Velocity imaging by ex situ NMR

A pulsed field gradient stimulated spin-echo NMR sequence is combined with imaging methods to spatially resolve velocity distributions and to measure 2D velocity maps ex situ. The implementation of these techniques in open sensors provides a powerful non-invasive tool to measure molecular displacement in a large number of applications inaccessible to conventional closed magnets. The method is implemented on an open tomograph that provides 3D spatial localization by combining slice selection in the presence of a uniform static magnetic field gradient along the depth direction with pulsed field gradients along the two lateral directions. Different pipe geometries are used to demonstrate that the sequence performs well even in the extremely inhomogeneous B0 and B1 fields of these sensors.     

A rapid measurement of flow propagators in porous rocks

NMR flow propagators have been obtained for brine flowing through Bentheimer sandstone using the rapid DiffTrain pulse sequence. In this way, 8 flow propagators at different observation times Delta were acquired in 67 mins, compared to 7 h for the same measurements implemented with conventional pulsed field gradient (PFG) sequences. DiffTrain allows this time saving to be achieved through the acquisition of multiple displacement probability distributions over a range of Delta in a single measurement. If only the propagator moments are required, this experiment time can be further reduced to 9 mins through appropriate sparse sampling at low q values. The propagator moments obtained from DiffTrain measurements with dense and sparse q-space sampling are shown to be equivalent to those obtained from conventional PFG measurements.     

Diffusion studies in confined nematic liquid crystals by MAS PFG NMR

Pulsed field gradient (PFG) NMR and magic-angle spinning (MAS) NMR have been combined in order to measure the diffusion coefficients of liquid crystals in confined geometry. Combination of MAS NMR with PFG NMR has a higher spectroscopic resolution in comparison with conventional PFG NMR and improves the application of NMR diffusometry to liquid crystals. It is found that the confinement of the liquid crystal 5CB in porous glasses with mean pore diameters of 30 and 200 nm does not notably change its diffusion behavior in comparison with the bulk state.     

A cumulant analysis for non-Gaussian displacement distributions in Newtonian and non-Newtonian flows through porous media

We use displacement encoding pulsed field gradient (PFG) nuclear magnetic resonance to measure Fourier components S(q) of flow displacement distributions P(zeta) with mean displacement (zeta) for Newtonian and non-Newtonian flows through rocks and bead packs. Displacement distributions are non-Gaussian; hence, there are finite terms above second order in the cumulant expansion of ln(S(q)). We describe an algorithm for an optimal self-consistent cumulant analysis of data, which can be used to obtain the first three (central) moments of a non-Gaussian P(zeta), with error bars. The analysis is applied to Newtonian and non-Newtonian flows in rocks and beads. Flow with shear-thinning xanthan solution produces a 15.6+/-2.3% enhancement of the variance sigma(2) of displacement distributions when compared to flow experiments with water.     

Sizing of emulsion droplets under flow using flow-compensating NMR-PFG techniques

Using the nuclear magnetic resonance (NMR) pulsed field gradient (PFG) technique, it is possible to determine the size distribution of emulsion droplets. This method is extended so that the same measurements can be performed in the presence of flow. The resultant flow-compensating NMR-PFG technique is used to determine the oil droplet-size distribution of an oil-in-water emulsion flowing in a narrow tube at various flow rates. Comparison with the nonflowing oil droplet-size distribution enables the effect of velocity shear on the oil droplet-size distribution to be quantified.     

Microscopic displacement imaging with pulsed field gradient turbo spin-echo NMR

We present a pulse sequence that enables the accurate and spatially resolved measurements of the displacements of spins in a variety of (biological) systems. The pulse sequence combines pulsed field gradient (PFG) NMR with turbo spin-echo (TSE) imaging. It is shown here that by ensuring that the phase of the echoes within a normal spin-echo train is constant, displacement propagators can be generated on a pixel-by-pixel basis. These propagators accurately describe the distribution of displacements, while imaging time is decreased by using separate phase encoding for every echo in a TSE train. Measurements at 0.47 T on two phantoms and the stem of an intact tomato plant demonstrate the capability of the sequence to measure complete and accurate propagators, encoded with 16 PFG steps, for each pixel in a 128 x 128 image (resolution 117 x 117 x 3,000 microm) within 17 min. Dynamic displacement studies on a physiologically relevant time resolution for plants are now within reach.     

