonate rock formations.Interpretation work is focused on the petrophysical assessment of both partial oil/water saturations and pore structures exhibiting diffusive coupling. Simulation examples are designed to quantify whether the inclusion of diffusion under a magnetic field gradient can improve the interpretation of multiphase fluid saturations when diffusion coupling is significant. The simulation algorithm sheds light on new NMR data-acquisition strategies that could be used to improve the detection and quantification of fluid types, complex fluid saturations, and complex pore geometries.

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, T 2 (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.In this equation, ␥ is the proton gyromagnetic ratio, G is the average magnitude of the background magnetic field gradient over the spatial zone of investigation, and TE the interecho time or the interval between two radio-frequency pulses.Limits of the Relaxation Model. The model described previously assumes that the protons relax within one pore independently from the surrounding pores. When the bulk and diffusion terms in the

Archie’s empirical power laws are strictly valid only for homogeneous, water-wet (WW) rocks deprived of microporosity or substantial clay-exchange cations. When these conditions are not met, non-Archie electrical behavior arises whereby relationships among rock resistivity, porosity, and water saturation no longer exhibit power-law dependence. Currently, such an unreliable behavior of empirical laws can be quantified only through pore-scale modeling of electrical conductivity under specific sets of geometric assumptions and with substantial computation memory requirements. We introduce a new geometric concept to simulate direct-current electrical-conductivity phenomena in arbitrary rock models on the basis of 3D grain and pore objects that include explicit distributions of intragranular porosity, clay-exchange cations, nonwetting fluid blobs, thin films, and pendular rings. These objects are distributed in the pore space following simple heuristic principles of drainage/imbibition that honorcapillary-pressure curves. They provide a simple way to parameterize the 3D pore space and to calculate the electrical conductivity of porous media saturated with two immiscible fluid phases by way of diffusive random walks within the brine-filled pore space. Not only is the random-walk method memory efficient but it also allows the inclusion of clay/brine cation exchange surfaces otherwise not possible with conventional pore-network models. By comparing results stemming from random-walk, pore-network, and percolation simulations, we show the importance of grain surface roughness and thin film thickness, even in water-wet rocks where those factors usually are neglected. For the case of strongly oil-wet rocks, we show that thin films, snap-offs, and pore microgeometry have a primary impact on hysteresis-dominated rock resistivity during imbibition (increasing water saturation). Our simulation method agrees well overall with percolation simulation results and is advantageously unaffected by assumptions concerning site-percolation imbibition.