Nuclear Magnetic Resonance Surface Relaxivity Research Articles

Determination of nuclear magnetic resonance surface relaxivity for the macropore system from wood cell lumen

To determine the surface relaxivity of pores plays a vital role in the application of time-domain nuclear magnetic resonance (TD-NMR) technology to porous structure characterization for wood. Currently, the surface relaxivity of pores is calibrated using a standard sample with a pore size of the same order as the wood pore system. However, the uniformly distributed pore size of standard sample is unfit to accurately indicate the complexity of porous structure of wood, which significantly affects the accuracy of test results. By integrating the TD-NMR technology with mercury intrusion porosimetry (MIP), the surface relaxivity of macropores in the lumen of wood cells is calibrated in this study using the tested sample, so as to avoid the error in measurement as caused by existing method. Data processing is performed using several mathematical methods including interpolation arithmetic and least square principle. Notably, the node segmentation method is applied to identify the T2 boundary of pores in cell lumen and to classify the porous structure of cell lumen into different pore systems. The approach proposed in this study is demonstrated to be effective in improving the accuracy of TD-NMR technology for characterizing the porous structure of wood. Also, it contributes a potential solution to accounting for the porous structure of wood based on the phenomenon of pore relaxation, which can improve the understanding of wood pore conformation.

Objective-Driven Solid-Surface-Roughness Characterization for Enhanced Nuclear-Magnetic-Resonance Petrophysics

Summary Typically, smooth solid surfaces of reservoir rocks are assumed in formation evaluation, such as nuclear-magnetic-resonance (NMR) petrophysics and reservoir-wettability characterization through contact-angle measurements. Measuring the degree of surface roughness (R), or smoothness, and evaluating its effects on formation evaluation are topics of much research. In this paper, we primarily focus on details in characterizing solid-surface roughness and its applications in NMR pore-size analysis. R can be measured by contact techniques and noncontact techniques, such as stylus profilometer, atomic-force microscopy, and different kinds of optical measurements. Each technique has different sensitivities, measurement artifacts, resolutions, and field of view (FOV). Intuitively, although a finer resolution measurement provides the closest account of all surface details, the correspondingly small FOV might compromise the representativeness of the measurement, which is particularly challenging for charactering heterogeneous samples such as carbonates. To balance the FOV and measurement representativeness, and to minimize artifacts, laser scanner confocal microscopy (LSCM) is selected in this study. Results for the more than 27 rock samples tested indicate that rocks of similar rock types have similar R-values. Grainy limestones have relatively higher R-values compared with dolostones, consistent with the dolostone’s crystallization surface features. Muddy limestones have smoother surfaces, resulting in the lowest R-values among the rocks studied. For sandstones, R varies with clay types and content. For rocks containing two distinct minerals, two R-values are observed from the R profiles, which for these rock types justifies the use of two NMR surface relaxivity (ρ2) parameters for determining the pore-size distribution (PSD) from the NMR T2 distribution. The novelty here is the integration of LSCM and NMR to obtain an NMR PSD relevant for permeability, capillary pressure, and other petrophysical parameters. Typically, ρ2 is calibrated using the total surface area from Brunauer-Emmett-Teller (BET; Brunauer et al. 1938) gas adsorption, but this underestimates the NMR pore size because of surface-roughness effects. In our novel approach, we use R measured from LSCM to correct ρ2 for surface-roughness effects, and thereby obtain the NMR pore size more relevant for permeability and other petrophysical parameters. We then compare the roughness-corrected NMR PSD against pore size from microcomputed tomography (micro-CT) scanning (which is roughness independent). The good agreement between roughness-corrected NMR and micro-CT pore sizes in the micropore region validates our new technique, and highlights the importance of surface-roughness characterization in NMR petrophysics.

