Analytical models of probe dynamics effects on NMR measurements.

This paper provides a detailed analysis of three common NMR probe circuits (untuned, tuned, and impedance-matched) and studies their effects on multi-pulse experiments, such as those based on the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. The magnitude of probe dynamics effects on broadband refocusing pulses are studied as a function of normalized RF bandwidth. Finally, the probe circuit models are integrated with spin dynamics simulations to design hardware-specific RF excitation and refocusing pulses for optimizing user-specified metrics such as signal-to-noise ratio (SNR) in grossly inhomogeneous fields. Preliminary experimental results on untuned probes are also presented.

Effect of off-resonance on T1 saturation recovery measurement in inhomogeneous fields.

Saturation-recovery measurements with Carr-Purcell-Meiboom-Gill sequences are commonly employed to measure the longitudinal relaxation time constant, T1, in grossly inhomogeneous fields. We show that in general the off-resonant effect generates unexpected extra signals in the T1 measurement. In the present study, we derive a modified T1 kernel that accounts for this off-resonance effect quantitatively. The new kernel has been tested with numerical simulations and experiments, and excellent agreement is found.

Sensitivity and resolution of two-dimensional NMR diffusion-relaxation measurements.

The performance of 2D NMR diffusion-relaxation measurements for fluid typing applications is analyzed. In particular, we delineate the region in the diffusion - relaxation plane that can be determined with a given gradient strength and homogeneity, and compare the performance of the single and double echo encoding with the stimulated echo diffusion encoding. We show that the diffusion editing based approach is able to determine the diffusion coefficient only if the relaxation time T2 exceeds a cutoff value T2,cutoff, that scales like T2,cutoff∝g(-2/3)D(-1/3). For stimulated echo encoding, the optimal diffusion encoding times (Td and δ), that provide the best diffusion sensitivity, rely only on the T1/T2 ratios and not on the diffusion coefficients of the fluids or the applied gradient strengths. Irrespective of T1, for high enough gradients (i.e. when γ(2)g(2)DT2(3)>10(2)), the Hahn echo based encoding is superior to encoding based on the stimulated echo. For weaker gradients, the stimulated echo is superior only if the T1/T2 ratio is much larger than 1. For single component systems, the diffusion sensitivity is not adversely impacted by the uniformity of the gradients and the diffusion distributions can be well measured. The presence of non-uniform gradients can affect the determination of the diffusion distributions when you have two fluids of comparable T2. In such situations the effective single component diffusion coefficient is always closer to the geometric mean diffusion coefficient of the two fluids.

Absolute phase effects on CPMG-type pulse sequences.

We describe and analyze the effects of transients within radio-frequency (RF) pulses on multiple-pulse NMR measurements such as the well-known Carr-Purcell-Meiboom-Gill (CPMG) sequence. These transients are functions of the absolute RF phases at the beginning and end of the pulse, and are thus affected by the timing of the pulse sequence with respect to the period of the RF waveform. Changes in transients between refocusing pulses in CPMG-type sequences can result in signal decay, persistent oscillations, changes in echo shape, and other effects. We have explored such effects by performing experiments in two different low-frequency NMR systems. The first uses a conventional tuned-and-matched probe circuit, while the second uses an ultra-broadband un-tuned or non-resonant probe circuit. We show that there are distinct differences between the absolute phase effects in these two systems, and present simple models that explain these differences.

Direct optimization of signal-to-noise ratio of CPMG-like sequences in inhomogeneous fields.

The performance of the standard CPMG sequence in inhomogeneous fields can be improved with the use of broadband excitation and refocusing pulses. In previous work we have developed short composite broadband refocusing pulses together with practical excitation pulses to realize such performance gains, and quantified them using the ratio of signal to noise power (SNR). In this work we systematically explore the performance of refocusing pulses as a function of the overall pulse length up to ten times the length of the regular 180° pulse. This is in the regime of non-adiabatic pulses. We introduce a new performance functional for numerical pulse optimization that directly maximizes SNR and study the effect of symmetry constraints on the pulses. We find that for the optimal pulses, the SNR per asymptotic echo increases with pulse length but, for typical echo spacings, the SNR per unit time is maximized for refocusing pulses that are between two and four times longer than the duration of the standard rectangular 180° pulse. The performance is limited by the control bandwidth and the inability of finding the global maximum. The best performance was obtained with symmetric phase-alternating (SPA) refocusing pulses optimized with our novel performance functional. To test them in the CPMG sequence, we also developed axis-matching excitation (AMEX) pulses for use with these SPA refocusing pulses and tested the new AMEX-SPA sequences experimentally in a grossly inhomogeneous field, observing excellent agreement with the theoretical expectations. One of these sequences produced over 4.5 times higher SNR per asymptotic echo and 3.9 times higher SNR per unit time than the standard CPMG sequence with the same instantaneous RF power level. We also found that the new sequences are at least as robust to changes in the RF field strength as the standard CPMG sequence.

