Pore size distributions and hydraulic conductivities of rocks derived from Magnetic Resonance Sounding relaxation data using multi-exponential decay time inversion

In hydrogeology there is a variety of empirical formulae available for determination of hydraulic conductivity of porous media, all based on the analysis of grain size distributions of aquifer materials. Sensitivity of NMR measurements to pore sizes makes it a good indicator of hydraulic conductivity. Analogous to laboratory NMR, Magnetic Resonance Sounding (MRS) relaxation data are of a multi-exponential (ME) nature due to the distribution of different pore sizes in an investigated rock layer. ME relaxation behaviour will also arise due to the superposition of NMR signals which originate from different layers. It has been shown, that both kinds of ME behaviour coexist in MRS and can principally be separated by ME inversion of the field data. Only a few publications exist that have proposed approaches to qualitatively and quantitatively estimate petrophysical parameters such as the hydraulic conductivity from MRS measurements, i.e. MRS porosity and decay times. The so far used relations for the estimation of hydraulic conductivity in hydrogeology and NMR experiments are compared and discussed with respect to their applicability in MRS. Taking into account results from a variety of laboratory NMR and MRS experiments mean rock specific calibration factors are introduced for a data-base-calibrated estimation of hydraulic conductivity when no on-site calibration of MRS is available. Field data have been analysed using conventional and ME inversion using such mean calibration values. The results for conventional and ME inversion agree with estimates obtained from well core analysis for shallow depths but are significantly improved using a ME inversion approach for greater depths.     

Inversion of resistivity in Magnetic Resonance Sounding

Magnetic Resonance Sounding (MRS, or Surface Nuclear Magnetic Resonance - SNMR) is used for groundwater exploration and aquifer characterization. Since this is an electromagnetic method, the excitation magnetic field depends on the resistivity of the subsurface. Therefore, the resistivity has to be taken into account in the inversion: either as a priori information or as an inversion parameter during the inversion process, as introduced in the presented paper. Studies with synthetic data show that water content and resistivity can be resolved for a low resistive aquifer even using only the amplitude of the MRS signal. However, the inversion result can be significantly improved using amplitude and phase of the MRS signal. The successful implementation of the inversion for field data shows that the resistivities derived from MRS are comparable to those from conventional geoelectric methods such as DC resistivity and transient electromagnetic. By having information about both the resistivity and the water content, MRS inversions give information about the quality of the water in the aquifer. This is of utmost interest in hydrogeological studies as this specific information cannot be determined solely by geoelectric measurements, due to the nonunique dependence of resistivity on water content and salinity.     

分层多指数磁共振弛豫信号反演方法研究

磁共振测深技术传统反演方法包括平滑反演和分块反演,通过分别获取初始振幅和平均弛豫时间构建地层含水量及有效孔隙度.然而,这些方法局限于单指数拟合方式,损失了大部分有效采集信息,受限于多孔地质环境解释,并在某些情况下无法刻画含水层清晰分界面.针对上述问题,本文建立了基于MRS全数据的多指数反演方法,依据全部采集时间下的有效信息,通过弛豫时间e指数分解,推导出新的磁共振正演核函数,结合泛函极小值方程,直接反演建立含水量,弛豫时间及地层深度三个重要参数关系,适用于复杂地质环境解释.为得到快速稳定的反演结果和更清晰的含水层分界面,本文借鉴分块反演思想,进一步构建了新的反演目标函数,利用基于不等式约束的空间信赖域算法进行优化,最终实现了一种基于分层反演与多指数结合的磁共振弛豫信号反演方法.模型数据以及实测算例表明该方法的效果和优势,并具备较高的计算效率,本研究为地面磁共振反演提供了一种新的思路与方法.     

