Estimation of Permeability by Integrating Nuclear Magnetic Resonance (NMR) Logs with Mercury Injection Capillary Pressure (MICP) Data in Tight Gas Sands

It has been a great challenge to determine permeability in tight gas sands due to the generally poor correlation between porosity and permeability. The Schlumberger Doll Research (SDR) and Timur–Coates permeability models, which have been derived for use with nuclear magnetic resonance (NMR) data, also lose their roles. In this study, based on the analysis of the mercury injection experiment data for 20 core plugs, which were drilled from tight gas sands in the Xujiahe Formation of central Sichuan basin, Southwest China, two empirical correlations between the pore structure index ( $ \sqrt {{K \mathord{\left/ {\vphantom {K \varphi }} \right. \kern-0em} \varphi }} $ , defined by the square root of the ratio of rock permeability and porosity) and the R ₃₅ (the pore throat radius corresponding to 35.0 % of mercury injection saturation), the pore structure index and the Swanson parameter have been developed. To consecutively estimate permeability in field applications, based on the study of experimental NMR measurements for 36 core samples, two effective statistical models, which can be used to derive the Swanson parameter and R ₃₅ from the NMR T ₂ logarithmic mean value, have been established. These procedures carried out on the experimental data set can be extended to reservoir conditions to estimate consecutive formation permeability along the intervals with which NMR logs were acquired. The processing results of several field examples using the proposed technique show that the classification scale models are effective only in tight gas reservoirs, whereas the SDR and Timur–Coates models are inapplicable. The R ₃₅-based model is of significance in thin sands with high porosity and high permeability, but the predicted permeability curves in tight gas sands are slightly lower. In tight gas and thin sands, the Swanson parameter model is all credible.     

NMR in well logging and hydrocarbon exploration

Nuclear magnetic resonance (NMR) has become a versatile tool for the evaluation of underground hydrocarbon reservoirs. Formation attributes such as rock porosity and rock pore size distributions, as well as the relative concentrations of water, oil and gas, can be inferred from subsurface NMR. The hydrogen NMR signal encodes porosity as amplitude, pore sizes as relaxation times and fluid properties as a mixture of relaxation and diffusion rates. The paper describes the basic operating principles for NMR on cable (wireline), NMR on a drill string (logging-while-drilling) and NMR for downhole fluid sampling. The geometry of the borehole requires a magnet that projects its field into the surrounding rock, implying a grossly inhomogeneous field distribution. Experience shows that even under these circumstances, saturation-recovery and Carr-Purcell-Meiboom-Gill sequences can work well and yield meaningfulT ₁ andT ₂ information.     

Influential Factors of Internal Magnetic Field Gradient in Reservoir Rock and Its Effects on NMR Response

Nuclear magnetic resonance (NMR) plays a significant role in porous media analysis and petroleum exploration, but its response is significantly influenced by the internal magnetic field gradient in fluid saturated porous medium, which obviously limits the accuracy of rock core analysis and logging interpretation. The influential factors of the internal magnetic field gradient in formation and its influences on NMR response are studied in this paper, based on NMR mechanism through one- and two-dimensional core NMR experiments. The results indicate that the internal magnetic field gradient is positively correlated with the static magnetic field strength and the magnetic susceptibility difference between pore fluid and solid grains, while it presents negative correlation with pore radius. The internal magnetic field gradient produces an additional diffusion relaxation in hydrogen relaxation system and accelerates the attenuation of magnetization vector. As a result, T₂ spectrum shifts to the left and NMR porosity and diffusion coefficient of the fluid could be inaccurate. This research sets a foundation for the NMR porosity correction and fluid distribution on T₂-G maps based on the internal magnetic field gradient correction.     

岩心核磁共振实验对低孔低渗碳酸盐岩储层的适应性研究

低孔低渗碳酸盐岩储层矿物成分复杂、岩石骨架参数难以确定、储集空间类型多样、孔隙结构及孔渗关系复杂、常规测井曲线响应特征不明显,使其测井评价极其困难．本文利用核磁共振测井定量评价低孔低渗碳酸盐岩储层岩心的孔隙结构、计算储层参数．利用T₂谱分布曲线分析孔隙结构、计算T₂截止值;在此基础上计算岩心总孔隙度、有效孔隙度、束缚水孔隙度、渗透率等储层参数,并与常规岩心实验结果进行对比分析;最后,总结出核磁共振测井在低孔低渗储层中的应用优势与局限,为核磁共振测井评价模型的建立提供基础数据．     

Estimation of Saturation Exponent from Nuclear Magnetic Resonance (NMR) Logs in Low Permeability Reservoirs