Dispersion of T1 and T2 nuclear magnetic resonance relaxation in crude oils.

Crude oils, which are complex mixtures of hydrocarbons, can be characterized by nuclear magnetic resonance diffusion and relaxation methods to yield physical properties and chemical compositions. In particular, the field dependence, or dispersion, of T1 relaxation can be used to investigate the presence and dynamics of asphaltenes, the large molecules primarily responsible for the high viscosity in heavy crudes. However, the T2 relaxation dispersion of crude oils, which provides additional insight when measured alongside T1, has yet to be investigated systematically. Here we present the field dependence of T1-T2 correlations of several crude oils with disparate densities. While asphaltene and resin-containing crude oils exhibit significant T1 dispersion, minimal T2 dispersion is seen in all oils. This contrasting behavior between T1 and T2 cannot result from random molecular motions, and thus, we attribute our dispersion results to highly correlated molecular dynamics in asphaltene-containing crude oils.

Adsorption of superparamagnetic iron oxide nanoparticles on silica and calcium carbonate sand.

Superparamagnetic iron oxide (SPIO) nanoparticles have the potential to be used in the characterization of porous rock formations in oil fields as a contrast agent for NMR logging because they are small enough to traverse through nanopores and enhance contrast by shortening NMR T2 relaxation time. However, successful development and application require detailed knowledge of particle stability and mobility in reservoir rocks. Because nanoparticle adsorption to sand (SiO2) and rock (often CaCO3) affects their mobility, we investigated the thermodynamic equilibrium adsorption behavior of citric acid-coated SPIO nanoparticles (CA SPIO NPs) and poly(ethylene glycol)-grafted SPIO nanoparticles (PEG SPIO NPs) on SiO2 (silica) and CaCO3 (calcium carbonate). Adsorption behavior was determined at various pH and salt conditions via chemical analysis and NMR, and the results were compared with molecular theory predictions. Most of the NPs were recovered from silica, whereas far fewer NPs were recovered from calcium carbonate because of differences in the mineral surface properties. NP adsorption increased with increasing salt concentration: this trend was qualitatively explained by molecular theory, as was the role of the PEG grafting in preventing NPs adsorption. Quantitative disagreement between the theoretical predictions and the data was due to NP aggregation, especially at high salt concentration and in the presence of calcium carbonate. Upon aggregation, NP concentrations as determined by NMR T2 were initially overestimated and subsequently corrected using the relaxation rate 1/T2, which is a function of aggregate size and fractal dimension of the aggregate. Our experimental validation of the theoretical predictions of NP adsorption to minerals in the absence of aggregation at various pH and salt conditions demonstrates that molecular theory can be used to determine interactions between NPs and relevant reservoir surfaces. Importantly, this integrated experimental and theoretical approach can be used to gain insight into NP mobility in the reservoir.

Axis-matching excitation pulses for CPMG-like sequences in inhomogeneous fields.

The performance of the standard CPMG sequence in inhomogeneous fields can be improved with the use of broadband excitation and refocusing pulses. Here we introduce a new class of excitation pulses, so-called axis-matching excitation pulses, that optimize the response for a given refocusing pulse. These new excitation pulses are tailored to the refocusing pulses and take their imperfections into account. Rather than generating purely transverse magnetization, these pulses are designed to generate magnetization pointing along the axis of the effective rotation of the refocusing cycle. This approach maximizes the CPMG component and minimizes the CP component of the signal. Replacing a standard 90° pulse with a new excitation pulse matched to the 180° refocusing pulse increases the signal bandwidth and improves the echo amplitudes by 30% in inhomogeneous fields in comparison to the standard CPMG sequence. Larger gains are obtained with more advanced refocusing pulses. Recent work demonstrated that it is possible to increase the signal to noise ratio (SNR) of individual echoes by more than a factor of 1.5 (in power units) without increasing the duration or amplitude of the refocusing pulses. This was achieved by replacing the standard 180° refocusing pulse by a short phase alternating pulse and the standard 90° excitation pulse by a broadband excitation pulse. We show here that with suitable axis-matching excitation pulses, the SNR further increases by over a factor of 2. We discuss the underlying theory and present several practical implementations of purely phase modulated axis-matching excitation pulses for a number of different refocusing pulses that were derived using methods of optimal control. To gain the full benefit of these new excitation pulses, it is essential to replace the standard phase cycling scheme based on 180° phase shifts by a new scheme involving phase inversion. We tested the new pulses experimentally and observe excellent agreement with the theoretical expectations. We also demonstrate that an additional benefit of axis-matching excitation pulses is the decrease of the transient that appears in the amplitudes of the first few echoes, thus enabling better measurements of short relaxation times.