Applications of fast diffusion measurement using Difftrain

Novel applications of fast self-diffusion measurement are presented. Difftrain (Diffusion train), which uses successive stimulated echoes from a single excitation pulse where a portion of the available magnetisation is recovered for each echo, is used to measure self-diffusion by varying the observation time. It is applied to produce the droplet size distribution of an oil-in-water emulsion in less than 4s. This is verified by comparison with the droplet size distribution produced by a standard pulsed field gradient (PFG) technique. Difftrain is also extended to enable the application of incremental gradients, in addition to varying the observation time. This is used to produce propagators or displacement probabilities of water flowing through a packed bed for a range of 16 observation times in under 10 min. Again verification is provided by acquisition of the same propagators using a conventional PFG technique.     

Electric field driven flow in natural porous media

Electric fields were applied to fluid-saturated packed sand beds (0.23+/-0.03 mm average pore diameter), and the effects on the mobility of the water molecules were monitored using stimulated echo (STE) and pulsed field gradient (PFG) experiments. The mean flow velocity, averaged over the entire sample, is expected to vanish in closed systems, but the PFG and time dependent signal decay was enhanced beyond the effects of thermal diffusion, due to velocity dispersion. The internal flow generated by the electric field was shown to be fully time-reversible upon inverting the electric field polarity (for total flow times of up to 0.4s), a strong indication that the NMR detected displacements were mainly due to electro-osmotic flow (EOF). However, a comparison of the velocity dispersion for different electrolyte concentrations showed that the measured effect scaled with the applied power VI (V = voltage, I = electric current), rather than with the voltage alone, contrary to the prediction of the basic model for EOF in a single capillary channel.     

Spatially resolved emulsion droplet sizing using inverse Abel transforms

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) is well established as a tool for determining emulsion droplet-size distributions via measurement of restricted self-diffusion. Most measurements made to date have not been spatially resolved, but have measured an average size distribution for a certain volume of emulsion. This paper demonstrates a rapid method of performing spatially resolved, restricted diffusion measurements, which enables emulsion droplet sizing to be spatially resolved as a function of radius in cylindrical geometries or pipes. This is achieved by the use of an Abel transform. The technique is demonstrated in various annular systems containing two emulsions, with different droplet-size distributions, and/or a pure fluid. It is also shown that by modifying the pulse sequence by the inclusion of flow-compensating magnetic field gradients, the technique can measure spatially resolved droplet-size distributions in flowing emulsions, with potential applications in spatially resolved on-line droplet-size analysis.     

PFG NMR measurements of flow through porous media: effects of spatial correlations of the magnetic field and the velocity field

Used for a long time for diffusion studies, PFG NMR techniques are now widely used to study flow through porous media. We discuss here the effects of the magnetic field inhomogeneities and the finite gradient pulse duration in this case. We propose a statistical model based on spatial correlations of the magnetic field and velocity field and as far as we can, we draw practical conclusions on the PFG NMR measurements conditions.     

Rapid surface-to-volume ratio and tortuosity measurement using Difftrain

Analysis of diffusion measurements as a function of observation time (Delta), to calculate surface-to-volume ratios (S/V) and tortuosities (kappa), is a useful tool in the characterisation of porous media using NMR. However, using conventional pulsed field gradient (PFG) measurements, this requires long total experiment times (typically hours). Here, we show how the rapid diffusion measurement pulse sequence, Difftrain, can be used to provide the required experimental data much more rapidly (typically within minutes) with a consequential reduction in total experiment time of typically over an order of magnitude. Several novel modifications to the Difftrain pulse sequence are also presented to tailor it to this particular application; these include a variable delay between echoes (to ensure optimal echo position with respect to Delta) and a variable tip angle for the refocusing pulse (to ensure optimal use of available signal). Difftrain is applied to measure both S/V and kappa for a model glass bead pack; excellent agreement is found with both a conventional PFG measurement and with a bulk gravimetric measurement of S/V.     

