(T2,D)二维核磁共振测井混合反演方法与参数影响分析

一维核磁共振(1D NMR)测井技术在流体识别中具有一定的局限性.二维核磁共振(2D NMR)测井能同时测量到多孔介质中横向弛豫时间(T₂)和扩散系数(D)等信息,利用这两个参数区分流体性质,较一维核磁共振测井技术具有明显的优越性.针对梯度场下的2D NMR测井弛豫机理和数学模型,提出了适用于求解大型稀疏矩阵方程的反演方法-基于非负最小二乘法(LSQR)和截断奇异值分解(TSVD)法的混合算法.为验证方法的有效性,先根据多回波观测模式合成回波串数据,然后再用混合反演算法进行反演,反演得到横向弛豫时间(T₂)和扩散系数(D),并构建T₂-D二维谱图.结果对比表明,该混合反演算法得到的T₂-D二维谱与流体模型一致性好,计算精度均比单一反演方法有较大改善,表明该混合反演方法可用于油气储集层2D NMR测井的反演和流体识别.此外,分别对油水同层和气水同层模型进行了正演模拟和反演实验, 系统考察了不同磁场梯度、不同回波间隔组合对反演效果的影响,为2D NMR参数设计提供依据.     

核磁共振共轭梯度解谱方法研究

核磁共振（NMR）解谱技术是核磁共振资料应用的基础和关键.本文将核磁共振解谱的混定线性反演问题转化为求目标函数极小值的最优化问题,然后利用共轭梯度算法具有二次终止性、收敛速度快的特点解决上述最优化问题.将该方法应用于无噪声和不同信噪比的理论数据解谱以及岩心NMR实验解谱并与真谱及实验室国外软件解谱结果对比表明：在信噪比SNR≥5时解谱结果和真谱符合得很好,谱线光滑连续;随着信噪比的降低对初始点的要求随之提高;两块岩心解谱结果与实验室结果符合得很好,利用解谱结果计算的核磁孔隙度与实验室氦孔隙度绝对误差分别为0.78%和0.57%.因此,本文方法有效、实用,具有较强的抗噪能力,对初始点的要求不高,能够应用于生产和科研实践中.     

核磁共振双TW测井数据联合反演与流体识别

针对核磁共振测井双TW观测数据分析和流体识别的需要,研究了基于全局搜索的遗传算法和局部搜索的最小二乘法的联合反演算法,实现了核磁共振双TW观测数据处理.首先,研究了饱和油气水岩石物理模型的核磁共振双TW观测模式的测井响应机理;然后,利用全局搜索性能优良的遗传算法, 对核磁共振回波差数据进行了反演,计算出了流体的核磁弛豫性质及其体积;最后,以遗传算法的反演结果为初值, 利用阻尼最小二乘方法对双TW回波串进行更精细的反演,计算出了双TW的T₂分布、孔隙度和流体饱和度.理想模型的合成数据和实际测井资料应用表明,遗传算法与最小二乘方法相结合是一种行之有效的联合反演方法,能较好地实现核磁共振测井双TW观测数据的处理和流体评价.     

Permeability Prediction for Low Porosity Rocks by Mobile NMR

Estimating permeability from NMR well logs or mobile NMR core scanner data is an attractive method as the measurements can be performed directly in the formation or on fresh cores right after drilling. Furthermore, the method is fast and non-destructive. Compared to T ₁ relaxation times, commonly measured T ₂ distributions are influenced by external and internal magnetic field gradients. We performed two-dimensional T ₁ and T ₂ relaxation experiments on samples of Rhaetian sandstone, a rock with low porosity and small pore radii, using a mobile NMR core scanner which operates within a nearly homogeneous static magnetic field. Because small pore sizes are associated with high internal magnetic field gradients, standard methods from NMR logging in the oil industry cannot be applied for accurate permeability prediction. Therefore, a new model theory was developed, which describes the pore radius dependence of the surface relaxivity ρ ₂ by both an analytical and a more practical empirical equation. Using corrected ρ ₂ values, permeability can be predicted accurately from the logarithmic mean of the T ₂ distribution and the physically based Kozeny-Carman equation. Additional core plug measurements of structural parameters such as porosity, permeability, specific inner surface area and pore radius distributions supported the NMR results.     