Broadband CPMG sequence with short composite refocusing pulses.

We demonstrate that CPMG sequences with phase-modulated refocusing pulses of the same duration as the standard 180° pulses can generate echo trains with significantly increased amplitudes compared to the standard CPMG sequence in the case when there is a large range of Larmor frequencies across the sample. The best performance is achieved with symmetric phase-alternating (SPA) composite refocusing pulses of the form α-yß+yα-y. In comparison to standard 180° pulses, we show that with SPA refocusing pulses with α≈27° and ß≈126°, it is possible to double the signal-to-noise ratio without increasing the total pulse duration or power consumption of the refocusing pulses. The increased bandwidth of these pulses more than compensates for the decrease in performance in the vicinity of resonance. To achieve the full benefit of the broadband nature of the SPA pulses in a CPMG sequence, it is necessary to combine these refocusing pulses with a broadband excitation pulse. When it is not possible to use a short, high amplitude excitation pulse, we show that phase-alternating (PA) excitation pulses are suitable for this purpose. We present a detailed analysis of the underlying spin dynamics of these new pulse sequences and confirm the simulations with experiments. We show that for samples with T1/T2>1, the new sequences in grossly inhomogeneous fields do not only generate echoes with an increased amplitude, but also with an increased decay time. Finally, we analyze the diffusion properties and show quantitatively that the broadband sequences have a substantially higher diffusion sensitivity compared with the standard CPMG sequence.

Stability of superparamagnetic iron oxide nanoparticles at different pH values: experimental and theoretical analysis.

The detection of superparamagnetic nanoparticles using NMR logging has the potential to provide enhanced contrast in oil reservoir rock formations. The stability of the nanoparticles is critical because the NMR relaxivity (R(2) ≡ 1/T(2)) is dependent on the particle size. Here we use a molecular theory to predict and validate experimentally the stability of citric acid-coated/PEGylated iron oxide nanoparticles under different pH conditions (pH 5, 7, 9, 11). The predicted value for the critical surface coverage required to produce a steric barrier of 5k(B)T for PEGylated nanoparticles (MW 2000) was 0.078 nm(-2), which is less than the experimental value of 0.143 nm(-2), implying that the nanoparticles should be stable at all pH values. Dynamic light scattering (DLS) measurements showed that the effective diameter did not increase at pH 7 or 9 after 30 days but increased at pH 11. The shifts in NMR relaxivity (from R(2) data) at 2 MHz agreed well with the changes in hydrodynamic diameter obtained from DLS data, indicating that the aggregation behavior of the nanoparticles can be easily and quantitatively detected by NMR. The unexpected aggregation at pH 11 is due to the desorption of the surface coating (citric acid or PEG) from the nanoparticle surface not accounted for in the theory. This study shows that the stability of the nanoparticles can be predicted by the theory and detected by NMR quantitatively, which suggests the nanoparticles to be a possible oil-field nanosensor.

Low-frequency NMR with a non-resonant circuit.

Nuclear magnetic resonance typically utilizes a tuned resonance circuit with impedance matching to transmit power and receive signal. The efficiency of such a tuned coil is often described in terms of the coil quality factor, Q. However, in field experiments such as in well-logging, the circuit Q can vary dramatically throughout the depth of the wellbore due to temperature or fluid salinity variations. Such variance can result in erroneous setting of NMR circuit parameters (tuning and matching) and subsequent errors in measurements. This paper investigates the use of a non-resonant transmitter to reduce the circuit sensitivity on Q and demonstrates that such circuits can be efficient in delivering power and current to the coil. We also describe a tuned receiver circuit whose resonant frequency can be controlled digitally. Experimental results show that a range of common NMR experiments can be performed with our circuits.

