Diffusion NMR of Confined Systems: Fluid Transport in Porous Solids and Heterogeneous Materials: Volume 9 (New Developments in NMR) - Hardcover

Hardcover

ISBN 10: 1782621903 ISBN 13: 9781782621904

Publisher: Royal Society of Chemistry, 2016

Synopsis

Having both academic and industrial relevance, this unique reference will be for specialists working in the research areas and for advanced graduate and postgraduate studies who want information on the versatility of diffusion NMR.

About this title

About the Author

Laboratoire de Physique de la Matière Condensée, France

From the Back Cover

With the increasing role of porous solids in conventional and newly emerging technologies, there is an urgent need for a deeper understanding of fluid behaviour confined to pore spaces of these materials especially with regard to their transport properties. From its early years, NMR has been recognized as a powerful experimental technique enabling direct access to this information. In the last two decades, the methodological development of different NMR techniques to assess dynamic properties of adsorbed ensembles has been progressed. This book will report on these recent advances and look at new broader applications in engineering and medicine.
Having both academic and industrial relevance, this unique reference will be for specialists working in the research areas and for advanced graduate and postgraduate studies who want information on the versatility of diffusion NMR.

Excerpt. © Reprinted by permission. All rights reserved.

Diffusion NMR of Confined Systems

Fluid Transport in Porous Solids and Heterogeneous Materials

By Rustem Valiullin

The Royal Society of Chemistry

Copyright © 2017 The Royal Society of Chemistry
All rights reserved.

ISBN: 978-1-78262-190-4

Contents

Chapter 1 NMR under Confinement: Roots in Retrospect Robert J. S. Brown, Paola Fantazzini, Jorg Karger and Rainer Kimmich, 1, 
Chapter 2 Fundamentals of Diffusion Measurements using NMR Scott A. Willis, Tim Stait-Gardner, Allan M. Torres and William S. Price, 16, 
Chapter 3 From the Microstructure to Diffusion NMR, and Back Denis S. Grebenkov, 52, 
Chapter 4 Two-dimensional NMR of Diffusion and Relaxation Yi-Qiao Song, Lalitha Venkataramanan, Ravinath Kausik and Nick Heaton, 111, 
Chapter 5 Transport in Structured Media: Multidimensional PFG-NMR Applied to Diffusion and Flow Processes Siegfried Stapf, 156, 
Chapter 6 Real Time PGSE NMR Through Direct Acquisition of Averaged Propagators in the Time Domain Using Pulsed Second Order Magnetic Fields Wilfred Kittler, Sergei Obruchkov, Mark Hunter and Petrik Galvosas, 194, 
Chapter 7 NMR Methods for Studying Microscopic Diffusion Anisotropy Daniel Topgaard, 226, 
Chapter 8 Beyond the Limits of Conventional Pulsed Gradient Spin Echo (PGSE) Diffusometry: Generalization of the Magnetization-grating Principle Ioan Ardelean and Rainer Kimmich, 260, 
Chapter 9 Probing Exchange and Diffusion in Confined Systems by 129Xe NMR Spectroscopy Julia Hollenbach, Ben Anger and Jorg Matysik, 294, 
Chapter 10 Diffusive Dynamics in Porous Materials as Probed by NMR Relaxation-based Techniques J.-P. Korb, 318, 
Chapter 11 Industrial Applications of Magnetic Resonance Diffusion and Relaxation Time Measurements Jonathan Mitchell, 353, 
Chapter 12 Confined Fluids: NMR Perspectives on Confinements and on Fluid Dynamics Rustem Valiullin and Jörg Kärger, 390, 
Chapter 13 NMR and Complementary Approaches to Establishing Structure-Transport Relationships in Disordered Porous Solids Sean Patrick Rigby, 435, 
Chapter 14 NMR Diffusometry for the Study of Energy-related Soft Materials L. A. Madsen and J. Hou, 464, 
Chapter 15 Diffusion Magnetic Resonance Imaging in Brain Tissue Farida Grinberg, Ezequiel Farrher and N. Jon Shah, 497, 
Chapter 16 Surface Effect Dominates Water Diffusion at Nanoscopic Length Scales Brendan W. Allison, John M. Franck, Chi-Yuan Cheng and Songi Han, 529, 
Subject Index, 568, 

CHAPTER 1

NMR under Confinement: Roots in Retrospect

ROBERT J. S. BROWN, PAOLA FANTAZZINI, JORG KARGER AND RAINER KIMMICH

Nuclear magnetic resonance (NMR) has provided us with many beneficial opportunities for science and technology. Its continued use in novel fields has yielded impressive strength and attractiveness for nearly a century. This is particularly true with regards to the topic of this book, the exploration of "Fluid Transport in Porous Solids and Heterogeneous Materials".