地面磁共振测深分布式探测方法与关键技术

地面核磁共振方法(MRS)因具有对地下水探测定性、定量的特点而备受地球物理工作者关注.传统研究中,人们局限于一维探测方法,假设层状含水构造,导致复杂地质环境下难以确定井位、不均匀含水层小水体难以分辨的反演解释瓶颈.针对现有测量中的不足,本文提出了MRS二维分布式探测模式,依据激发场不均匀特性,定义了实际测量中的测线方位角α,推导了分布式接收线圈MRS响应核函数表达式,实现了二维正演计算,探索了α角与探测灵敏度之间的关系.在此基础上,首次将Occam方法用于MRS二维反演解释中,实现了磁共振断层成像MRT(magnetic resonance tomography).模型试算中,根据含水层位置以及环境噪声变化的磁共振响应,客观评价了分布式MRS探测适用范围.理论先行可推动仪器完善,本文通过分布式接收单元设计、接收线圈数量和匝数增加与调整、放大器参数自适应设置与矫正,成功研制了地面分布式磁共振探测系统,并进行了野外验证.本文的研究成果将为基岩裂隙水定位、堤坝渗漏灾害水源评价,喀斯特溶洞含水构造精确探测提供有力的科学支撑.     

多尺度孔隙岩石的核磁共振扩散耦合现象及其探测方法

油藏岩石的孔隙连通性是反映流体渗流难易程度的重要参数,对渗透率、有效孔隙度等岩石物理参数的评价具有重要作用.连通的孔隙中,核磁共振(NMR)弛豫的交换会产生扩散耦合现象,可作为孔隙连通性的表征和探测方法.本文提出利用横向弛豫T 2-T 2脉冲序列测量岩石的扩散耦合现象.运用随机游走方法模拟多孔岩石的核磁共振响应特征,分析扩散耦合的影响因素,推导表征扩散耦合强度的弛豫交换速率计算公式.结果表明:孔隙间的扩散耦合强度与T 2-T 2脉冲序列的混合时间呈正相关性,基于双孔弛豫交换模型推导的弛豫交换速率计算公式能够准确表征双尺度孔隙系统的扩散耦合强度.在孔隙尺寸不满足快扩散条件时,会出现与扩散耦合无关的非对角峰信号.针对含多类型孔隙的碳酸盐岩模型,随混合时间的增加,扩散耦合强度变大,一维T 2谱的形态畸变程度加重,在T 2-T 2二维谱中,代表微裂缝、粒间小孔、溶蚀大孔的信号能量变化趋势不同,反映不同类型孔隙间的连通性存在差异.本文的分析与讨论丰富了核磁共振弛豫在岩石物理性质评价中的应用方向,对利用核磁共振评价复杂孔隙岩石的孔隙结构和连通性提供了新思路和新方法.     

基于自适应遗传算法的MRS-TEM联合反演方法研究

地面磁共振法(MRS)因具有定性、定量分析地下水能力,而备受关注.传统磁共振地层含水量反演多采用均匀半空间模型,忽略电阻率分布信息对结果的影响.针对这一问题,本文基于多层电介质中磁共振响应理论,提出MRS与瞬变电磁(TEM)联合反演方法,通过电阻率分布信息对含水量反演过程的实时修正,提高了解释结果的准确度.反演算法采用自适应遗传算法(AGA)进行,基于繁殖规则,动态调整交叉概率和变异概率,解决了标准遗传算法易未成熟收敛而难以得到全局最优解问题.模型数据表明,含噪10%情况下,联合反演仍能较准确地反映地下含水单元模型结构,对比MRS单独反演优势明显.同时,内蒙古白旗野外观测数据联合反演结果与钻井资料基本一致,充分验证了AGA反演算法的实用性及MRS-TEM联合反演的实际意义.     