Application of optimal control to CPMG refocusing pulse design.

We apply optimal control theory (OCT) to the design of refocusing pulses suitable for the CPMG sequence that are robust over a wide range of B(0) and B(1) offsets. We also introduce a model, based on recent progress in the analysis of unitary dynamics in the field of quantum information processing (QIP), that describes the multiple refocusing dynamics of the CPMG sequence as a dephasing Pauli channel. This model provides a compact characterization of the consequences and severity of residual pulse errors. We illustrate the methods by considering a specific example of designing and analyzing broadband OCT refocusing pulses of length 10t(180) that are constrained by the maximum instantaneous pulse power. We show that with this refocusing pulse, the CPMG sequence can refocus over 98% of magnetization for resonance offsets up to 3.2 times the maximum RF amplitude, even in the presence of ±10% RF inhomogeneity.

Probing asphaltene aggregation in native crude oils with low-field NMR.

We show that low-field proton nuclear magnetic resonance (NMR) relaxation and diffusion experiments can be used to study asphaltene aggregation directly in crude oils. Relaxation was found to be multiexponential, reflecting the composition of a complex fluid. Remarkably, the relaxation data for samples with different asphaltene concentrations can be collapsed onto each other by a simple rescaling of the time dimension with a concentration-dependent factor xi, whereas the observed diffusion behavior is unaffected by asphaltene concentration. We interpret this finding in terms of a theoretical model that explains the enhanced relaxation by the transitory entanglement of solvent hydrocarbons within asphaltene clusters and their subsequent slowed motion and diffusion within the cluster. We relate the measured scaling parameters xi to cluster sizes, which we find to be on the order of 2.2-4.4 nm for an effective sphere diameter. These sizes are in agreement with the typical values reported in the literature as well as with the small-angle X-ray scattering (SAXS) experiments performed on our samples.

Correlation of transverse and rotational diffusion coefficient: a probe of chemical composition in hydrocarbon oils.

Measurements of relaxation time and diffusion coefficient by nuclear magnetic resonance are well-established techniques to study molecular motions in fluids. Diffusion measurements sense the translational diffusion coefficients of the molecules, whereas relaxation times measured at low magnetic fields probe predominantly the rotational diffusion of the molecules. Many complex fluids are composed of a mixture of molecules with a wide distribution of sizes and chemical properties. This results in correspondingly wide distributions of measured diffusion coefficients and relaxation times. To first order, these distributions are determined by the distribution of molecular sizes. Here we show that additional information can be obtained on the chemical composition by measuring two-dimensional diffusion-relaxation distribution functions, a quantity that depends also on the shape and chemical interactions of molecules. We illustrate this with experimental results of diffusion-relaxation distribution functions on a series of hydrocarbon mixtures. For oils without significant amounts of asphaltenes, the diffusion-relaxation distribution functions follow a power-law behavior with an exponent that depends on the relative abundance of saturates and aromatics. Oils with asphaltene deviate from this trend, as asphaltene molecules act as relaxation contrast agent for other molecules without affecting their diffusion coefficient significantly. In waxy oils below the wax appearance temperature a gel forms. This is reflected in the measured diffusion-relaxation distribution functions, where the restrictions due to the gel network reduce the diffusion coefficients without affecting the relaxation rates significantly.

Encoding of diffusion and T1 in the CPMG echo shape: single-shot D and T1 measurements in grossly inhomogeneous fields.

We present a new approach of NMR measurements in the presence of grossly inhomogeneous fields where information is encoded in the echo shape of CPMG trains. The method is based on sequences that consist of an initial encoding sequence that generates echoes with contributions from at least two different coherence pathways that are then both refocused many times by a long string of closely spaced identical pulses. The generated echoes quickly assume an asymptotic shape that encodes the information of interest. High signal-to-noise ratios can be achieved by averaging the large number of echoes. We demonstrate this approach with different implementations of the measurements of longitudinal relaxation time, T(1), and diffusion coefficient, D. It is shown that the method can be used for novel single-shot measurements.

Relationship between susceptibility induced field inhomogeneities, restricted diffusion, and relaxation in sedimentary rocks.