Estimating the nuclear magnetic resonance surface relaxivity of Eocene sandstones: A comparison of different approaches

Nuclear magnetic resonance (NMR) relaxometry typically involves the analysis of a relaxation time distribution. The surface relaxivity ([Formula: see text]) is the key parameter that relates the relaxation time to the pore radius. Only a good estimate of the surface relaxivity enables a reliable determination of the pore radius distribution in a rock or sediment sample. A wide variety of approaches for the estimation of [Formula: see text] has been proposed; however, the accuracy of [Formula: see text] determination approaches has rarely been checked. We have compared different approaches of [Formula: see text] determination for a set of Eocene sandstone samples. Most approaches based on a weighted logarithmic mean of relaxation times or the peak relaxation time result in significant underestimation of [Formula: see text]. However, the correct weighting of the set of relaxation times has proven to be a crucial approach in [Formula: see text] determination. The consequent application of geometric rules suggests the application of the weighted harmonic mean ([Formula: see text]). The specific surface area per unit pore volume ([Formula: see text]), which results from the gas adsorption method, is another crucial parameter in most approaches for [Formula: see text] estimation. The quantities [Formula: see text] and [Formula: see text] depend on the resolution of the used method. Applying the fractal theory, we adopt an approach that performs an upscaling of [Formula: see text] to the resolution of the NMR relaxometry. Using equal resolution for [Formula: see text] and [Formula: see text], we obtain more reliable [Formula: see text] estimates. The resulting [Formula: see text] values are comparable with the ones determined by using the median relaxation time from NMR and the median pore-throat radius from the mercury injection capillary pressure method.

Effect of paramagnetic mineral content and distribution on nuclear magnetic resonance surface relaxivity in organic-rich Niobrara and Haynesville shales

Surface relaxivity is required to convert nuclear magnetic resonance (NMR) relaxation times to pore size distributions (PSD). In current practice, a constant value of surface relaxivity is used for an entire well, formation, or rock type, regardless of compositional and textural variations. The presence and distribution of paramagnetic minerals can affect surface relaxivity and, in turn, result in significant errors in PSD calculations. We present surface relaxivity calculations for two organic-rich formations, namely the Niobrara and the Haynesville formations. Surface relaxivity was calculated from surface to volume ratio and comparison of average pore radius measurements. We measured the transverse (T2) relaxation time with a low field (2 MHz) NMR instrument, porosity and PSD using nitrogen adsorption (N2) data, total specific surface area from N2 data and from cation exchange capacity (CEC), and mineralogy from X-ray diffraction (XRD). We find that surface relaxivity is linearly correlated with paramagnetic clay content, specifically chlorite and illite-smectite distributed in the matrix. The presence of smectite clay minerals increases uncertainty in surface to volume ratio and consequently in surface relaxivity calculations. Our surface relaxivity – clay correlations could be applied for surface relaxivity calculations from mineralogy and to invert NMR logs and laboratory data to PSD.

Nuclear magnetic resonance surface relaxivity and its advanced application in calculating pore size distributions

Abstract Both laboratory and downhole nuclear magnetic resonance (NMR) measurements are commonly used to calculate the pore size distribution (PSD) that is important in determining the reservoir storage capacity and evaluating producibility, etc. The surface relaxivity is a key parameter to calculate the PSD using NMR transversal relaxation time (T2) distributions. Accurate surface relaxivity value would result in a reasonable PSD. In order to comprehensively study surface relaxivity, the conventional sandstone, tight sandstone, and shale samples are selected to perform experiments including porosity, permeability, NMR, mercury injection capillary pressure (MICP) and low temperature nitrogen adsorption (LTNA), etc. Three approaches, including LTNA, MICP, and Kozeny's equation, are used to determine the surface relaxivity. We find that for all samples, the surface relaxivity determined with Kozeny's equation is greater than that using LTNA and MICP data, indicating that surface relaxivity of smaller pores is less than that of bigger pores. It is also observed that the surface relaxivity of conventional sandstone is greater than that of tight sandstone and shales. The surface relaxivity of sandstone and shale samples are both affected by clay content. For shale samples, the surface relaxivity ranges from 3.41 μm/s to 9.79 μm/s and is influenced by organic matter contents as well. An equation for predicting surface relaxivity of shale is established. Finally, we propose an advanced method for calculating reasonable PSDs of sandstone and shale formation by the combination of two surface relaxivities, which could be applied to laboratory and field wells.

