Effects Of Internal Gradients Research Articles

Effects of internal gradients on pore-size distribution in shale

In porous media, effects of internal gradient caused by magnetic susceptibility contrast between the matrix and infilling fluid shifts transverse relaxation time (T2) to shorter time, resulting in imprecise classification of pore sizes. In shale, details of the effects of paramagnetic and clay minerals that induce the internal gradients are poorly understood. We measured a brine mixture with a granular form of minerals, including kaolinite, montmorillonite, glauconite, illite, pyrite, celadonite, and chamosite, to infer contributions of each to T2 relaxation in shale. Nuclear magnetic resonance (NMR) response of these samples was used to calculate the total mean logarithm of T2 (T2ML) and volume of water in the samples. Additionally, physical properties such as magnetic susceptibility, specific surface area, and elemental composition were acquired. Pore geometry, magnitude of internal gradients, pore-size distributions, and secular regimes in which the media relaxed (based on their shortest characteristic time scales) were characterized from these properties. These time scales measure the behavior of the relaxation regimes such as longitudinal relaxation time-to-T2 ratio and dependence of relaxation rate on echo spacing (tE). Glauconite illite, pyrite, chamosite, and kaolinite grouped into a small-pore system, whereas montmorillonite and celadonite grouped into large-pore systems. A free diffusion regime governed secular relaxation for kaolinite; a motional-averaging regime governed montmorillonite, celadonite, and large tE chamosite; whereas a localization regime dominated the rest of the minerals. We conclude that understanding the effects of internal gradients in shale is important to quantify the shortening of T2ML, which leads to overestimation of bulk fluid volume and, thus, underestimating NMR permeability when used as an input into permeability estimator equations.

Temperature-Dependent Oxygen Effect on NMR D-[Formula: see text] Relaxation-Diffusion Correlation of n-Alkanes.

Nuclear magnetic resonance (NMR) diffusion-relaxation correlation experiments (D-T_2) are widely used for the petrophysical characterisation of rocks saturated with petroleum fluids both in situ and for laboratory analyses. The encoding for both diffusion and relaxation offers increased fluid typing contrast by discriminating fluids based on their self-diffusion coefficients, while relaxation times provide information about the interaction of solid and fluid phases and associated confinement geometry (if NMR responses of pure fluids at particular temperature and pressure are known). Petrophysical interpretation of D-T_2 correlation maps is typically assisted by the “standard alkane line”—a relaxation-diffusion correlation valid for pure normal alkanes and their mixtures in the absence of restrictions to diffusing molecules and effects of internal gradients. This correlation assumes fluids are free from paramagnetic impurities. In situations where fluid samples cannot be maintained at air-free state the diffusion-relaxation response of fluids shift towards shorter relaxation times due to oxygen paramagnetic relaxation enhancement. Interpretation of such a response using the “standard alkane line” would be erroneous and is further complicated by the temperature-dependence of oxygen solubility for each component of the alkane mixture. We propose a diffusion-relaxation correlation suitable for interpretation of low-field NMR D-T_2 responses of normal alkanes and their mixtures saturating rocks over a broad temperature range, in equilibrium with atmospheric air. We review and where necessary revise existing viscosity-relaxation correlations. Findings are applied to diffusion-relaxation dependencies taking into account the temperature dependence of oxygen solubility and solvent vapour pressure. The effect is demonstrated on a partially saturated carbonate rock.

Relaxation mechanisms and shales

Unconventional petroleum resources present in shales have recently seen increased development due to growing demand for energy worldwide, declining conventional petroleum discoveries, and improved technology for production. Shale reservoirs differ from more conventional reservoirs in both matrix composition and structure, tending to be low in porosity and ultralow in permeability, making traditional laboratory characterization methods difficult to apply. The noninvasiveness of nuclear magnetic resonance (NMR) makes it a favored technique for shale analysis. However, interpretation of NMR relaxometry results for shales is more complex than in traditional reservoirs. Surface relaxivity in conventional reservoirs is predominantly caused by the interaction of fluid molecules with paramagnetic impurities on pore surfaces. However, in shales, small pore sizes coupled with the presence of hydrogen‐rich organic matter can result in more interactions. This article discusses different relaxation mechanisms that may be present in shales and situations where they are relevant. Surface relaxation in organic matter is likely caused by homonuclear dipolar coupling, not paramagnetic impurities, and as such, will have a significant temperature dependence. Due to the small pore sizes in shales, the effect of internal gradients on the signal appears negligible in almost all situations. Analysis of transverse relaxation resulting from organic solids by an inverse Laplace transform may lead to results that are anomalously short and overcall signal intensity. Diffusional coupling between the shale pores confounds interpretation of the NMR response as a pore size distribution. There also appears to be rapid exchange of magnetization between mobile and immobile phases in the samples. © 2014 Wiley Periodicals, Inc. Concepts Magn Reson Part A 43A: 57–78, 2014.

Effect of internal gradients in the nuclear magnetic resonance measurement of the surface-to-volume ratio.

We consider a system of spins diffusing in a static inhomogeneous (nonuniform-gradient) magnetic field B in a restricted geometry and in the presence of surface relaxation. We show that the short-time diffusional decay of nuclear magnetization is controlled by the field scattering kernel F(t) identical with [B(t)-B(0)](2), which is a measure of the average field inhomogeneity sampled by the spins in time t and does not depend on the particular sequence of radio-frequency pulses used. Magnetization in arbitrary sequences can be straightforwardly computed by evaluating elementary integrals of F(t). Diffusion takes place while the field is on, so that the spins precess as they diffuse, in contrast to the simpler problem of purely classical diffusion considered in [P. P. Mitra, P. N. Sen, and L. M. Schwartz, Phys. Rev. B 47, 8565 (1993)] which is applicable only to the ideal pulsed-field gradient experiment. We compute the short-time asymptotic form of F(t) and find that it depends on the surface-to-volume ratio (S/V) of the pore space as well as on the average of the gradients over the bounding surface. In a system with nonuniform gradients that vary faster near the surface than in the bulk, as for internal susceptibility fields, this gradient surface average may be much larger than the gradients in the bulk, significantly enhancing the apparent S/V. We discuss the application of our results to the widely used Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence as well as proposing a modification of it, which we term "padded" CPMG, that may be preferable in systems with significant surface relaxation. We indicate how each sequence can be used to probe the internal fields.