Here, the benefit of NMR in being able to look "from the outside" into a system becomes particularly evident. NMR operates as an "ideal spy", providing information without interfering with internally occurring phenomena. NMR is able to give information on pore spaces as well as anything that might happen within them. This wide-range of information that is accessible is illustrated by the examples in this book. The origin of some of these developments can, most remarkably, be traced back over many decades, to the very beginning of NMR research. In this chapter we will recollect some of the roots of the challenges we face today with applying NMR to studying "Fluid Transport in Porous Solids and Heterogeneous Materials" — albeit with some bias by personal experiences and impressions.

The output of nuclear magnetic relaxation on pore space architecture and guest dynamics in porous materials is, generally, based on model assumptions. These assumptions are, as a rule, well established and supported by experimental evidence. In its early years, however, NMR was used for studying molecular diffusion. The information gained stands on its own. Hahn's seminal paper in 1950 provided us with an opportunity that, in subsequent years, has been extensively exploited for diffusion measurements with liquids. With the application of pulsed field gradients by Stejskal and Tanner, the gradient intensity could be chosen large enough so that, eventually, diffusion measurements with porous materials have become possible. In his seminal paper of 1965 John Tanner introduced the technique under the title "Pulsed Field Gradients for NMR Spin-Echo Diffusion Measurements". Since then, the method has found application in quite a number of different communities. Its widespread use might have contributed to a diversification in nomenclature, with currently two names in common use: pulsed field gradient (PFG) and pulsed gradient spin echo (PGSE) NMR. In either case, Tanner's original wording is easily recognized.

The development of NMR was, essentially from its very beginning, closely related with the search for its application to petrophysical studies. The oil industry became aware of the potential of this novel source of information and vigorously promoted research on logging projects. The data in Table 1.1, taken from the paper of Kleinberg and Jackson, illustrate this intense and most rewarding partnership from its beginning until 2000.

In 1948, two years after the discovery of NMR in condensed matter by Bloch and Purcell, the thesis of Bloembergen and the classical paper by Bloembergen, Purcell and Pound (BPP theory) explained many features of the relaxation of NMR signals in bulk liquids by interpreting the dependence of the relaxation times on parameters related to molecular motion, including temperature, viscosity and distance between spins. A retrospective article by Bloembergen gives a review of NMR attempts before 1946 and of early work on relaxation. It has also been recognized that fluid molecules can be adsorbed near a solid surface, resulting in a decrease in their mobility. The existence and influence of pore walls were later found to appear in the relaxation patterns of NMR. The application of the BPP theory to the adsorbed layers could have caused researchers to think that the relaxation times of molecules in the adsorbed layers could have been decreased and so decreasing the relaxation times of fluids inside the pore space of porous media; but it seems that nobody had that intuition.

However, the idea was raised to build a device to be lowered inside the wells to get the signals of oil and water from the porous rock formation outside the borehole at depths of thousands of meters. Russel Varian had demonstrated that it was possible to observe NMR by free precession (at about 2 kHz) in the Earth's field. Numerous studies about the feasibility of the application of Nuclear Magnetic resonance for well Logging (NML) by Varian Associates followed. In those pioneering researches, the now widespread use and importance of the NMR single-sided NMR devices, that led to the evolution of the concept of compact and mobile devices, able to detect NMR signal outside the magnet, outside the laboratory, in a non-destructive way, regardless of the sample sizes emerged. The key feature of NML was intended to be the possibility to exploit the different relaxation times of bulk oil and water (10 times larger for water than for oil) to distinguish their signals. Since water and oil have about the same H nuclei density, the fraction of water and oil could have been determined by their signal ratio and the porosity of the rock formation by the total signal, and all this at depths of thousands of meters. Three NML research projects started at that time: Varian with Byron-Jackson, Schlumberger in Ridgefield, and what is now Chevron; nuclear Magnetic Resonance studies for fluids in Porous Media (MRPM) also started at Shell and Magnolia (later Mobil) to understand the properties of fluids in porous media for the purpose of characterizing reservoir rocks.

