Emulation of petroleum well-logging D-T2 correlations on a standard benchtop spectrometer

An experimental protocol is described that allows two-dimensional (2D) nuclear magnetic resonance (NMR) correlations of apparent diffusion coefficient D_app and effective transverse relaxation time T_2,eff to be acquired on a bench-top spectrometer using pulsed field gradients (PFG) in such a manner as to emulate D_app − T_2,eff correlations acquired using a well-logging tool with a fixed field gradient (FFG). This technique allows laboratory-scale NMR measurements of liquid-saturated cored rock to be compared directly to logging data obtained from the well by virtue of providing a comparable acquisition protocol and data format, and hence consistent data processing. This direct comparison supports the interpretation of the well-logging data, including a quantitative determination of the oil/brine saturation. The D − T₂ pulse sequence described here uses two spin echoes (2SE) with a variable echo time to encode for diffusion. The diffusion and relaxation contributions to the signal decay are then deconvolved using a 2D numerical inversion. This measurement allows shorter relaxation time components to be probed than in conventional diffusion measurements. A brief discussion of the numerical inversion algorithms available for inverting these non-rectangular data is included. The PFG-2SE sequence described is well suited to laboratory-scale studies of porous media and short T₂ samples in general.     

MRI study of Fickian, case II and anomalous diffusion of solvents into hydroxypropylmethylcellulose

Magnetic resonance imaging was used to investigate the diffusion and swelling processes of a hydroxypropylmethylcellulose (HPMC) matrix. Polymer in the form of a cylinder was hydrated in a water solvent with pH 2, 7, and 12 at 37 °C and monitored at equal intervals on a Bruker Avance 300 MHz spectrometer. The spatially resolved spin-spin relaxation times and spin densities together with the change in the dimension of the glass core of the polymer were determined for the HPMC tablets as a function of hydration times. FromT ₂ parameters, the solvent molecule mobility within the gel layer of the HPMC was estimated. All studied parameters allow the determination of the diffusion of the solvent into the HPMC matrix as Fickian diffusion for alkaline solvents, case II for acidic solvent, and anomalous diffusion for neutral solvent.     

Vortex Excitations Above Tc in the Cuprate Superconductor Bi2Sr2Ca2Cu3O10 as Revealed by ESR

Using electron spin resonance (ESR) technique we have obtained data evidencing the existence of magnetic vortices in high-temperature superconductors at temperatures above the critical one T _c. We have studied magnetic excitations in Bi₂Sr₂Ca₂Cu₃O₁₀ single crystals above T _c with the method of surface spin decoration. The surface layer of diphenylpicrylhydrazyl was used as a sensitive probe of magnetic field distortions. The temperature dependence of the ESR signal parameters has indicated that far above T _c the magnetic flux of a sample is affected by the superconducting order parameter fluctuations while close to T _c its changes are due to vortex-type excitations.     

Influence of magnetic impurities on proton spin relaxation of water in clay

The¹H nuclear magnetic spin relaxation of water in slurry of kaolin clay was investigated in the presence of magnetite (black iron oxide, Fe₃O₄) at 0.2 T and room temperature. The water spectra at high magnetite contents showed two different resonances, presumably from surface-associated water and free interstitial water. The difference in observed resonance frequencies increased as much as 200 ppm with increasing magnetite content. The apparent nuclear magnetic resonance intensity decreased biexponentially as a function of magnetite added. The observedT ₂^* values at low magnetite contents were in accordance with the predicted values from the resonance intensities and the estimated magnetic susceptibilities. TheT ₁ relaxation was multiexponential in character, so a uniform penalty program was used for the analysis of distribution. At 0.2 T for¹H, kaolin slurry containing less than 5.5 ppm magnetite did not differ significantly from magnetite-free clay in the longitudinal relaxation rates of water. However, higher concentrations of magnetite produced features in theT ₁ distribution significantly different from those of magnetite-free clay. TheT ₂ could be approximated by monoexponential relaxation, probably because the fast-decaying components relaxed before they could be recorded. The apparent transverse relaxation ratesR ₂ increased linearly as a function of magnetite content. On the basis of the comparison of spin-echo and Carr-Purcell-Meiboom-Gill data, an empirical relation was derived to describe the signal loss due to diffusion. It can be expressed by a power function of magnetite amount, which is multiplied by the sum of volume-dependent and volume-independent terms.     