Nuclear magnetic resonance surface relaxivity of coals

Nuclear magnetic resonance (NMR) transverse relaxation time (T2) measurements of fully water-saturated rock samples can provide a reference for pore size distribution (PSD). Commonly, surface relaxivity of the rock must be known before obtaining an absolute PSD sample using NMR data. There are many reports concerning the surface relaxivity of sandstones, shales, and carbonate rocks, however, little research has been performed on the surface relaxivity of coals, which limit the application of the NMR in PSD evaluation of coals. To obtain a standard surface relaxivity for PSD measurements of coals, we performed NMR, low-temperature N2 adsorption (LTNA), and mercury intrusion porosimetry (MIP) measurements for 15 bituminous and anthracite coals, whose Ro range from 0.52% to 3.07%. The results show that the values of surface relaxivity from LTNA (ρ2-SVR) are inconsistent with those from MIP (ρ2-MIP) for all samples. Moreover, the applications of ρ2-SVR and ρ2-MIP for PSD conversions are valid only for the smaller pores and larger pores, respectively. Evidently, both these two surface relaxivities cannot be used individually to calculate full-scale PSD. To obtain the actual surface relaxivity (ρ2) for full-scale PSD, we rebuilt a full-scale PSD by combining the pores smaller than 25 nm from LTNA and the pores larger than 25 nm from MIP. The results indicate that the calculated ρ2 provides excellent function for PSD transformation for all coal samples. Finally, the references of ρ2 for different coals are provided, i.e., values of 2.1 μm/s for sub-bituminous coal (low-rank coal), 3.0 μm/s for bituminous coal (medium-rank coal) and 1.6 μm/s for anthracite coal (high-rank coal). Using these referential surface relaxivities, a T2 distribution from NMR measurement can be converted to a PSD, which is applicable not only in the laboratory but also in field applications such as well logging.

Nuclear magnetic resonance surface relaxation mechanisms of kerogen

Nuclear magnetic resonance (NMR) relaxometry is an excellent tool for probing the interactions between solid pore surface and pore fluids in porous media. Surface relaxation is a key component of NMR relaxation. It is well-known that in conventional rocks, paramagnetic centers contribute most to the surface relaxation phenomenon. However, the interactions between organic pore surfaces and pore fluids, and the mechanism of surface relaxation in organic shale pores, are not well-understood. We tackle the issue using deuterated compounds to adjust the proton density in the liquid phase and monitoring the transverse relaxation rate changes of kerogen-fluid mixtures. With the Barnett and Eagle Ford kerogen isolates, we found that for alkanes, it is intramolecular dipolar coupling that dominates among the magnetic interactions. As a result, the transverse relaxation rate of alkane proton spins is more likely to be dependent on the concentration of active adsorption sites on the kerogen surface, rather than the kerogen proton density. For water inside organic pores, surface relaxation most likely originates from hydrogen bonding and intermolecular dipolar coupling. We also examined the temperature effect on kerogen surface relaxation and found temperature-dependent behavior that is consistent with surface relaxation by hydrogen bonding and homonuclear dipolar coupling interactions.

Low field NMR surface relaxivity studies of chalk and argillaceous sandstones

This paper addresses how the surface relaxivity, ρ, of rock forming minerals as assesed from low field Nuclear Magnetic Resonance (NMR) spectrometry, is affected by temperature and Larmor frequency. This is relevant for connecting laboratory data and reservoir logging data while increasing the accuracy of predictions of petrophysical properties of various rocks with the use of NMR spectrometry. We perform laboratory transverse relaxation (T2) measurements on water saturated Gorm field chalk, Stevns Klint chalk, Solsort field greensand and Berea sandstone. These rocks are of particular interest in studies related to the North Sea oil and gas reservoirs, since they cover a wide range of formations, ranging from homogeneous to inhomogeneous chalk, chloritic and quartz mineralogy. Comparison of T2 distributions at Lamor frequency of 2 and 20 MHz at 40 °C shows that paramagnetic minerals in the Gorm field chalk and Solsort field greensand have higher ρ at higher Larmor frequency. By contrast, ρ of the purely calcitic Stevns chalk and quartzitic Berea sandstone proved not to be affected by the changes in frequency. T2 distributions at temperatures ranging from 10 °C to 60 °C provided comparison between lab and field T2 measurements: ρ for calcite decreases with temperature; whereas ρ for quartz increases with temperature. These findings illustrate differences in the porosity and pore size distribution obtained in the lab, compared to those from logs using NMR tools.