The resistivity experimental measurements of 36 core samples, which were drilled from low permeability reservoirs of southwest China, illustrate that the saturation exponents are not agminate, but vary from 1.627 to 3.48; this leads to a challenge for water saturation estimation in low permeability formations. Based on the analysis of resistivity experiments, laboratory nuclear magnetic resonance (NMR) measurements for all 36 core samples, and mercury injection measurements for 20 of them, it was observed that the saturation exponent is proportional to the proportion of small pore components and inversely proportional to the logarithmic mean of NMR T ₂ spectrum (T _2lm). For rocks with high proportion of small pore components and low T _2lm, there will be high saturation exponents, and vice versa. The proportion of small pore components is characterized by three different kinds of irreducible water saturations, which are estimated by defining 30, 40 and 50 ms as T ₂ cutoffs separately. By integrating these three different kinds of irreducible water saturations and using T _2lm, a technique of calculating the saturation exponent from NMR logs is proposed and the corresponding model is established. The credibility of this technique is confirmed by comparing the predicted saturation exponents with the results from the core analysis. For more than 85 % of core samples, the absolute errors between the predicted saturation exponents from NMR logs and the experimental results are lower than 0.25. Once this technique is extended to field application, the accuracy of water saturation estimation in low permeability reservoirs will be improved significantly.     

Structural Nature of 7Li and 11B Sites by Static NMR and MAS NMR in Nonlinear Optical Material LiCsB6O10

The relationship between structure and nonlinear optical properties in LiCsB₆O₁₀ is characterized using single-crystal nuclear magnetic resonance (NMR) and magic-angle spinning (MAS) NMR. Although the quadrupole parameters for B(1) and B(2) sites were obtained using single-crystal NMR, the T ₁ values for these atomic sites could not be distinguished in this way. Thus, the structural nature of lithium and boron sites in LiCsB₆O₁₀ was investigated using MAS NMR. B(1) and B(2) sites could be distinguished based on the spectrum and T _1ρ obtained from ¹¹B MAS NMR. In addition, the T ₁ and T _1ρ values and activation energies for ⁷Li and ¹¹B are compared. No significant changes were seen in the T _1ρ at the lithium and boron nuclei in LiCsB₆O₁₀.     

Mechanical spectrum study of glass transition by a composite method

Normalized mechanical spectra of glycerol, 1,2-propanediol carbonate and poly(vinyl chloride)/di(2-ethyl-hexyl) phthalate (PVC/DOP) blends were studied in the temperature range from 100 to 300 K by a composite method. The dynamic glass transition was observed, which exhibits a peak of temperature-dependent loss modulus. The peak moves toward higher temperature with higher measuring frequency, which accords with the relaxation feature of the dynamic glass transition. Another characteristic temperature can be marked in the mechanical spectrum by the onset of storage modulus change, which is labeled as T_gm. T_gm is found to be nearly equal to the calorimetric glass transition temperature in glycerol, 1,2-propanediol carbonate and di(2-ethyl-hexyl) phthalate. As we expected, this onset temperature in the mechanical spectrum has an intimate relation with the calorimetric glass transition of materials, and it can be regarded as a representative when the calorimetric glass transition temperature is not available. Finally, normalized mechanical spectra of PVC/DOP blends with different PVC content were obtained and mechanical glass transition temperatures T_gm were determined.     

核磁共振T2谱换算孔隙半径分布方法研究

岩芯核磁共振T2谱和压汞分析数据均在一定程度上反映了岩石的孔隙结构特征,理论分析和二者频率分布图对比表明,这两组数据有较好的相关性,核磁共振T₂谱能够换算为反映岩石孔隙结构特征的孔隙半径分布图. 本文应用最大相关性原理、最小二乘法及插值算法等数学方法,给出了一个改进的将T2谱换算为孔隙半径分布图的实用有效新方法,求得了T2弛豫时间与岩芯孔隙半径r之间的换算系数C,计算过程中着重对比了T₂谱与压汞数据的主要分布区间,并考虑了压汞进汞饱和度小于100%对换算结果的影响. 天然砂岩岩芯核磁共振T₂谱换算为孔隙半径分布图的实际应用效果表明,着重对比T₂谱与压汞数据的主要分布区间,同时考虑压汞进汞饱和度小于100%对换算结果的影响是必要的,换算结果更加真实可信.     

Study on ethyl groups with two different orientations in [N(C2H5)4]2CuBr4

The crystal structure and phase transition temperature of [N(C₂H₅)₄]₂CuBr₄ are studied using X-ray diffraction and differential scanning calorimetry (DSC); measurements revealed a tetragonal structure and the two phase transition temperatures T_C of 204 K and 255.5 K. The structural geometry near T_C is discussed in terms of the chemical shifts for ¹H magic angle spinning (MAS) nuclear magnetic resonance (NMR) and ¹³C cross-polarization (CP)/MAS NMR. The two inequivalent ethyl groups are distinguishable by the ¹³C NMR spectrum. The molecular motions are discussed in terms of the spin–lattice relaxation times T_1ρ in the rotating frame for ¹H MAS NMR and ¹³C CP/MAS NMR. The T_1ρ results reveal that the ethyl groups undergo tumbling motion, and furthermore that the ethyl groups are highly mobile.     