When it was found that surface effects shortened water relaxation times to where water could not be distinguished from oil or even to where it could not be observed, it appeared that NML might not be very useful. However, it was soon realized that relaxation times inversely proportional to pore surface areas gave information on pore size distributions, thereby giving information on the permeability of the rock to the flow of pore fluids, even more important than the original objectives.

In the 1950s many kinds of data were interpreted to suggest thick reduced-mobility liquid layers of water or other fluids adsorbed on surfaces including those of rock grains. Field dependent relaxation measurements at Chevron (from a micro-Tesla to a Tesla) did not support this and even showed that the postulated ice-like layers in DNA did not exist. The enhanced pore fluid relaxation comes mainly from a single adsorbed liquid layer at the surface.

In the late 1950s it was well understood that the local relaxation times for fluids were greatly shortened in not much more than one molecular layer at the solid surface. It was shown that if a pore is small enough that diffusion maintains nuclear magnetization uniform inside the pore, the rate of the observed relaxation time of the fluid in the pore is 1/T = 1/Tb + (Vs/V)/(Ts+t), where [Tb is the relaxation time of the bulk fluid, V the volume of the surface layer, V the pore volume, T the relaxation time of the surface layer, and t the residence time of a molecule in the surface layer. In 1956 Henry Torrey, Jan Korringa and Bob Brown wrote a U.S. Patent where many of the most basic features of MRPM were summarized, including relaxation for water and oils of different viscosity, and their behavior inside porous media at different temperatures. The first experimental NML was run in 1960 and limited commercial earth's-field NML service became available, and useful applications were found.

The effects of pore sizes and surface properties on relaxation were investigated at Shell. Wettability effects had already been noted by Brown and Fatt. Most of the papers used the longitudinal relaxation time T1, but also the transverse relaxation time T2 started to be studied.

The porosity of a water- or oil-saturated porous material can be determined from the NMR signal, with proper calibration. Other properties can be related to T1 or T2 relaxation curves. It was assumed that signal with T1 less than some "cutoff" time was "irreducible water" and that only fluid with longer relaxation times would be produced. Timur found a cutoff time of about 12 ms. Studies on the determination of water and oil when both phases are present in the pore space led also to the proposals of NMR estimates of the residual oil saturation. Permeability estimates from relaxation data were developed by Seevers and by Timur and later by Kenyon et al. The coming of MRI contributed to the understanding of oil industry applications.

Many porous media have a wide distribution of pore sizes, the distribution of classes of fluids with a distribution of relaxation times, possibly in different regimes of exchange, can determine a multi-exponential relaxation. A stochastic theory for the relaxation in heterogeneous systems with many exchanging water phases was proposed in 1957 by Zimmerman and Brittin. It started in an oil industry laboratory, to justify the behavior of T1 and T2 in water systems adsorbed on silica gel, and had great success in the study of systems also of biological interest, that for many aspects can be considered as porous media. An example is given by the study on DNA water reported by Brown. After some examples of sporadic interest for NMR relaxation in biological systems, interest grew significantly with the appearance of an NMR study on HeLa cells (the first "immortal" human cells grown in a lab), and the Damadian paper that indicated the possibility to detect tumors by increased relaxation times for the first time. Let's not forget that the papers, posing the basis for Magnetic Resonance Imaging (MRI), appeared around the same time with a clear focus on biological systems.

The two fields of petrophysical and biological studies enjoyed reciprocal advantages by exchange of experiences, methods, and theories, given by the MRPM studies. A clear example of this is given by the seminal work of Brownstein and Tarr that gave the interpretation of the multi-exponential behavior by classical diffusion in the presence of relaxation sinks on the confining surfaces, without the need of the assumption of different water phases. Written for cell water, later this theory influenced the interpretation of multi-exponential relaxation for porous media of any nature, including rocks. In any case, it became clear that the observed multi-exponential relaxation, giving rise to distributions of relaxation times strongly depended on the diffusion regimes in the complex network of the pore space. In a real porous medium, with the same surface properties, in the case of a fast diffusion regime, one would observe a single exponential decay only if the diffusion is fast enough inside each pore and among the pores to make the magnetization uniform inside the whole pore space, or, of course if the diffusion is fast and the pores are all the same. However, if the diffusion is fast inside each pore, but slow among pores, the relaxation will be multi-exponential. Algorithms have been developed to invert multi-exponential curves to distributions of relaxation times. An algorithm was proposed with a smoothing coefficient varying along the relaxation time distribution, in order to maintain uniform the penalty.

