Determining NMR flow propagator moments in porous rocks without the influence of relaxation

Low-Field Functional Group Resolved Nuclear Spin Relaxation in Mesoporous Silica

Solid-fluid interactions underpin the efficacy of functional porous materials across a diverse array of chemical reaction and separation processes. However, detailed characterization of interfacial phenomena within such systems is hampered by their optically opaque nature. Motivated by the need to bridge this capability gap, we report low-magnetic-field two-dimensional (2D) ¹H nuclear spin relaxation measurements as a noninvasive probe of adsorbate identity and interfacial dynamics, exploring the relaxation characteristics exhibited by liquid hydrocarbon adsorbates confined to a model mesoporous silica. For the first time, we demonstrate the capacity of this approach in distinguishing functional group-specific relaxation phenomena across a diverse range of alcohols and carboxylic acids employed as solvents, reagents, and liquid hydrogen carriers, with distinct relaxation responses assigned to the alkyl and hydroxyl moieties of each confined liquid. Uniquely, this relaxation behavior is shown to correlate with adsorbate acidity, with the observed relationship rationalized on the basis of surface-adsorbate proton-exchange dynamics. Our results demonstrate that nuclear spin relaxation provides a molecular-level perspective on sorbent/sorbate interactions, motivating the exploration of such measurements as a unique probe of adsorbate identity within optically opaque porous media.

Modelling and upscaling of transport in carbonates during dissolution: Validation and calibration with NMR experiments

We present an experimental and numerical study of transport in carbonates during dissolution and its upscaling from the pore (∼μm) to core (∼cm) scale. For the experimental part, we use nuclear magnetic resonance (NMR) to probe molecular displacements (propagators) of an aqueous hydrochloric acid (HCl) solution through a Ketton limestone core. A series of propagator profiles are obtained at a large number of spatial points along the core at multiple time-steps during dissolution. For the numerical part, first, the transport model-a particle-tracking method based on Continuous Time Random Walks (CTRW) by Rhodes et al. (2008)-is validated at the pore scale by matching to the NMR-measured propagators in a beadpack, Bentheimer sandstone, and Portland carbonate (Scheven et al., 2005). It was found that the emerging distribution of particle transit times in these samples can be approximated satisfactorily using the power law function ψ(t) ∼ t^-1-β, where 0 <β < 2. Next, the evolution of the propagators during reaction is modelled: at the pore scale, the experimental data is used to calibrate the CTRW parameters; then the shape of the propagators is predicted at later observation times. Finally, a numerical upscaling technique is employed to obtain CTRW parameters for the core. From the NMR-measured propagators, an increasing frequency of displacements in stagnant regions was apparent as the reaction progressed. The present model predicts that non-Fickian behaviour exhibited at the pore scale persists on the centimetre scale.

Characterizing dispersivity and stagnation in porous media using NMR flow propagators

Low-field nuclear magnetic resonance (NMR) displacement probability distributions (flow propagators) are presented for water flowing through heterogeneous porous materials. Four sedimentary rocks have been chosen as example systems: Dolostone, Bentheimer sandstone, Berea sandstone, and Indiana limestone (in order of decreasing permeability). The fluid displacement is characterized by pre-asymptotic Stokes' flow and so the probability distributions are bimodal, with peaks corresponding to stagnant fluid in dead-end pores and flowing fluid in the connected porosity. Cut-off Gaussian functions are used to fit the flowing and stagnant peaks independently. An effective dispersivity length scale Lv (also known as the mixing length scale) is estimated by fitting the portion of the probability distribution corresponding to the flowing fluid. For the relatively homogeneous Bentheimer sandstone, the ratio of effective dispersivity length scale to effective transport diameter dt is Lv/dt≈16, which is an order of magnitude larger than for randomly packed glass beads where Lv/dt≈1.8. We compare these dispersivity parameters to similar values extracted from a cumulant analysis of the entire propagator. Fitting a cut-off Gaussian avoids the usual complications of analyzing dispersion in the presence of the ubiquitous stagnant fluid, and results in a clear demonstration of the influence of long-range heterogeneities on the dispersivity for flow in real sedimentary rocks.