Spectral shifts and spectral switches of elliptical Gaussian beam propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the spectrum of elliptical Gaussian beam (EGB) propagating through turbulent atmosphere can be derived analytically by tensor method. It can avoid time-consuming numerical integral that was commonly used in the previous study of spectral changes. Analytical results show that the on-axis normalized spectrum S(ω) of EGB propagating through turbulent atmosphere is different from the original spectrum S₀(ω) and there exist spectral shifts and spectral switches for EGB propagating through turbulent atmosphere. Besides, spectral shifts and spectral switches of EGB are closely related with the structure constant of the turbulent atmosphere, the beam parameters and the coordinate of observation point. Compared with the Gaussian beam, there are two spectral switches for EGB propagating through turbulent atmosphere.     

Proton dynamics in antiferroelectric CsH3(SeO3)2 single crystal investigated by 1H NMR measurements

¹H nuclear magnetic resonance (NMR) measurements have been performed to study the proton dynamics associated with the antiferroelectric transition of a hydrogen-bonded single crystal of CsH₃(SeO₃)₂. Herein, ¹H NMR spectrum, shift, linewidth, and spin-lattice relaxation rate 1/T₁ are measured in the temperature range of 80–296 K with the c-axis parallel to a magnetic field of ~4.85 T. The spectrum exhibits a composite structure with two narrow peaks at 296 K; at a low temperature, this structure evolves into a single broad shape with three humps. This complex shape and evolution are deconvoluted into five or six components based on the number of inequivalent and disordered hydrogen sites. By estimating the chemical shift and linewidth for each proton site, we identify all peaks. The spin-lattice relaxation recovery exhibits a double-exponential behavior with two relaxation times, short T_1S and extremely large T_1L. Both T_1S and T_1L follow Arrhenius behavior. From the respective 1/T₁(T), the activation energies for proton motion are measured to be small: 1.16 ± 0.1 and 0.83 ± 0.06 kJ/mol for T_1S and T_1L, respectively. While the static NMR data, chemical shift and linewidth, show no evidence for the transition, the dynamic data 1/T_1L highlights a clear increase across T_N = 145 K, which is possibly a signature of the transition.     

Quantitative NMR spin-lattice-relaxation imaging of brine in sandstone reservoir cores

Two- and three-dimensional quantitative, saturation-recovery, NMR imaging has been applied to two sandstone reservoir cores. M₀ and T₁ images of high quality have been obtained with reasonable data-acquisition and data-processing times. The T₁ and T₂ processes have been shown to be correlated; the variations of the parameters within the images and the differences between the bulk and image relaxation values are discussed. The results of a quantitative T₁ imaging experiment of a phantom are also presented in order to demonstrate the advantages of quantitative NMR imaging over standard bulk measurements.     

Comparison of the texture functions describing the grain alignment in NdFeB magnets

Two types of Gaussian distribution function (`θ type’ and `tan θ type') describing the degree of grain alignment in sintered NdFeB magnets have been compared in the distribution coefficient σ (or σ_g), the distribution probability P(θ) and the grain alignment dependence of coercivity. The results show that when the grain alignment is good (the ratio of remanence-to-saturation polarization J_r/J_s⩾0.90), σ(σ_g) and P(θ) for the two types of Gaussian functions have similar variation tendencies, the calculated values of normalized coercivity based on the starting field theory are basically the same and are consistent with experiments. When the grain alignment is not good (J_r/J_s⩾0.80), the variation tendencies of σ and P(θ) are different. In addition, according to `tan θ type’ Gaussian function, the theoretical values of the normalized coercivity based on the starting field theory are still consistent with the experiments, but according to `θ type’ Gaussian function, the theoretical values seriously deviate from the experiments. This means that the `tan θ type’ Gaussian function is a better texture function for describing the grain alignment.     

An NMR-Based Analysis of Soil–Water Characteristics

Both direct and indirect methods for determining soil–water characteristic curves rely on determination of some empirical coefficients, which may not necessarily represent real microscopic mechanisms. Proton nuclear magnetic resonance (NMR) is a powerful tool for investigating water content and their interaction with solid particles in porous media. The NMR technique is widely used in food science and petroleum. In the present study, proton NMR spin–spin relaxation time (T ₂) distribution measurement is integrated with a Tempe apparatus to characterize the hydraulic processes of unsaturated soils, shedding insights into the microscopic mechanisms of pore water distribution and migration in the soil during hydraulic cycles. It is revealed that during a drying process the drainage of pore water occurs sequentially from larger pores to smaller pores, whereas in a wetting process the water invades into the soil sequentially from smaller pores to larger pores. A new procedure is developed which can be used to determine the pore size distribution of the soil based on the NMR T ₂ distribution measurements; compared to the traditional methods, the new method is rapid and non-destructive. The new procedure is validated by comparing the new result with the measurement of the mercury intrusion porosimetry.     