核磁共振多回波串联合反演方法

提出一种核磁共振多回波串数据联合反演方法,分别对核磁共振孔隙度测量的两组回波串数据、变等待时间多回波串数据以及变回波间隔多回波串数据进行了处理.结果表明,这样处理得到的一维核磁共振T₂分布不但连续,而且能够揭示短横向弛豫组分的细微特征,提高了核磁共振孔隙度的精度.处理变等待时间或变回波间隔下的多回波串数据,可以得到孔隙流体的 (T₂, T₁)或(T₂, D) 二维核磁共振分布图.与一维核磁共振T₂分布相比,二维核磁共振提高了识别流体的效果.     

Improved Interpretation of Nuclear Magnetic Resonance T1 and T2 Distributions for Permeability Prediction: Simulation of Diffusion Coupling for a Fractal Cluster of Pores

NMR relaxometry is a powerful tool for inferring porosity and permeability data. In practice, measured magnetization decay curves are inverted for relaxation time distributions. Subsequently, one presumes a linear relationship between the pore radius distribution and the T ₁ and T ₂ distribution, for longitudinal and transverse magnetization, respectively. The fundamental equations used are based on a pore model, in which pores are assumed to be isolated from each other with respect to the NMR process and have smooth walls. The present study is based on a geometrical pore space model with connected pores and structured pore walls. The physical processes of surface relaxation, irreversible dephasing of magnetic spins and diffusive proton exchange between pores, are described by a system of differential equations. The solution yields a set of exponential functions representing the relaxation time distribution. We describe the difference between the distributions obtained for diffusion coupling and for isolated pores. With diffusion coupling on, the spectral width of the T ₁ distribution is strongly reduced, which indicates that the influence of large and small radii according to the T ₁-pore radius relationship is mixed to some extent. For a fractal pore space structure, where large pores are surrounded by adjacent minor pores, the T ₁ distribution does not resolve these substructures. Nevertheless, permeability values calculated from the logarithmic mean relaxation time T _1,LM are quite the same for diffusion coupling and for isolated pores. The T ₂ distribution for diffusion coupling is little constricted and gives a better resolution of the pore wall structures than the corresponding T ₁ distribution. The permeability values from T ₂ distributions agree with the values from longitudinal magnetization, provided that we use a corrected relaxation time T _2,corr, accounting for the dependence of the surface relaxivity ρ ₂ on pore radius. The study shows that radius distributions calculated from a T ₁ and from a T ₂ distribution differ from one another and both present an altered image of the true pore radius distribution. In practice, this has no serious influence on estimating permeability of medium- to high-permeability sandstones with the currently applied methods. The presented methodology of calculating the NMR response of pore space models with diffusion coupling may facilitate understanding porosity-permeability relationships of different rock types such as carbonate rocks with micro-porosity.     

基于SVD和BRD的二维核磁共振测井正则化反演算法研究

二维核磁共振能从"弛豫-扩散"两个维度上展现流体性质,在识别稠油储层方面具有理论优势,是当前核磁共振测井技术的研究热点.本文深入研究二维核磁共振测井原理,系统分析CPMG-DE脉冲序列测量扩散系数与弛豫时间的方法,结合核磁共振二维谱数理模型,提出一种基于SVD和BRD的正则化反演算法.该算法通过SVD压缩数据,采用带非负约束的Tikhonov正则化方法求解流体"弛豫-扩散"分布,并基于BRD算法迭代确定最佳正则化因子.模拟实验与数值分析表明,该算法无需先验信息、运算效率高、相对误差小,在原始数据信噪比低至50时,仍可有效获取流体(T₂,D)二维分布.在二维核磁共振测井数据实时解释应用中,该方法较传统反演算法(如TSVD)具有较大优势.同时,在自主研发的核磁共振测井仪测量CuSO₄溶液(T₂,D)分布的实验显示,本文设计算法对弛豫时间和扩散系数的反演误差分别仅为2%和4%,较TSVD算法有较大改善.     