Offset Profiles of Selective Pulses in Isotopically Labeled Macromolecules

The experimental verification of offset profiles and calibration of selective pulses in NMR is usually carried out with doped water samples but not under conditions typical of macromolecules with shortT₂, longT₁, and possibly homo- and heteronuclear couplings. A new method for selective excitation in isotopically labeled macromolecules is shown to be particularly suited to this purpose. This is illustrated for a backbone amide resonance in a sample of¹⁵N-labeled human ubiquitin.     

NMR relaxation study of avocado quality

Four nuclear magnetic resonance relaxation protocols are investigated as potential candidates for off-line and on-line determination of avocado maturity. Two-dimensionalT ₁-T ₂ andT ₂-D correlation spectroscopy provides the most information but is only suitable for off-line quality control. The CPMGT ₂ spectrum gives avocado oil content but requires intensive data processing. Suppression of the tissue water signal byT ₁-Null methods is shown to be unreliable but a new, single-shot pulse sequence which uses diffusive attenuation to suppress the tissue water is shown to give a good correlation with oil content and is suitable for both off-line and on-line implementation.     

Vibrational relaxation in liquids

A new theory is presented for vibrational energy relaxation in a liquid. It is shown that a vibrationally excited probe molecule relaxes through interaction with the density fluctuations in the surrounding solvent fluid. This interaction occurs through a potential V(k), which is expressed in terms of the intermolecular force between the excited probe molecule and the surrounding fluid molecules. By assuming spherically symmetric solvent particles the T ₁ energy relaxation time for direct V-T processes is related to the translational dynamic structure factor for the fluid S(k, ω_v), evaluated at the vibrational resonance frequency. It is shown that this is described by gas-like particle motions on a very short distance scale corresponding to k vectors lying well beyond the first or second peaks of the fluid structure factor S(k). Such motions can be pictured as high-frequency, short-distance distortions of the local equilibrium configuration of the solvent particles around the probe. T ₁ ^-1 is found to be proportional to ρ_e T ^1/2 ω_v ^-3. The V-V energy exchange relaxation time is also calculated. This is found to be proportional to S(k, ω′) evaluated at a frequency ω′, corresponding to the vibrational energy missmatch. An energy gap law for the V-V process is derived.     

Stimulated Echoes and Spin Echoes. Simultaneous Determination of T2, Diffusion Coefficient,and RF Homogeneity

By comparing information encoded in multiple signals it is possible to measure several sample-dependent parameters in a single experiment with the advantages that the measurements are less susceptible to changes in the sample over the course of an experiment and the total experiment time is reduced. An imaging sequence is presented that allows simultaneous determination of the spatial variation in RF field strength, T₂ relaxation rate, and a combination of T₁ and diffusion coefficient. This sequence can be extended to provide information on other parameters such as chemical shift or flow.     

Compensation Effect for Grain Boundary Diffusion in a Bicrystalline Experiment

The paper is devoted to the problem of the compensation effect for grain boundary (GB) diffusion, i.e. the linear dependence of the pre-exponential factor of the GB diffusion coefficient on the activation energy. Specific features of GB diffusion as a thermally activated process namely, the influence of segregation factor, K, and variation of the GB width, d, on the diffusion rate are discussed. A special diffusion experiment was designed to estimate the contribution of the separate component parts of the triple product, KdD_GB (D_GB is the GB diffusion coefficient). The experiment was performed with Al bicrystals. The variation of the GB width d, and a value of the segregation factor K, due to GB structure change are estimated. It is concluded that D_GB is the main GB structure-sensitive parameter in the triple product. This circumstance allows us to consider the GBs in Al bicrystals as a series of uniform objects and to describe the kinetics of GB diffusion in terms of the compensation temperature T_c and a “barrier” phase. The value of T_c for GB diffusion of Zn and Ge in Al bicrystals is practically the same and equals 709 and 706 K, respectively. The character of the “barrier” phase is discussed.     