NMR studies of magnetic properties in Heusler-type Mn 3 Si

In order to microscopically investigate the magnetic properties of both paramagnetic and antiferromagnetic phases in Mn₃Si (T _N?=?23 K), the ⁵⁵Mn NMR has been carried out at temperatures between 2.2 K and 300 K. The temperature dependences of the spectrum, Knight shift (or resonance frequency shift) and spin-lattice relaxation time T ₁ of ⁵⁵Mn NMR have been measured. In the paramagnetic phase, only one resonance spectrum can be obtained. The observed spectrum is identified to be a signal corresponding to the Mn(II) site. In the antiferromagnetic phase, two different spectra corresponding to the Mn(I) and Mn(II) sites are found at the resonance frequencies of 145 and 6 MHz, respectively, by the zero field NMR at 4.2 K. From these results, the internal magnetic fields on the ⁵⁵Mn(I) and ⁵⁵Mn(II) nuclei are found to be 13.6 and 0.6 T, respectively. According to the NMR results, the helical structure in incommensurate Mn spin states is better explained compared with the transverse sinusoidal structure.     

Light scattering from moving cluster walls in a model of displacive phase transitions

We calculated the spectrum of light scattered from moving cluster walls which were recently found to be important excitations for strongly anharmonic one-dimensional models exhibiting displacive phase transitions at T_c = 0. It is found that the scattering spectrum consists of a Gaussian central peak.     

<Superscript>1</Superscript>H NMR studies of cyclohexane confined in mesoporous solids: Melting point depression and pore size distribution

The pore size distributions of four controlled pore glasses and two silica gels with nominal diameters ranging from 6–24 nm were determined by measuring the¹H nuclear magnetic resonance (NMR) signal from the nonfrozen fraction of confined cyclohexane as a function of temperature, in steps of ca. 0.1–1 K. The intensity curves of the liquid component are well represented by a sum of two error functions. The mean melting point depression of cyclohexane confined in pores with radiusR follows the simplified Gibbs-Thompson equation δT=k _p/R with ak _p value of 72.4 Knm. To our knowledge, this is the first time that thek _p value of cyclohexane has been directly and accurately calibrated by NMR. As expected, thek _p value mainly determines the position of the pore size distribution curve, i.e., the mean pore radius. The overall pore size distributions determined by NMR are in reasonable agreement with the results specified by the manufacturer, or measured by us by the N₂ sorption technique. Although the melting point depression of confined cyclohexane is found to be less than previously assumed, this compound is still one of the most suitable candidates for NMR-based pore size determinations. However, pore sizes larger than approximately 50 nm in diameter will be difficult to determine accurately by NMR unless adsorbates undergoing larger melting point depressions than cyclohexane can be found.     

Nuclear magnetic relaxation,correlation time spectrum,and molecular dynamics in a linear polymer

The pulsed nuclear magnetic resonance (NMR) method at a proton frequency of 25 MHz at temperatures of 22–160°C is used to detect the transverse magnetization decay in polyisoprene rubbers with various molecular masses, to determine the NMR damping time T ₂, and to measure spin-lattice relaxation time T ₁ and time T _2eff of damping of solid-echo signals under the action of a sequence of MW-4 pulses modified by introducing 180° pulses. The dispersion dependences of T _2eff obtained for each temperature are combined into one using the temperature-frequency equivalence principle. On the basis of the combined dispersion dependence of T _2eff and the data on T ₂ and T ₁, the correlation time spectrum of molecular movements is constructed. Analysis of the shape of this spectrum shows that the dynamics of polymer molecules can be described in the first approximation by the Doi-Edwards tube-reptation model.     

Decoherence control mechanisms of a charged magneto-oscillator in contact with different environments

In this work, we consider two different techniques based on reservoir engineering process and quantum Zeno control method to analyze the decoherence control mechanism of a charged magneto-oscillator in contact with different type of environment. Our analysis reveals that both the control mechanisms are very much sensitive on the details of different environmental spectrum (J?(ω)), and also on different system and reservoir parameters, e.g., external magnetic field (r _c ), confinement length (r ₀), temperature (T), cut-off frequency of reservoir spectrum (ω _cut ), and measurement interval (τ). We also demonstrate the manipulation scheme of the continuous passage from decay suppression to decay acceleration by tuning the above mentioned system or reservoir parameters, e.g., r _c , r ₀, T and τ.