Modeling rock permeability from NMR relaxation data by PLS regression

This study explores the application of the partial least squares regression (PLSR) technique to rock permeability prediction from nuclear magnetic resonance (NMR) relaxation data. A total of 68 Brazilian sandstone cores selected from reservoirs and outcrop analogs were fully saturated and analyzed by NMR. The permeability of the cores ranged from 0.007 to 9,800 mD. From their ¹H transverse relaxation times (T₂) measured at 2 MHz, two PLSR models were developed for the relaxation spectra and the raw relaxation curves. Both models led to more uniform and accurate predictions (RMSE = 0.47 and 0.50 log mD, respectively) compared with the classical Kenyon model (RMSE = 0.78 log mD).     

Biofilm Detection in a Model Well‐Bore Environment Using Low‐Field NMR

This research addresses the challenges of the lack of non‐invasive methods and poor spatiotemporal resolution associated with monitoring biogeochemical activity central to bioremediation of subsurface contaminants. Remediation efforts often include growth of biofilm to contain or degrade chemical contaminants, such as nitrates, hydrocarbons, heavy metals, and some chlorinated solvents. Previous research indicates that nuclear magnetic resonance (NMR) is sensitive to the biogeochemical processes of biofilm accumulation. The current research focuses on developing methods to use low‐cost NMR technology to support in situ monitoring of biofilm growth and geochemical remediation processes in the subsurface. Biofilm was grown in a lab‐scale radial flow bioreactor designed to model the near wellbore subsurface environment. The Vista Clara Javelin NMR logging device, a slim down‐the‐borehole probe, collected NMR measurements over the course of eight days while biofilm was cultivated in the sand‐packed reactor. Measured NMR mean log T₂ relaxation times decreased from approximately 710 to 389 ms, indicating that the pore environment and bulk fluid properties were changing due to biofilm growth. Destructive sampling employing drop plate microbial population analysis and scanning electron and stereoscopic microscopy confirmed biofilm formation. Our findings demonstrate that the NMR logging tool can detect small to moderate changes in T₂ distribution associated with environmentally relevant quantities of biofilm in quartz sand.     

（T2,D）二维核磁共振测井识别储层流体的方法

当地层孔隙中油气和水同时存在时,在核磁共振T₂分布上不同流体信号往往重叠,很难有效识别.本文采用改变回波间隔测量多组自旋回波串序列实现了（T₂,D）二维核磁共振方法,为有效识别储层流体提供了基础.通过数值模拟系统研究了（T₂,D）方法在不同储层、不同测量信噪比以及不同外加磁场梯度条件下识别流体的效果.结果表明：（T₂,D）方法识别中、低黏度油层具有优势,随着信噪比增加和外加磁场梯度加大,分辨油和水的效果将变好.在气层,对磁场梯度有一定要求,并且,测量数据的信噪比越高,分辨气与水的效果越好,当测量数据信噪比低于70时（T₂,D）方法在气层可能失效.在2MHz共振频率下,利用MARAN核磁共振岩芯分析仪器,对含顺磁性物质的饱和流体岩样进行了实验测量,验证了（T₂,D）方法的有效性.     

Hydraulic Conductivity Calibration of Logging NMR in a Granite Aquifer,Laramie Range,Wyoming

In granite aquifers, fractures can provide both storage volume and conduits for groundwater. Characterization of fracture hydraulic conductivity (K) in such aquifers is important for predicting flow rate and calibrating models. Nuclear magnetic resonance (NMR) well logging is a method to quickly obtain near-borehole hydraulic conductivity (i.e., K_NMR) at high-vertical resolution. On the other hand, FLUTe flexible liner technology can produce a K profile at comparable resolution but requires a fluid driving force between borehole and formation. For three boreholes completed in a fractured granite, we jointly interpreted logging NMR data and FLUTe K estimates to calibrate an empirical equation for translating borehole NMR data to K estimates. For over 90% of the depth intervals investigated from these boreholes, the estimated K_NMR are within one order of magnitude of K_FLUTe. The empirical parameters obtained from calibrating the NMR data suggest that “intermediate diffusion” and/or “slow diffusion” during the NMR relaxation time may occur in the flowing fractures when hydraulic aperture are sufficiently large. For each borehole, “intermediate diffusion” dominates the relaxation time, therefore assuming “fast diffusion” in the interpretation of NMR data from fractured rock may lead to inaccurate K_NMR estimates. We also compare calibrations using inexpensive slug tests that suggest reliable K_NMR estimates for fractured rock may be achieved using limited calibration against borehole hydraulic measurements.     