EPR studies on aqueous sucrose solutions using (Cu(H2O)6)2+ spin probe

EPR investigations using Cu²⁺ ion as a probe have been performed on supersaturated sucrose solution with percent concentration c = 66 as a function of temperature T, and at room temperature as a function of c. The motionally averaged spectrum of [Cu(H₂O)₆]²⁺ was used to monitor the changes in intermolecular interactions that occur as a function of [c, T]. A drastic increase in the line width, symptomatic of increase in the rotational correlation time of [Cu(H₂O)₆]²⁺, is observed between 293 and 288 K. The motionally averaged spectrum disappears below 281 K. The motionally averaged spectrum is also absent in the room temperature spectra of the solution with c= 85. Even in the [c, T] range where [Cu(H₂O)₆]² is found to be nearly static, these molecules appear to have an orientational fluctuation manifesting in the m ₁ dependence of the line width of the parallel component.     

Mechanisms of bulk diffusion at “high” and “low” temperatures

A phenomenological model has been proposed for bulk self-diffusion and diffusion of interstitial atoms in the ranges of high (T > T _D) and low (T < T _D) temperatures (where T _D is Debye temperature). It has been shown that the mechanisms of diffusion at high and low temperatures differ significantly. In the high-temperature range, the diffusion is provided by fluctuations, which can be described in terms of local melting, i.e., the formation of a “liquid diffusion channel.” In the low-temperature range, when melting for some reasons is hindered, the diffusion is due to the fluctuation formation of a “hollow diffusion channel.” The calculation of the activation energies of these processes in the case of self-diffusion agrees well with the experiment in the temperature range T > T _D and has demonstrated that the activation energy increases significantly at T < T _D. The calculation of the activation energy for diffusion of interstitial atoms in bcc metals agrees well with the experiment in the entire temperature range and provides an explanation of the decrease in the activation energy of diffusion at low temperatures.     

Homogeneous FID signals in polypyrroles:T 1-estimate from a two-pulse sequence in homogeneous systems

Several experiments using pulse electron spin resonance (ESR) equipment reveal that homogeneous free induction decay (FID) signals are given by electron spins in polypyrrole (PPy). FID signals obtained from PPy are accurately fitted via single-exponential curves, thus indicating that PPy can be used as a standard sample for several experiments with pulse ESR. We particularly pay attention to the nutation phenomena resulting from two-pulse irradiation (θ-t−2θ-t) in the homogeneous systems. The analysis by the vector model suggests that the nutation curves are affected by spin-lattice relaxation. Such a tendency is actually observed for two types of PPy used as examples ofT ₁ >T ₂ andT ₁ ≈T ₂. Thus the fitting over the nutation curve can be utilized for estimatingT ₁. We particularly point out that such a procedure can be advantageously performed for electron spins with a short spin-lattice relaxation time.     

London field penetration in heavy fermion superconductors

We present results of a series of high resolution, low fielddc-magnetization measurements on the heavy fermion superconductors UPt₃, UBe₁₃, U_1–x Th _X Be₁₃ and CeCu₂Si₂, from which values of the magnetic penetration depth can be extracted. A study of the temperature variation reveals aT ² power law in all cases. This can not be reconciled with a BCS-like isotropic energy gap but may be explained by the presence of low energy quasiparticle states inside the gap. In the case of very pure superconductors, one such possibility is the assumption of point-nodes in the gap function. We argue, however, that an interpretation in terms of resonant impurity scattering in various anisotropic superconducting states is more likely to explain a broad range of experimental data. The results on differently oriented single crystals of UBe₁₃ and UPt₃ reveal no pronounced anisotropy related to the crystal lattice. Absolute values of atT=0 are deduced by a novel method in which the field is first screened out from the sample by means of an evaporated superconducting film (of lowerT _c ). Above this lowerT _c the sudden penetration of field into the sample can then be measured absolutely.     