Enhanced (13)C PFG NMR for the study of hydrodynamic dispersion in porous media

PFG NMR methods are frequently used as a means of probing both coherent and incoherent molecular motions of fluids contained within heterogeneous porous media. The time scale over which molecular displacements can be probed in a conventional PFG NMR experiment is limited by the relaxation characteristics of (1)H - the nucleus that is typically observed. In multiphase systems, due to its sensitivity to susceptibility gradients and interactions with surfaces,(1)H signal is frequently characterized by rapid T(1) and T(2) relaxation. In this work, a heteronuclear approach to PFG NMR is demonstrated which allows the study of molecular displacement over extended time scales (and, consequently, length scales) by exploiting the longer relaxation time of (13)C. The method presented employs the DEPT technique of polarization transfer in order to enhance both the sensitivity and efficiency of (13)C detection. This hybrid coherence transfer PFG technique has been used to acquire displacement propagators for flow through a bead pack with an observation time of up to 35 s.     

Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios

By evaluating the spin echo attenuation for a generalized 13-interval PFG NMR sequence consisting of pulsed field gradients with four different effective intensities (F(p/r) and G(p/r)), magic pulsed field gradient (MPFG) ratios for the prepare (G(p)/F(p)) and the read (G(r)/F(r)) interval are derived, which suppress the cross term between background field gradients and the pulsed field gradients even in the cases where the background field gradients may change during the z-store interval of the pulse sequence. These MPFG ratios depend only on the timing of the pulsed gradients in the pulse sequence and allow a convenient experimental approach to background gradient suppression in NMR diffusion studies with heterogeneous systems, where the local properties of the (internal) background gradients are often unknown. If the pulsed field gradients are centered in the tau-intervals between the pi and pi/2 rf pulses, these two MPFG ratios coincide to eta=G(p/r)/F(p/r)=1-8/[1+(1/3)(delta/tau)(2)]. Since the width of the pulsed field gradients (delta) is bounded by 0< or =delta< or =tau, eta can only be in the range of 5< or =-eta< or =7. The predicted suppression of the unwanted cross terms is demonstrated experimentally using time-dependent external gradients which are controlled in the NMR experiment as well as spatially dependent internal background gradients generated by the magnetic properties of the sample itself. The theoretical and experimental results confirm and extend the approach of Sun et al. (J. Magn. Reson. 161 (2003) 168), who recently introduced a 13-interval type PFG NMR sequence with two asymmetric pulsed magnetic field gradients suitable to suppress unwanted cross terms with spatially dependent background field gradients.     

Fast measurements of average flow velocity by Low-Field ¹H NMR

In this paper, we describe a method for measuring the average flow velocity of a sample by means of Nuclear Magnetic Resonance. This method is based on the Carr-Purcell-Meiboom-Gill (CPMG) sequence and does not require the application of any additional static or pulsed magnetic field gradients to the background magnetic field. The technique is based on analyzing the early-time behavior of the echo amplitudes of the CPMG sequence. Measurements of average flow velocity of water are presented. The experimental results show a linear relationship between the slope/y-intercept ratio of a linear fit of the first echoes in the CPMG sequence, and the average flow velocity of the flowing fluid. The proposed method can be implemented in low-cost Low-Field NMR spectrometers allowing a continuous monitoring of the average velocity of a fluid in almost real-time, even if the flow velocity changes rapidly.     