基于Backus-Gilbert理论的孔隙介质核磁共振弛豫反演

孔隙介质核磁共振(NMR)弛豫数据的多指数反演在NMR测井和岩心分析中均非常重要.本文基于Backus-Gilbert(BG)理论,提出一种NMR弛豫多指数反演的新方法.从解的非唯一性出发,不仅构造出一种解估计,更重要的是评价各种可接受的解估计,通过引入解估计分辨率和解估计方差对解进行评价,找出最佳折中解.通过算例,比较了新方法与传统正则化方法的效果,结果表明新方法具有明显优越性,在低信噪比条件下解稳定.最后分析了新方法的影响因素.     

核磁共振测井探测岩石内部磁场梯度的方法

岩石内部磁场梯度对核磁共振测井横向弛豫T₂分布有较大的影响.本文提出了一种利用自旋回波脉冲序列探测岩石内部磁场梯度的二维核磁共振方法,发展了相应的反演方法,得到了含顺磁性物质的饱和水砂岩和泥质砂岩的内部磁场梯度分布规律.结果表明,随顺磁物质含量的增加,岩石内部磁场梯度增大.含顺磁物质的饱和水砂岩颗粒均匀,不含粘土矿物,内部磁场梯度呈单峰分布特征.含绿泥石粘土矿物的饱和水泥质砂岩,T₂分布呈双峰特征,束缚水峰明显,小孔短T₂对应的梯度值大于大孔长T₂对应的梯度值.当绿泥石含量小于15%时,随绿泥石含量的增加,对应束缚水峰的短T₂组分明显增多,T₂分布展宽;当绿泥石含量大于15%以后,较大的岩石内部磁场梯度使短弛豫信息衰减迅速,表现出随绿泥石含量的增加,短T₂组分减少,T₂分布变窄.     

Estimation of the apertures of water-saturated fractures by nuclear magnetic resonance well logging

Fracture aperture is an important transport property in subsurface hydrology because it influences well productivity and the volume of the water resource. Nuclear magnetic resonance (NMR) well logging measures the hydrogen‐bearing fluid molecules in porous or fractured strata, and the NMR signal intensity increases with the amount of fluid in the sensed region of the NMR sonde. Fluid confined in a large fracture of >>0.2 mm in aperture has T2 (i.e. spin‐spin relaxation time) values as long as those of the bulk fluid. The bulk‐fluid porosity (i.e. porosity calculated using this long T2 component in a T2 histogram data) increases linearly with aperture. Therefore, NMR logging enables quantitative estimation of fracture apertures of >>0.2 mm using the bulk‐fluid porosity data if the calibration of the NMR sonde is performed adequately. We applied NMR logging to a borehole in a Holocene andesite lava at Sumikawa, Japan, to estimate the aperture of open fractures within the lava. A test well of 100 m depth and 20 cm diameter, filled with bentonite drilling mud, was scanned with an NMR sonde to obtain a profile of the porosity and the T2 histogram of the andesite. The bulk‐fluid porosity was calculated from the T2 histogram data, as the porosity at which the T2 value is larger than or equal to a threshold T2 of bulk bentonite mud. The bulk‐fluid porosity of a specific inclined fracture responsible for the total loss of circulation at 61.2 m depth during drilling was calculated assuming a threshold or T2 cut‐off of 33 ms, and again for a cut‐off of 100 ms. Calibration of the NMR sensor in a laboratory and measurement of the fracture dip angle by electrical microimaging logging enabled us to estimate the fracture aperture as 1.7 cm, assuming a T2 cut‐off of 33 ms, or 1.6 cm for a T2 cut‐off of 100 ms. The method of aperture determination described in this study is independent of fluid species and lithology, and is applicable to various hydrogen‐bearing borehole fluids (clean water, mud and oil) and geological settings.     