利用分段时频峰值滤波法抑制磁共振全波信号随机噪声

磁共振信号极其微弱,容易受到周围环境中各种电磁噪声干扰.其中随机噪声,由于频带宽、不规则、无规律、与有效信号混叠,难以抑制.近年来,采用数量级为10⁴~10⁵ Hz采样频率收录的全波磁共振信号,以其携带丰富全面的信息量,为数据处理及解释提供了更多的潜能.然而,只要随机噪声的幅度大于信号幅度,拟合得到的信号特征参数准确度就会降低.目前普遍采用的数据叠加方法仅能抑制部分随机噪声,且需要多次采集信号,探测效率低.本文针对全波磁共振信号采样点数多和信号非线性强的特点,提出采用分段时频峰值滤波（STFPF）法消噪,将全波磁共振信号分成若干段,编码为解析信号的瞬时频率,采用短窗长PWVD计算解析信号的时频分布,利用时频分布沿瞬时频率集中的特性,通过提取时频分布的峰值获得信号的无偏估计,达到抑制全波磁共振信号随机噪声的目的.为了验证消噪效果,与传统叠加法进行对比分析,仿真结果表明,对于单次采集信号,信噪比低至-5 dB时,STFPF方法依然能有效抑制信号中的随机噪声,消除随机噪声后信噪比提高23.19 dB,信号的初始振幅拟合误差为3.03%,平均横向弛豫时间拟合误差为2.7%,消噪效果优于传统叠加法,且由于无需多次采集磁共振信号,可有效提高探测效率.模型数据的反演解释进一步验证了STFPF方法的有效性,本文研究结果为实际数据处理奠定了良好的基础.     

Influence of pore size and geometry on peat unsaturated hydraulic conductivity computed from 3D computed tomography image analysis

In organic soils, hydraulic conductivity is related to the degree of decomposition and soil compression, which reduce the effective pore diameter and consequently restrict water flow. This study investigates how the size distribution and geometry of air‐filled pores control the unsaturated hydraulic conductivity of peat soils using high‐resolution (45 µm) three‐dimensional (3D) X‐ray computed tomography (CT) and digital image processing of four peat sub‐samples from varying depths under a constant soil water pressure head. Pore structure and configuration in peat were found to be irregular, with volume and cross‐sectional area showing fractal behaviour that suggests pores having smaller values of the fractal dimension in deeper, more decomposed peat, have higher tortuosity and lower connectivity, which influences hydraulic conductivity. The image analysis showed that the large reduction of unsaturated hydraulic conductivity with depth is essentially controlled by air‐filled pore hydraulic radius, tortuosity, air‐filled pore density and the fractal dimension due to degree of decomposition and compression of the organic matter. The comparisons between unsaturated hydraulic conductivity computed from the air‐filled pore size and geometric distribution showed satisfactory agreement with direct measurements using the permeameter method. This understanding is important in characterizing peat properties and its heterogeneity for monitoring the progress of complex flow processes at the field scale in peatlands. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

地下磁共振响应特征与超前探测

地下（矿井和隧道内）超前探测灾害水源是磁共振测深（Magnetic Resonance Sounding,MRS）方法应用的新领域,在地球物理方法中是一个难题.本文在地面磁共振探测理论的基础上,建立地下全空间模型,推导直立线圈的磁共振响应信号表达式,对比国际标准模型验证了数值计算的准确性.引入旋转系数矩阵,计算任意地磁场方向和线圈方向的激发场垂直分量.研究了磁共振响应信号与线圈法向偏角和倾角的关系,指出当线圈法向方向垂直于地磁场方向时,磁共振响应信号最大.同时,研究表明磁共振超前探测距离与激发脉冲矩和接收灵敏度紧密相关,激发脉冲矩越大,接收灵敏度越高,则超前探测距离越大,但存在极限距离.在地下线圈尺寸受限的情况下,为使检测信号灵敏度为5 nV时,超前探测距离达到30 m,提出了边长2 m线圈的匝数优化方案,共圈模式最少需要100匝,分离线圈模式最少需要10匝发射线圈和160匝接收线圈.仿真模型试验结果证明,随着噪声水平增大,磁共振超前探测距离和反演分辨率均减小.泽雅隧道探测实践表明,本文提出的地下空间磁共振理论在矿井和隧道环境中进行超前探测是可行的.     