D-T2二维核磁共振脉冲序列及反演方法改进设计

面对日益复杂的勘探对象, D-T₂二维核磁共振技术在实际应用中面临无法兼顾扩散系数测量范围和横向弛豫分辨率的困境. 脉冲序列作为D-T₂二维核磁共振数据采集的核心技术, 其性能优劣直接影响应用效果, 在综合对比PFG, STE-PFG, BP-PFG、改良式CPMG, 扩散编程, 多回波间隔CPMG脉冲序列性能的基础上, 有效融合脉冲梯度场、恒定梯度场D-T₂脉冲序列的优点, 本文提出一种基于脉冲梯度场的双变量、两窗口D-T₂脉冲序列改进设计. 针对两个窗口的D-T₂二维核磁共振数据反演, 为突破现有反演方法无法兼顾反演精度和解谱效率的瓶颈, 本着第二个窗口回波信号为主、第一个窗口回波信号为辅的原则, 本文提出一种同时使用两个窗口数据参与解谱的联合TSVD反演方法. 气水、油水、稠油、油气水模型不同信噪比条件下的数值模拟结果表明, 本文提供的D-T₂改进脉冲序列达到了平衡扩散系数测量范围和横向弛豫分辨率的设计要求, 本文提供的联合TSVD反演方法也有效平衡了反演精度要求和解谱效率. 文中的D-T₂改进脉冲序列及联合TSVD反演方法在复杂油气藏流体识别和产能预测中具有广泛的应用前景, 可为促进国内D-T₂二维核磁共振岩心分析技术的发展提供有利条件.     

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.     

Velocity and diffusion imaging in dynamic NMR microscopy

The imposition of resolution gradients in a pulsed-gradient spin-echo (PGSE) NMR sequence induces motionally dependent phase and amplitude modulation in the image, a technique which we have termed dynamic NMR microscopy. Fourier analysis of this modulation gives a dynamic displacement profile for each pixel which can then be analyzed to obtain velocity and diffusion maps. The application of this method at high spatial resolution is motivated by a desire to measure vascular flow in living plants and variations in molecular self-diffusion under the influence of velocity shear in narrow capillaries. The theory of dynamic NMR microscopy is presented and potential artifacts discussed, including the effect of slice selection gradients, PGSE gradient nonuniformity, and specific problems associated with the measurement of self-diffusion in the presence of velocity gradients. It is demonstrated that a double-echo PGSE pulse sequence can be used to restore coherent phase shifts associated with steady-state flow, and examples of self-diffusion maps and signed velocity maps from sequences of phase-encoded images obtained by projection reconstruction are given. This method has been applied at 20,um transverse resolution in laminar capillary flow.     

Velocity distribution of slow fluid flows in bentheimer sandstone: An NMRI and propagator study

This work addresses the special problems of measuring flow velocity distributions in rock by NMR methods. Specifically, these problems are to measure very slow flows as well as flows in the presence of background magnetic field gradients caused by heterogeneities of the rock. We modify a stimulated echo sequence for use in diffusion measurements, in order to maximize velocity sensitivity and minimize background gradient effects. Accurate velocity images of Soltrol 220 oil in sandstone were made for flow velocities up to around 0.04 mm/s with an imager that does not have echo-planar capability. Accurate velocity distributions by the propagator method can be obtained even with stimulated echo delays of 1.9 T₁ by phase cycling combined with suitable crusher gradients.     

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.     

Structure-mobility relations of molecular diffusion in nanoporous materials

Depending on the measuring conditions, pulsed field gradient (PFG) NMR measurements of molecular diffusion in beds of nanoporous particles may provide information about the propagation rate of guest molecules in both the intra- and interparticle spaces, as well as through the interface between them. Recent progress in both PFG NMR instrumentation and computational techniques have initiated studies of novel aspects in each of these areas, which are reviewed in this communication. They concern the possibility of multicomponent diffusion measurements with ultra-high pulsed field gradients, the peculiarities of molecular diffusion in channel networks, the determination of the surface-to-volume ratio of nanoporous particles and the dependence of the tortuosity factor of long-range diffusion on the diffusion mode in the intercrystalline space.