Spatial Heterogeneity Length Scales in Carbonate Rocks

Spatially resolved distributions of T ₂ relaxation times in carbonate rocks are measured with slice-selective multiple spin echo magnetic resonance imaging to study the length scales of heterogeneity in these samples. Single-voxel Carr–Purcell–Meiboom–Gill decays are fit to double exponential functions, and the results of those fits are combined into a histogram. We describe a novel qualitative method of assessing the importance of different length scales of heterogeneity, involving comparing various aspects of these histograms to the full-core T ₂ distributions. Using this technique, it is found that almost all individual voxels relax not only with more than one time constant but indeed with a range of relaxation times that approximates the full breadth of relaxation times for the entire core, indicating significant subvoxel heterogeneity. In addition, different voxels are found to exhibit relaxation times that differ by orders of magnitude, indicating significant heterogeneity between the scale of a voxel (1 mm) and that of the entire core (several centimeters). These results reflect the importance of a broad range of length scales of heterogeneity in these carbonate rocks. Authors' address: Yi-Qiao Song, Schlumberger-Doll Research, 36 Old Quarry Road, Ridgefield, CT 06877, USA     

Investigation of phase transition mechanisms of CsH3(SeO3)2 single crystals by observation of nuclear magnetic resonance

The relaxation times of the ¹H and ¹³³Cs nuclei in CsH₃(SeO₃)₂ crystals were investigated using FT NMR. The ¹³³Cs spectrum does change from seven resonance lines to one resonance line near T_m (=350 K). The presence of only one ¹³³Cs signal is due to the liquid state resulting from the melting of the crystal. The variation in the separation of the ¹³³Cs resonance lines with temperature indicates that the EFG at the Cs sites produced by the (SeO₃)²⁻ groups varies with temperature, which in turn means that the atoms neighboring ¹³³Cs are displaced. And, the T₁ for ¹³³Cs is very long and undergoes significant changes near T_m. The change in the temperature dependence of T₁ at T_m for the ¹³³Cs nuclei coincides with the melting temperature. These results are compared with those obtained for MH₃(SeO₃)₂ (M=Na, K, and Cs) crystals.     

Influence of isotopic substitution on the diffusion and thermal diffusion coefficient of binary liquids

The mutual mass diffusion coefficient (D) and the thermal diffusion coefficient ( D _T) of the liquids acetone, benzene, benzene-d ₁, benzene-d ₃, benzene-d ₅, benzene-d ₆, benzene- ¹³C₆, n-hexane, toluene, 1, 2, 3, 4-tetrahydronaphtalene, isobutylbenzene, and 1, 6-dibromohexane in protonated and perdeuterated cyclohexane have been measured with a transient holographic grating technique at a temperature of 25 ^°C. The mass diffusion coefficient shows a pronounced concentration dependence. Perdeuteration of cyclohexane only leads to marginal changes of the mass diffusion coefficient. The Stokes-Einstein equation describes the limiting tracer diffusion coefficients well if the solute molecule is smaller than the solvent. It is not capable to describe the small isotope effect of a few percent. On the other hand, the isotope effect, which is independent of concentration, is in agreement with the Enskog theory, that does not provide the absolute value of the mass diffusion coefficient of the liquid mixtures. The thermal diffusion coefficient of all the binary mixtures shows a moderate and almost linear concentration dependence. Its isotope effect, which is the change of D _T upon deuteration of cyclohexane, varies with mole fraction. The thermophoretic force acting on any tracer molecule in cyclohexane changes by the same amount when cyclohexane is perdeuterated, irrespective of the magnitude of the thermophoretic force before deuteration. This change of the thermophoretic force is equal but of opposite sign to the difference between the thermophoretic forces acting on cyclohexane and perdeuterated cyclohexane as tracers in any of the above liquids.     