球管孔隙模型的核磁共振(NMR)弛豫特征及应用

将岩石孔隙归结为由毛细管和球形孔组成的孔隙系统,提出孔隙球管孔隙模型. 岩石孔隙按大小分组后,每一组孔隙的氢核弛豫时间可以用球管孔隙模型计算. 将此弛豫时间作为反演T2分布的时间控制点,反演岩芯的核磁共振弛豫信号. 研究表明, T2分布与特定的孔隙结构相联系. 使用不同结构的球管孔隙模型,可以使反演T2分布最大限度地拟合弛豫信号,此时的球管模型以最近似的方式模拟了岩芯的孔隙结构. 使用球管模型对实验室核磁共振资料进行了处理,对比压汞分析得到毛管力分布数据,结果证明球管孔隙模型描述了岩石孔隙的弛豫特征,而且,岩石特定孔隙结构的弛豫特征与孔隙流体有关.     

油水双相饱和孔隙模型核磁特性理论研究

利用特征函数展开方法，给出了基于扩散效应的核磁共振Bloch控制方程的弛豫模式解表达式, 在此基础上分别给出了水饱和与油水双相饱和孔隙模型的核磁共振特性模拟结果. 结果表明，孔隙流体的核磁弛豫与孔隙大小、孔隙表面弛豫率、孔隙流体的扩散能力以及含油饱和度等有密切的关系. 对于水饱和孔隙，弛豫时间主要由孔隙大小控制. 当孔隙较大时，即使均匀大小孔隙，孔隙流体的弛豫也会表现为多指数弛豫. 而且最小模式弛豫时间与孔隙大小为非线性关系. 对于油水双相饱和孔隙，在孔隙较小时，含油饱和度对弛豫的影响主要表现在弛豫时间随含油饱和度的增加而线性减小；但在孔隙较大时，含油饱和度的增加对弛豫影响表现在两个方面，其一，孔隙水弛豫由多个弛豫模式控制逐渐转变为由最小弛豫模式控制；其二，孔隙水弛豫时间与含油饱和度表现为非线性关系. 对由实际岩芯抽象出的孔隙模型，采用本文获得的理论公式，在油水双相饱和时进行了正反演模拟. 计算结果与已有的实验结果较为一致.     

Understanding of hydraulic properties from configurations of stochastically distributed fracture networks

A systematic investigation of the effect of configurations of stochastically distributed fracture networks on hydraulic behaviour for fractured rock masses could provide either quantitative or qualitative correlation between the structural configuration of the fracture network and its corresponding hydraulic behaviour, and enhance our understanding of appropriate application of groundwater flow and contaminant transport modelling in fractured rock masses. In this study, the effect of block sizes, intersection angles of fracture sets, standard deviations of fracture orientation, and fracture densities on directional block hydraulic conductivity and representative elementary volume is systematically investigated in two dimensions by implementing a numerical discrete fracture fluid flow model and incorporating stochastically distributed fracture configurations. It is shown from this investigation that the configuration of a stochastically distributed fracture network has a significant quantitative or qualitative effect on the hydraulic behaviour of fractured rock masses. Compared with the deterministic fracture configurations that have been extensively dealt with in a previous study, this investigation is expected to be more practical and adequate, since fracture geometry parameters are inherently stochastically distributed in the field. Moreover, the methodology and approach presented in this study may be generally applied to any fracture system in investigating the hydraulic behaviours from configurations of the fracture system while establishing a ‘bridge’ from the discrete fracture network flow modelling to equivalent continuum modelling in fractured rock masses. Copyright © 2007 John Wiley & Sons, Ltd.     