Nuclear magnetic resonance <Emphasis Type="Italic">T</Emphasis><Subscript>2</Subscript> spectrum: multifractal characteristics and pore structure evaluation

Pore structure characteristics are important to oil and gas exploration in complex low-permeability reservoirs. Using multifractal theory and nuclear magnetic resonance (NMR), we studied the pore structure of low-permeability sandstone rocks from the 4th Member (E_S4) of the Shahejie Formation in the south slope of the Dongying Sag. We used the existing pore structure data from petrophysics, core slices, and mercury injection tests to classify the pore structure into three categories and five subcategories. Then, the T₂ spectra of samples with different pore structures were interpolated, and the one- and three-dimensional fractal dimensions and the multifractal spectrum were obtained. Parameters α (intensity of singularity) and f (α) (density of distribution) were extracted from the multifractal spectra. The differences in the three fractal dimensions suggest that the pore structure types correlate with α and f (α). The results calculated based on the multifractal spectrum is consistent with that of the core slices and mercury injection. Finally, the proposed method was applied to an actual logging profile to evaluate the pore structure of low-permeability sandstone reservoirs.     

Self-diffusion studies of pore fluids in unconsolidated sediments by PFG NMR

The self-diffusion of water and hexadecane in medium and coarse sands from glacial sand deposits in central Germany were investigated by pulsed field gradient nuclear magnetic resonance (PFG NMR). Due to the restriction of the diffusion path at the pore/grain interface, the measured apparent self-diffusion coefficients (D(Δ)) in the pore space depend on the observation time (Δ) in the PFG NMR experiment. Although the bulk self-diffusion coefficients of water and hexadecane differ by about one order of magnitude, the apparent self-diffusion coefficients in the pore space obey the same characteristic time-behaviour, which depends only on geometrical properties of the pore system. Using the “short-time diffusion” model, surface-to-volume (S/V) ratios and inherent self-diffusion coefficients (D₀) of the pore fluids were extracted from these diffusion measurements. The S/V ratios obtained are independent of the pore fluid used and agree with known geometrical properties of the sand grains. Moreover, the D₀ values are consistent with the corresponding bulk self-diffusion coefficients measured separately. In contrast to these results of PFG NMR, simultaneous investigations of longitudinal (T₁) nuclear magnetic relaxation reveal that the relaxation time of the pore fluid is a less suitable parameter for a quantitative estimation of geometrical properties of the pore/grain interface in these unconsolidated sediments since it depends on chemical properties of the fluid/grain interface.     

Hydraulic Conductivity from Nuclear Magnetic Resonance Logs in Sediments with Elevated Magnetic Susceptibilities

This study examined the application of slim-hole nuclear magnetic resonance (NMR) tools to estimate hydraulic conductivity (K_NMR) in an unconsolidated aquifer that contains a range of grain sizes (silt to gravel) and high and variable magnetic susceptibilities (MS) (10⁻⁴ to 10⁻² SI). A K calibration dataset was acquired at 1-m intervals in three fully screened wells, and compared to K_NMR estimates using the Schlumberger-Doll research (SDR) equation with published empirical constants developed from previous studies in unconsolidated sediments. While K_NMR using published constants was within an order of magnitude of K, the agreement, overprediction, or underprediction of K_NMR varied with the MS distribution in each well. An examination of the effects of MS on NMR data and site-specific empirical constants indicated that the exponent on T_2ML (n-value in the SDR equation, representing the diffusion regime) was found to have the greatest influence on K_NMR estimation accuracy, while NMR porosity did not improve the prediction of K. K_NMR was further improved by integrating an MS log into the NMR analyses. A first approach detrended T_2ML for the effects of MS prior to calculating K_NMR, and a second approach introduced an MS term into the SDR equation. Both were found to produce similar refinements of K_NMR in intervals of elevated MS. This study found that low frequency NMR logging with short echo times shows promise for sites with moderate to elevated MS levels, and recommends a workflow that examines parameter relationships and integrates MS logs into the estimation of K_NMR.     