Calculation of Irreducible Water Saturation (S wirr) from NMR Logs in Tight Gas Sands

It is difficult to calculate irreducible water saturation (S _wirr) from nuclear magnetic resonance (NMR) logs in tight gas sands due to the effect of diffusion relaxation on the NMR T ₂ spectrum at present. By combining with classical Timur and Schlumberger—Doll Research (SDR) models, a novel model of calculating S _wirr is derived. The advantage of this novel model is that S _wirr can be calculated without a T ₂ cutoff, and all input information can be acquired from NMR logs accurately. With the calibration of 36 core samples, which were drilled from Xujiahe Formation in Bao-jie region of Triassic, Sichuan basin, southwest China, the values of these statistic model parameters are defined. Field examples of tight gas sands show that the proposed model is reliable. The S _wirr calculated with the proposed model match well with core analyzed results both in tight gas formations and water-saturated layers, the absolute error is in the range of ±4%. The calculated results by using 20.75 ms as the T ₂ cutoff are accurate in water-saturated layers but are overestimated in gas-bearing intervals. Defining 33 ms as the T ₂ cutoff is unusable both in gas-bearing and water layers.     

Comparison of methods for calculating turbulent diffusion coefficients

Different methods for calculating the turbulent diffusion coefficient D _T of a passive scalar impurity in an infinite homogeneous isotropic stationary turbulent medium are examined. The values of D _T calculated by these methods are compared for two limiting types of turbulence, viz., turbulence with a δ-function spectrum and turbulence with a Kolmogorov-type spectrum. The temporal dependence of the velocity correlators is assumed to be exponential. It is shown that the most accurate method is based on the use of the solution of the nonlinear equation for the averaged Green’s function with consideration of the contribution from the four-point turbulent velocity correlators. A comparison with the results of other methods that are simpler from the mathematical standpoint shows that some of them also permit the calculation of D _T with relatively good accuracy. Zh. éksp. Teor. Fiz. 111, 871–881 (March 1997)     

Anisotropic rotational diffusion model calculations of spin-rotation interaction in fluids of asymmetric-top molecules

The spin-lattice relaxation time, T ₁, due to the spin-rotation interaction in fluids of asymmetric-top molecules are calculated by using the rotational diffusion equation of Favro. In the rotational diffusion model, T ₁ is expressed in terms of three principal rotational diffusional constants. The results of the present calculation should aid interpretations of the experimental T ₁ data of fluids of asymmetric-top molecules.     

Molecular motion in liquid benzene by nuclear magnetic resonance

The proton spin-lattice relaxation time, T ₁, has been measured for a series of mixtures of benzene in perdeuterobenzene for the liquid in equilibrium with its vapour over the temperature range from below the normal freezing point up to the critical temperature. The two contributions to T ₁ due to interactions within the molecule (T _{1 intra}) and between molecules (T _{1 inter}) have been separated and are found to be very different in magnitude and in variation with temperature. The variation and magnitude of T _{1 inter} correlates well with other translational motion dependent properties such as self diffusion and viscosity. The correlation of T _{1 intra} with other re-orientation dependent properties such as deuteron T ₁ and Rayleigh scattering is poor.

The observed variation in T _{1 intra} and in particular the broad maximum at higher temperatures is then interpreted as due to a combination of dipolar and spin-rotation effects. This interpretation results in good agreement between the activation energies for re-orientational molecular motion deduced from proton T ₁ and deuteron T ₁. It supports the Hubbard theory for the relation between the dipolar and spin-rotation correlation times τ_d and τ_sr. It gives a rough value, 3·8 kc/s, for the spin-rotation interaction constant for protons in benzene. Reasonable values for τ_d and τ_sr are predicted and for all temperatures τ_sr < τ_d as expected.

There is clearly a considerable difference between the re-orientational and translational motion of the molecules in liquid benzene but the exact nature of the difference cannot be elucidated.