Low field relaxation and diffusion measurements have become essential tools to study the pore space of sedimentary rocks with important practical applications in the field of well logging and hydrocarbon extractions. Even at Larmor frequencies below 2 MHz, diffusion measurements are often affected noticeably by internal field inhomogeneities. These field inhomogeneities are induced by susceptibility contrast between the rock and the fluid and are evident in most sandstones. Using sets of two-dimensional diffusion-relaxation measurements in applied and internal gradients, we study in detail the correlation between the field inhomogeneities, restricted diffusion, and relaxation time in three rocks of different susceptibility. We find that in the sandstone cores, the field inhomogeneities in large pores can be described by a local gradient that scales inversely with relaxation time above 250 ms. At shorter relaxation times, the extracted internal gradients deviate from this scaling relationship and we observe a dependence on diffusion time. This demonstrates that in this case, the internal field has structure on a length scale of a few microns.

Quantitative characterization of food products by two-dimensional D-T2 and T1-T2 distribution functions in a static gradient.

We present new NMR techniques to characterize food products that are based on the measurement of two-dimensional diffusion-T2 relaxation and T1-T2 relaxation distribution functions. These measurements can be performed in magnets of modest strength and low homogeneity and do not require pulsed gradients. As an illustration, we present measurements on a range of dairy products that include milks, yogurt, cream, and cheeses. The two-dimensional distribution functions generally exhibit two distinct components that correspond to the aqueous phase and the liquid fat content. The aqueous phase exhibits a relatively sharp peak, characterized by a large T1/T2 ratio of around 4. The diffusion coefficient and relaxation times are reduced from the values for bulk water by an amount that is sample specific. The fat signal has a similar signature in all samples. It is characterized by a wide T2 distribution and a diffusion coefficient of 10(-11) m2/s for a diffusion time of 40 ms, determined by bounded diffusion in the fat globules of 3 microm diameter.

Fixed and pulsed gradient diffusion methods in low-field core analysis.

We review diffusion-weighted relaxation protocols for two-dimensional diffusion/relaxation time (D, T(2)) distributions and their application to fluid-saturated sedimentary rocks at low fields typical of oil-well logging tools (< or = 2 MHz for 1H). Fixed field gradient (FFG) protocols may be implemented in logging tools and in the laboratory; there, pulsed field gradient (PFG) protocols are also available. In either category, direct or stimulated echoes may be used for the diffusion evolution periods. We compare the results of several variant FFG and PFG protocols obtained on liquids and two contrasting sedimentary rocks. For liquids and rocks of negligible internal gradients (g(int)), results are comparable, as expected, for all the studied protocols. For rocks of strong g(int), protocol-dependent artifacts are seen in the joint (D, T2) distributions, consistent with the effects of the internal fields. For laboratory petrophysics, the PFG methods offer several advantages: (a) significantly improved signal-to-noise ratio and acquisition times for repetitions over many samples; (b) freedom from heteronuclear contamination when fluorinated liquids are used in core holders; and (c) a palette of variants--one comparable with the FFG--for the study of rocks of significant g(int). Given suitable hardware, both PFG and FFG methods can be implemented in the same bench-top apparatus, providing a versatile test bed for application in a petrophysical laboratory.

Probing short length scales with restricted diffusion in a static gradient using the CPMG sequence.

We experimentally verify a new method of extracting the surface-to-volume ratio (S/V) of porous media with diffusion NMR. In contrast to the widely used pulsed field gradient (PFG) technique, which employs the stimulated echo coherence pathway, we use here the direct Carr-Purcell-Meiboom-Gill (CPMG) path. Even for high echoes, which exhibit ample attenuation due to diffusion in the field gradient, the relevant ruler length for the direct pathway is fixed by the diffusion length during a single inter-pulse spacing. The direct path, therefore, is well suited for probing shorter length scales than is possible with the conventional approach. In our experiments in a low-field static-gradient system, the direct CPMG pathway was found to be sensitive to structure an order of magnitude smaller than accessible with the stimulated-echo pathway.

Short-time restricted diffusion in a static gradient and the attenuation of individual coherence pathways.

We experimentally explore some of the implications of a recent theoretical study [J. Magn. Reson. 64 (2003) 145] for the measurement of restricted diffusion in connected porous media in a static gradient. In particular, we examine how restriction affects the short-time attenuation of different coherence pathways, all excited with the same sequence of slice-selective radiofrequency (RF) pulses, and how the various pathways make the transition to the long-time or tortuosity regime. We confirm that every pathway contains equivalent diffusional information and, for short times, yields the surface-to-volume ratio (S/V) of the confining space. We find also, in agreement with the theoretical predictions, that different pathways are controlled by different time scales and, thus, exhibit different sensitivity to restriction. This property might be exploited when designing optimal sequences to study restricted motion.