Effect of mineralogy on nuclear magnetic resonance surface relaxivity: A case study of Middle Bakken and Three Forks formations

Porosity and pore size distribution (PSD) are crucial for reserve and producibility estimation and production planning. PSD properties are evaluated in the subsurface from nuclear magnetic resonance (NMR) logs and require knowledge about surface relaxivity. In common industry practice, a constant surface relaxivity value is used for a well, formation or rock type, regardless of mineralogical and textural variation. We present a case study of the Middle Bakken and Three Forks formations to evaluate surface relaxivity using porosity, PSD and total specific surface area data. To avoid error propagation from the input parameters to surface relaxivity estimates, we first acquired reliable porosity and PSD by combining different techniques. We analyzed the data using information on mineralogy, mass magnetic susceptibility (MMS) and scanning electron microscopy. We find that:(a)Surface relaxivity (ρ [μm/s]) depends on paramagnetic mineral content, magnetic susceptibility and distribution in natural rocks.(b)The linear correlation between surface relaxivity and illite content (ρ=0.067×fil+0.56) has a goodness of fit R2=0.79; where fil is wt% of illite.(c)This linear correlation only holds if the illite is distributed in the matrix.(d)Clay bound water cut off times lie between 2.13–2.23ms for T1 and 1.34–1.40ms for T2 distributions based on our mineralogy-guided calculations. The commonly-used T2 value of 3ms results in large errors in clay bound porosity calculations (>100%) especially for high clay content samples.Our results can help improve NMR logs interpretations for surface relaxivity, PSD and clay content evaluation in Middle Bakken and Three Forks Formations. We suggest using our methodology to find similar correlations between surface relaxivity and distributed clay content and, in turn, to calculate surface relaxivity for other formations.

Permeability relation with other petrophysical parameters for periodic porous media

We modeled permeability (k) estimation based on porosity (ϕ), electrical formation factor (F), and nuclear magnetic resonance (NMR) relaxation time (T), using periodic structures of touching and overlapping spheres. The formation factors for these systems were calculated using the theory of bounds of bulk effective conductivity for a two‐component composite. The model allowed variations in grain consolidation (degree of overlap), scaling (grain size), and NMR surface relaxivity. The correlation of the permeability (k) with the predictor a [Formula: see text] was slightly higher than [Formula: see text] (i.e., a correlation coefficient of 0.98 versus 0.95). The exponent b ranged from 1.4 for a pure grain consolidation system to 2 for a pure scaling system. Variations in surface relaxivity are shown to cause significant scatter in the correlations.

A p-version finite-element formulation for modeling magnetic resonance relaxation in porous media

A new finite element (FE) technique for simulating nuclear magnetic resonance (NMR) relaxation of fluids in porous media has been developed to investigate the effects of pore geometry on NMR response of fluids in reservoir rocks that are not studied readily by other methods. The method uses a polynomial, or “p-version”, FE formulation derived using the classical variational principle with the hierarchical approximation concept and the Crank-Nicolson time-marching scheme, to solve the governing differential equations for magnetization decay in pores of arbitrary shape. Our p-FE simulation program is applicable to two-dimensional and axisymmetric three-dimensional pore geometries. However, extension of the formulation to a full three-dimensional simulator is straightforward. To validate the model, we compare numerical results to analytical solutions for magnetization decay in planar, cylindrical, and spherical pore geometries under various diffusion conditions in both the time and frequency domains. These tests also demonstrate stability and rapid convergence of the numerical solutions. Because it is based on a continuum representation of the physics of NMR relaxation, the FE program can be used to model local, that is pore-level, variations in the magnetization field, as well as relaxation of the total magnetization for the entire pore network. The capability of yielding a detailed map of the magnetization field at the pore-level could be a powerful tool for investigating some poorly understood controls on pore fluid relaxation, such as rough pore surfaces, interpore diffusion, and spatial variability in NMR surface relaxation rates.