Contributed review: nuclear magnetic resonance core analysis at 0.3 T

Nuclear magnetic resonance (NMR) provides a powerful toolbox for petrophysical characterization of reservoir core plugs and fluids in the laboratory. Previously, there has been considerable focus on low field magnet technology for well log calibration. Now there is renewed interest in the study of reservoir samples using stronger magnets to complement these standard NMR measurements. Here, the capabilities of an imaging magnet with a field strength of 0.3 T (corresponding to 12.9 MHz for proton) are reviewed in the context of reservoir core analysis. Quantitative estimates of porosity (saturation) and pore size distributions are obtained under favorable conditions (e.g., in carbonates), with the added advantage of multidimensional imaging, detection of lower gyromagnetic ratio nuclei, and short probe recovery times that make the system suitable for shale studies. Intermediate field instruments provide quantitative porosity maps of rock plugs that cannot be obtained using high field medical scanners due to the field-dependent susceptibility contrast in the porous medium. Example data are presented that highlight the potential applications of an intermediate field imaging instrument as a complement to low field instruments in core analysis and for materials science studies in general.

Low-field permanent magnets for industrial process and quality control

In this review we focus on the technology associated with low-field NMR. We present the current state-of-the-art in low-field NMR hardware and experiments, considering general magnet designs, rf performance, data processing and interpretation. We provide guidance on obtaining the optimum results from these instruments, along with an introduction for those new to low-field NMR. The applications of lowfield NMR are now many and diverse. Furthermore, niche applications have spawned unique magnet designs to accommodate the extremes of operating environment or sample geometry. Trying to capture all the applications, methods, and hardware encompassed by low-field NMR would be a daunting task and likely of little interest to researchers or industrialists working in specific subject areas. Instead we discuss only a few applications to highlight uses of the hardware and experiments in an industrial environment. For details on more particular methods and applications, we provide citations to specialized review articles.

Monitoring bacterially induced calcite precipitation in porous media using magnetic resonance imaging and flow measurements

A range of nuclear magnetic resonance (NMR) techniques are employed to provide novel, non-invasive measurements of both the structure and transport properties of porous media following a biologically mediated calcite precipitation reaction. Both a model glass bead pack and a sandstone rock core were considered. Structure was probed using magnetic resonance imaging (MRI) via a combination of quantitative one-dimensional profiles and three-dimensional images, applied before and after the formation of calcite in order to characterise the spatial distribution of the precipitate. It was shown through modification and variations of the calcite precipitation treatment that differences in the calcite fill would occur but all methods were successful in partially blocking the different porous media. Precipitation was seen to occur predominantly at the inlet of the bead pack, whereas precipitation occurred almost uniformly along the sandstone core. Transport properties are quantified using pulse field gradient (PFG) NMR measurements which provide probability distributions of molecular displacement over a set observation time (propagators), supplementing conventional permeability measurements. Propagators quantify the local effect of calcite formation on system hydrodynamics and the extent of stagnant region formation. Collectively, the combination of NMR measurements utilised here provides a toolkit for determining the efficacy of a biological-precipitation reaction for partially blocking porous materials.

Insights into non-Fickian solute transport in carbonates

[1] We study and explain the origin of early breakthrough and long tailing plume behavior by simulating solute transport through 3-D X-ray images of six different carbonate rock samples, representing geological media with a high degree of pore-scale complexity. A Stokes solver is employed to compute the flow field, and the particles are then transported along streamlines to represent advection, while the random walk method is used to model diffusion. We compute the propagators (concentration versus displacement) for a range of Peclet numbers (Pe) and relate it to the velocity distribution obtained directly on the images. There is a very wide distribution of velocity that quantifies the impact of pore structure on transport. In samples with a relatively narrow spread of velocities, transport is characterized by a small immobile concentration peak, representing essentially stagnant portions of the pore space, and a dominant secondary peak of mobile solute moving at approximately the average flow speed. On the other hand, in carbonates with a wider velocity distribution, there is a significant immobile peak concentration and an elongated tail of moving fluid. An increase in Pe, decreasing the relative impact of diffusion, leads to the faster formation of secondary mobile peak(s). This behavior indicates highly anomalous transport. The implications for modeling field-scale transport are discussed. Citation: Bijeljic, B., P. Mostaghimi, and M. J. Blunt (2013), Insights into non-Fickian solute transport in carbonates, Water Resour. Res., 49, 2714-2728, doi:10.1002/wrcr.20238.