Using data assimilation method to calibrate a heterogeneous conductivity field conditioning on transient flow test data

A data assimilation method is developed to calibrate a heterogeneous hydraulic conductivity field conditioning on transient pumping test data. The ensemble Kalman filter (EnKF) approach is used to update model parameters such as hydraulic conductivity and model variables such as hydraulic head using available data. A synthetical two-dimensional flow case is used to assess the capability of the EnKF method to calibrate a heterogeneous conductivity field by assimilating transient flow data from observation wells under different hydraulic boundary conditions. The study results indicate that the EnKF method will significantly improve the estimation of the hydraulic conductivity field by assimilating continuous hydraulic head measurements and the hydraulic boundary condition will significantly affect the simulation results. For our cases, after a few data assimilation steps, the assimilated conductivity field with four Neumann boundaries matches the real field well while the assimilated conductivity field with mixed Dirichlet and Neumann boundaries does not. We found in our cases that the ensemble size should be 300 or larger for the numerical simulation. The number and the locations of the observation wells will significantly affect the hydraulic conductivity field calibration.     

Estimation of anisotropic hydraulic conductivity using geophysical data in a coastal aquifer of Karnataka,India

Estimation of hydraulic parameters is essential to understand the interaction between groundwater flow and seawater intrusion. Though several studies have addressed hydraulic parameter estimation, based on pumping tests as well as geophysical methods, not many studies have addressed the problem with clayey formations being present. In this study, a methodology is proposed to estimate anisotropic hydraulic conductivity and porosity values for the coastal aquifer with unconsolidated formations. For this purpose, the one-dimensional resistivity of the aquifer and the groundwater conductivity data are used to estimate porosity at discrete points. The hydraulic conductivity values are estimated by its mutual dependence with porosity and petrophysical parameters. From these estimated values, the bilinear relationship between hydraulic conductivity and aquifer resistivity is established based on the clay content of the sampled formation. The methodology is applied on a coastal aquifer along with the coastal Karnataka, India, which has significant clayey formations embedded in unconsolidated rock. The estimation of hydraulic conductivity values from the established correlations has a correlation coefficient of 0.83 with pumping test data, indicating good reliability of the methodology. The established correlations also enable the estimation of horizontal hydraulic conductivity on two-dimensional resistivity sections, which was not addressed by earlier studies. The inventive approach of using the established bilinear correlations at one-dimensional to two-dimensional resistivity sections is verified by the comparison method. The horizontal hydraulic conductivity agrees with previous findings from inverse modelling. Additionally, this study provides critical insights into the estimation of vertical hydraulic conductivity and an equation is formulated which relates vertical hydraulic conductivity with horizontal. Based on the approach presented, the anisotropic hydraulic conductivity of any type aquifer with embedded clayey formations can be estimated. The anisotropic hydraulic conductivity has the potential to be used as an important input to the groundwater models.     

Evaluating the effect of using artificial pore water on the quality of laboratory hydraulic conductivity measurements of peat

Pore dilation, the compaction of humic acids on peat fibres due to the process of flocculation, causes the hydraulic conductivity of peat to increase with increasing pore water electrical conductivity. This is a reversible process and a reduction in the pore water conductivity produces a decrease in the hydraulic conductivity due to the constriction of pores. We verify how this dilation and constriction of pores, resulting from the application of artificial pore water (primarily deionized water), affects laboratory measurements of the hydraulic conductivity of peat. Repeat measurements of the hydraulic conductivity were performed on samples of Sphagnum peat. It is shown that the application of deionized water during constant head permeameter tests causes a significant decrease in the hydraulic conductivity. Between tests, the hydraulic conductivity of the peat continues to decline without an associate decrease in the pore water electrical conductivity because of a lagged pore constriction effect. We suggest that the use of artificially high or low pore water electrical conductivities, during laboratory hydraulic conductivity measurements, is likely to lead to significant errors. Experimental protocols must, therefore, be revised to take better account of the pore water chemistry. The ionic concentrations of the natural pore fluid should be replicated during hydraulic conductivity tests, either by using pore fluid extracted from the study site or by artificially replicating the major ionic composition of the natural pore fluid. In addition, prior to the hydraulic conductivity measurements, peat samples should be flushed with this solution until the hydraulic conductivity stabilizes and the samples subsequently allowed to equilibrate. Copyright © 2010 John Wiley & Sons, Ltd.     