Over time these methods have been exploited to study the pore size distributions of porous media of different nature and for different applications. Simple methods to separate solid and liquid components on the free induction decay, combined with quasi-continuous analysis of the two data sets, have been exploited to follow the kinetics of Portlandite and liquid component formation in hydrate cements. In coral skeletons, the pore-sizes can be analyzed, with a single NMR measurement, at multiple length scales. The effect of increasing acidity on increasing the macro-scale porosity, whilst the linear extension rate remained the same, revealed the acclimation of the corals in a warming acidifying ocean.

Later, algorithms were developed for two-dimensional (2D) inversion of experimental 2D data, in order to obtain Relaxation-Relaxation and Diffusion-Relaxation correlation functions or pore-to-pore exchange parameters (for more details see Chapter 4). It is clear that caution is needed to interpret multi-exponential relaxation in terms of pore-size distributions, especially for T2, for water subjected to diffusion inside field gradients. Not only large scale gradients can be present, but also internal gradients inside the pore due to the susceptibility difference between water and the solid material. For water diffusing inside a constant gradient, for unrestricted diffusion, the dependence of 1/T on the half-echo time in a CPMG sequence is expected to be quadratic. In many porous media it was found to be linear instead of quadratic, and this was interpreted as due to a distribution of correlation times for molecular diffusion.

Shortly after, NMR with pulsed field gradients enabled diffusion measurements of water in zeolites, probably the most important representative of "microporous" materials. Pore sizes of such substances are known to be of molecular dimensions. Transverse nuclear magnetic relaxation times of guest molecules in such host materials are generally very small so that, as a rule, NMR diffusion studies necessitate the use of "pulsed" field gradients. As a most astonishing outcome of these studies, water diffusion in zeolites was found to be only slightly exceeded by that in the neat liquid.

This puzzling result gave rise to an in-depth study of molecular diffusion in zeolites in the very place where Felix Bloch was working as the first PhD student of Werner Heisenberg. Owing to the activities of Artur Losche and Harry Pfeifer and their groups, Leipzig was now on the way to becoming a place which Richard Ernst, during a talk in Leipzig in 1992, referred to as the "East Pole of Magnetic Resonance". Benefitting from being part of the Eastern hemisphere, researchers in Leipzig had access to probably the largest zeolite crystals available at this time, synthesized in the famous laboratory of Sergey Petrovitch Zhdanov in Leningrad. In this way, by a purposeful variation of the diffusion path lengths in relation to the crystal sizes, the high diffusivities reported in ref. 57 could be attributed to "long-range" diffusion, i.e. to mass transfer in free space between the individual zeolite crystallites. Water diffusivities in the micropores, however, was determined to be notably smaller, in complete agreement with the expected behavior. The application of diffusion NMR to beds of zeolite crystals gave rise to the development of two concepts of data analysis, which have become part of the general tool box of NMR, namely the formalism of two-range diffusion for taking account of mass exchange between different compartments such as biological cells and the introduction of the "mean" propagator.

The diffusion of guest molecules in zeolites was (so far) mainly based on the measurement of transient uptake and release curves initiated by a pressure step in the surrounding atmosphere. Diffusivities were determined with the understanding that these phenomena were controlled by the guest diffusivity within the zeolite pore space. It came as a great surprise, therefore, when in many cases the intracrystalline diffusivities — now directly measured owing to the potentials of NMR — proved to exceed the so far generally accepted values by several orders of magnitude. As the only solution of the problem, mass transfer in such crystals had to be required to be controlled by additional transport resistances on the external crystal surface or in intracrystalline space rather than by exclusively the diffusional resistance of the genuine pore space as so far generally implied. NMR diffusion studies did thus provide evidence of these barriers long before they became an object of high-resolution electron microscopy and initiated a paradigm shift in the understanding of mass transfer in nanoporous materials.

(Continues...)

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Edition details

• Publisher: Royal Society of Chemistry
• Publication date: 2016
• Language: English
• ISBN 10: 1782621903
• ISBN 13: 9781782621904
• Binding: Hardcover
• Number of pages: 576
• Editor: Rustem Valiullin