Predictions of non-Fickian solute transport in different classes of porous media using direct simulation on pore-scale images

We present predictions of transport through micro-CT images of porous media that include the analysis of correlation structure, velocity, and the dynamics of the evolving plume. We simulate solute transport through millimeter-sized three-dimensional images of a beadpack, a sandstone, and a carbonate, representing porous media with an increasing degree of pore-scale complexity. The Navier-Stokes equations are solved to compute the flow field and a streamline simulation approach is used to move particles by advection, while the random walk method is employed to represent diffusion. We show how the computed propagators (concentration as a function of displacement) for the beadpack, sandstone, and carbonate depend on the width of the velocity distribution. A narrow velocity distribution in the beadpack leads to the least anomalous behavior, where the propagators rapidly become Gaussian in shape; the wider velocity distribution in the sandstone gives rise to a small immobile concentration peak, and a large secondary mobile peak moving at approximately the average flow speed; in the carbonate with the widest velocity distribution, the stagnant concentration peak is persistent, with a slower emergence of a smaller secondary mobile peak, characteristic of highly anomalous behavior. This defines different types of transport in the three media and quantifies the effect of pore structure on transport. The propagators obtained by the model are in excellent agreement with those measured on similar cores in nuclear magnetic resonance experiments by Scheven, Verganelakis, Harris, Johns, and Gladden, Phys. Fluids 17, 117107 (2005).

Velocity field measurements in sedimentary rock cores by magnetization prepared 3D SPRITE

A time-efficient MRI method suitable for quantitative mapping of 3-D velocity fields in sedimentary rock cores, and granular samples is discussed. The method combines the 13-interval Alternating-Pulsed-Gradient Stimulated-Echo (APGSTE) scheme and three-dimensional Single Point Ramped Imaging with T(1) Enhancement (SPRITE). Collecting a few samples near the q-space origin and employing restricted k-space sampling dramatically improves the performance of the imaging method. The APGSTE-SPRITE method is illustrated through mapping of 3-D velocity field in a macroscopic bead pack and heterogeneous sandstone and limestone core plugs. The observed flow patterns are consistent with a general trend for permeability to increase with the porosity. Domains of low permeability obstruct the flow within the core volume. Water tends to flow along macroscopic zones of higher porosity and across zones of lower porosity.

Signature of non-Fickian solute transport in complex heterogeneous porous media

We simulate transport of a solute through three-dimensional images of different rock samples, with resolutions of a few microns, representing geological media of increasing pore-scale complexity: a sandpack, a Berea sandstone, and a Portland limestone. We predict the propagators (concentration as a function of distance) measured on similar cores in nuclear magnetic resonance experiments and the dispersion coefficient as a function of Péclet number and time. The behavior is explained using continuous time random walks with a truncated power-law distribution of travel times: transport is qualitatively different for the complex limestone compared to the sandstone or sandpack, with long tailing, an almost immobile peak concentration, and a very slow approach to asymptotic dispersion.

A rapid measurement of T1/T2: the DECPMG sequence

The Driven-Equilibrium Carr-Purcell Meiboom-Gill (DECPMG) pulse sequence is a rapid method for obtaining the average ratio of longitudinal to transverse relaxation times (T(1)/T(2)) as a function of T(2). Since this is a one-dimensional experiment, the (T(1)/T(2))T(2) ratio can be acquired, potentially, in just two scans; the second scan being a reference CPMG measurement. Conventionally, T(1)/T(2) is determined from a two-dimensional T(1)-T(2) relaxation correlation experiment. The method described here offers a significant reduction in experimental time without a reduction in signal-to-noise. The (T(1)/T(2)) ratio is useful for comparing the behaviour of liquids in porous media. Here we demonstrate the application of the DECPMG sequence to the study of oil-bearing rocks by differentiating oil or water saturated rock cores, and by observing the relative strengths of surface interaction for water in two types of rock by measuring (T(1)/T(2)) as a function of magnetic field strength.