Near Surface Electrical Characterization of Hydraulic Conductivity: From Petrophysical Properties to Aquifer Geometries—A Review

This paper reviews the recent geophysical literature addressing the estimation of saturated hydraulic conductivity (K) from static low frequency electrical measurements (electrical resistivity, induced polarization (IP) and spectral induced polarization (SIP)). In the first part of this paper, research describing how petrophysical relations between electrical properties and effective (i.e. controlling fluid transport) properties of (a) the interconnected pore volumes and interconnected pore surfaces, have been exploited to estimate K at both the core and field scale is reviewed. We start with electrical resistivity measurements, which are shown to be inherently limited in K estimation as, although resistivity is sensitive to both pore volume and pore surface area properties, the two contributions cannot be separated. Efforts to utilize the unique sensitivity of IP and SIP measurements to physical parameters that describe the interconnected pore surface area are subsequently introduced and the incorporation of such data into electrical based Kozeny–Carman type models of K estimation is reviewed. In the second part of this review, efforts to invert geophysical datasets for spatial patterns of K variability (e.g. aquifer geometries) at the field-scale are considered. Inversions, based on the conversion of an image of a geophysical property to a hydrological property assuming a valid petrophysical relationship, as well as joint/constrained inversion methods, whereby multiple geophysical and hydrological data are inverted simultaneously, are briefly covered. This review demonstrates that there currently exists an opportunity to link, (1) the petrophysics relating low frequency electrical measurements to effective hydraulic properties, with (2) the joint inversion strategies developed in recent years, in order to obtain more meaningful estimates of spatial patterns of K variability than previously reported.     

AN EXERCISE IN GROUND-WATER MODEL CALIBRATION AND PREDICTION

Abstract. For a classroom exercise, nine groups of graduate students calibrated a numerical ground-water flow model to a set of perfectly observed hydraulic head data for a hypothetical phreatic aquifer. All groups used exactly the same numerical model and identical sets of observed data. After calibration, the students predicted the hydraulic head distribution in the aquifer resulting from a modification in one boundary condition. A quantitative analysis of the results of this calibration-prediction exercise vividly demonstrates some of the difficulties in parameter identification for ground-water flow models. Group predictions differed significantly. Successful prediction was strongly correlated with successful estimation of conductivity values, and was essentially unrelated to successful estimation of aquifer bottom elevations or with the number of trial-and-error simulations required for calibration. Most importantly, success in prediction was unrelated to success in matching observed heads under premodification conditions. In this sense, good calibration did not lead to good prediction.     

Comments on “Steady- and transient-state inversion in hydrogeology by successive flux estimation” by P. Pasquier and D. Marcotte

Pasquier and Marcotte [Pasquier P, Marcotte D. Steady- and transient-state inversion in hydrogeology by successive flux estimation. Adv Wat Res 2006;29:1934–52] propose some modifications to the Comparison Model Method (CMM), in order to apply it to transient 3D ground water flow data for conductivity identification. We present some remarks on that paper to improve the comprehension of the basic features of the CMM and of the real value of the novelties introduced by Pasquier and Marcotte.     

核磁共振测深方法的新进展

核磁共振测深(MRS)方法是目前唯一直接探查地下水的新方法.本文概要介绍了参加第二届核磁共振测深(MRS)国际学术研讨会的主要收获.阐述了核磁共振找水仪的研制和进展以及扩大了MRS方法的应用领域方面的情况.在应用MRS方法探测地下水取得很大成效的此基础上,我们率先用MRS方法进行了三峡滑坡监测和秦始皇陵考古工作,又取得了新成果.