Geomagnetotail dynamics: Different types of equilibriums and transitions between them

Two time scales are distinguished in the geomagnetotail dynamics. The small scale (T ₁) corresponds to disturbances propagating in the tail lobes, which have a relatively strong magnetic field and low plasma density. The larger scale (T ₂) corresponds to plasma motions in the plasma sheet and has a relatively weak magnetic field and a relatively higher density. A disturbance, which is initiated by a localized burst of magnetic reconnection and appears in the geomagnetotail on the time scale T ₁, generates the upset of equilibrium in the plasma sheet zones with intermediate spatial dimensions (about R _E). The theoretical considerations and numerical simulation indicate that the relaxation process, which subsequently proceeds on the larger time scale (T ₂), results in the appearance of extremely thin embedded current sheets and in the generation of fast plasma flows. This process gives an effective mechanism by which the magnetic energy stored in the geomagnetotail is transformed into the plasma flow kinetic energy. Such fast flows can also generate eddy plasma motions on smaller spatial scales. On the one hand, fast MHD components of this process carry a disturbance in other plasma sheet zones, where new magnetic reconnection bursts can originate at a large distance from the zone of an initial nonlinear disturbance. As a result, new recurrent processes of relaxation originate on the T ₂ time scale. Alternation originating in such a way is apparently the characteristic feature of eddy disturbances actually observed in the plasma sheet.     

Bootstrap Calibration and Uncertainty Estimation of Downhole NMR Hydraulic Conductivity Estimates in an Unconsolidated Aquifer

Characterization of hydraulic conductivity (K) in aquifers is critical for evaluation, management, and remediation of groundwater resources. While estimates of K have been traditionally obtained using hydraulic tests over discrete intervals in wells, geophysical measurements are emerging as an alternative way to estimate this parameter. Nuclear magnetic resonance (NMR) logging, a technology once largely applied to characterization of deep consolidated rock petroleum reservoirs, is beginning to see use in near‐surface unconsolidated aquifers. Using a well‐known rock physics relationship—the Schlumberger Doll Research (SDR) equation—K and porosity can be estimated from NMR water content and relaxation time. Calibration of SDR parameters is necessary for this transformation because NMR relaxation properties are, in part, a function of magnetic mineralization and pore space geometry, which are locally variable quantities. Here, we present a statistically based method for calibrating SDR parameters that establishes a range for the estimated parameters and simultaneously estimates the uncertainty of the resulting K values. We used co‐located logging NMR and direct K measurements in an unconsolidated fluvial aquifer in Lawrence, Kansas, USA to demonstrate that K can be estimated using logging NMR to a similar level of uncertainty as with traditional direct hydraulic measurements in unconsolidated sediments under field conditions. Results of this study provide a benchmark for future calibrations of NMR to obtain K in unconsolidated sediments and suggest a method for evaluating uncertainty in both K and SDR parameter values.     

Comparative study of models for predicting permeability from nuclear magnetic resonance (NMR) logs in two Chinese tight sandstone reservoirs

Based on the analysis of mercury injection capillary pressure (MICP) and nuclear magnetic resonance (NMR) experimental data for core plugs, which were drilled from two Chinese tight sandstone reservoirs, permeability prediction models, such as the classical SDR, Timur-Coates, the Swanson parameter, the Capillary Parachor, the R10 and R35 models, are calibrated to estimating permeabilities from field NMR logs, and the applicabilities of these permeability prediction models are compared. The processing results of several field examples show that the SDR model is unavailable in tight sandstone reservoirs. The Timur-Coates model is effective once the optimal T _2cutoff can be acquired to accurately calculate FFI and BVI from field NMR logs. The Swanson parameter model and the Capillary Parachor model are not always available in tight sandstone reservoirs. The R35 based model cannot effectively work in tight sandstone reservoirs, while the R10 based model is optimal in permeability prediction.