Simple Hydraulic Conductivity Estimation by the Kalman Filtered Double Constraint Method

This paper presents the Kalman Filtered Double Constraint Method (DCM‐KF) as a technique to estimate the hydraulic conductivities in the grid blocks of a groundwater flow model. The DCM is based on two forward runs with the same initial grid block conductivities, but with alternating flux‐head conditions specified on parts of the boundary and the wells. These two runs are defined as: (1) the flux run, with specified fluxes (recharge and well abstractions), and (2) the head run, with specified heads (measured in piezometers). Conductivities are then estimated as the initial conductivities multiplied by the fluxes obtained from the flux run and divided by the fluxes obtained from the head run. The DCM is easy to implement in combination with existing models (e.g., MODFLOW). Sufficiently accurate conductivities are obtained after a few iterations. Because of errors in the specified head‐flux couples, repeated estimation under varying hydrological conditions results in different conductivities. A time‐independent estimate of the conductivities and their inaccuracy can be obtained by a simple linear KF with modest computational requirements. For the Kleine Nete catchment, Belgium, the DCM‐KF yields sufficiently accurate calibrated conductivities. The method also results in distinguishing regions where the head‐flux observations influence the calibration from areas where it is not able to influence the hydraulic conductivity.     

A continuum representation of fracture networks. Part II: application to the Äspö Hard Rock laboratory

A method to represent fracture networks in a continuum model is evaluated by an application to the Äspö Hard Rock Laboratory (HRL). The basic approach of the method is to first generate a fracture network, based on data from field measurements and then represent the network as grid cell conductivities, using a staggered grid arrangement. It is argued that the resulting conductivity fields capture the correlation and anisotropy structures, as well as the mean conductivity, of the rock in a realistic way. The main objective is to evaluate if the suggested method can be used in an application to a real site. The objective is formulated in three questions: ‘Can the method utilize available field data?’, ‘Can the generated fields be calibrated and conditioned?’ and ‘Are realistic distributions of pressure, flow and density obtained?’. From the application to the Äspö HRL, it is concluded that the hydraulic conductivity fields, generated by the suggested method, can utilize field data and be calibrated. It is also demonstrated that realistic distributions of pressure, flow and density can be simulated.     

Anisotropic effective conductivity in fractured rocks by explicit effective medium methods

In this work, we assess the use of explicit methods for estimating the effective conductivity of anisotropic fractured media. Explicit methods are faster and simpler to use than implicit methods but may have a more limited range of validity. Five explicit methods are considered: the Maxwell approximation, the T‐matrix method, the symmetric and asymmetric weakly self‐consistent methods, and the weakly differential method, where the two latter methods are novelly constructed in this paper. For each method, we develop simplified expressions applicable to flat spheroidal “penny‐shaped” inclusions. The simplified expressions are accurate to the first order in the ratio of fracture thickness to fracture diameter. Our analysis shows that the conductivity predictions of the methods fall within known upper and lower bounds, except for the T‐matrix method at high fracture densities and the symmetric weakly self‐consistent method when applied to very thin fractures. Comparisons with numerical results show that all the methods give reliable estimates for small fracture densities. For high fracture densities, the weakly differential method is the most accurate if the fracture geometry is non‐percolating or the fracture/matrix conductivity contrast is small. For percolating conductive fracture networks, we have developed a scaling relation that can be applied to the weakly self‐consistent methods to give conductivity estimates that are close to the results from numerical simulations.     

电缆地层测试评价井旁裂缝的有限元数值模拟方法

本文采用有限元方法模拟了电缆地层测试器的双封隔器和谐波脉冲测试方法在井旁裂缝中的压力响应.根据裂缝性储层渗流力学原理,首先模拟了双封隔器压力测试在裂缝与井壁相交和不相交两种情况下的压力响应,模拟结果表明:当裂缝与井壁相交时,压力响应随裂缝导流性质的变化发生显著改变;当裂缝与井壁不相交时,除非裂缝的导流能力非常大或离井壁非常近,否则压力响应随着裂缝导流能力的变化并不明显.说明双封隔器测试方法可以有效评价与井壁相交裂缝的导流能力,而对远离井壁的裂缝并不敏感.谐波脉冲压力测试一直被用来探测地层的各向异性,本文通过数值模拟方法探讨和分析了谐波测试方法探测和评价与井壁不相交裂缝的可行性,数值模拟结果表明谐波的压力幅度和相位延迟对裂缝的导流能力变化敏感,说明该方法可以用来评价井旁裂缝.此外,本文还对脉冲频率和双探针间距对评价效果的影响进行了分析.     

3D inverse modelling of groundwater flow at a fractured site using a stochastic continuum model with multiple statistical populations

 3D groundwater flow at the fractured site of Asp? (Sweden) is simulated. The aim was to characterise the site as adequately as possible and to provide measures on the uncertainty of the estimates. A stochastic continuum model is used to simulate both groundwater flow in the major fracture planes and in the background. However, the positions of the major fracture planes are deterministically incorporated in the model and the statistical distribution of the hydraulic conductivity is modelled by the concept of multiple statistical populations; each fracture plane is an independent statistical population. Multiple equally likely realisations are built that are conditioned to geological information on the positions of the major fracture planes, hydraulic conductivity data, steady state head data and head responses to six different interference tests. The experimental information could be reproduced closely. The results of the conditioning are analysed in terms of ensemble averaged average fracture plane conductivities, the ensemble variance of average fracture plane conductivities and the statistical distribution of the hydraulic conductivity in the fracture planes. These results are evaluated after each conditioning stage. It is found that conditioning to hydraulic head data results in an increase of the hydraulic conductivity variance while the statistical distribution of log hydraulic conductivity, initially Gaussian, becomes more skewed for many of the fracture planes in most of the realisations.     

高温高压下地幔岩和苦橄质榴辉岩的电导率实验

为了探讨地幔岩模型和苦橄质榴辉岩模型在上地幔存在的合理性,建立上地幔的电性结构,本文利用YJ-3000t紧装式六面顶压机和Solartron IS-1260阻抗/增益-相位分析仪,在1.0~4.0GPa、700~1150℃的条件下,采用交流阻抗谱法(频率范围10-1~106 Hz)分别测量了地幔岩和苦橄质榴辉岩的电导率.实验结果表明:随着温度的升高,地幔岩和苦橄质榴辉岩的电导率大幅增加;随着压力的增大,地幔岩的电导率略有增加,活化体积ΔV为-4.73cm3·mol-1,而苦橄质榴辉岩的电导率几乎没有变化,活化体积ΔV为-0.11cm3·mol-1;在电性方面,用苦橄质榴辉岩来表示深部的物质较为合理,地幔岩解释浅部可能更恰当,但浅部物质的分布不均匀,电导率随深度的变化主要受控于温度的影响,其次才是成分.     

The application of electromagnetic techniques to groundwater recharge investigations

The use of electrical methods for estimating spatial patterns of groundwater recharge was evaluated at a field site in southeastern Australia. Here, recharge increased from less than 0.2 mm year⁻¹ under native Eucalyptus vegetation, to between 1 and 14 mm year⁻¹ under dryland agriculture. This increase in recharge results in progressive leaching of salts in the soil profile. Differences in recharge can be estimated from differences in depth of leaching. The estimated recharge rates are correlated with soil texture, with higher recharge rates generally occurring through sandier soils. The relationships of recharge to salt content and soil texture both contribute to lower apparent electrical conductivities for higher recharge rates.

The effect of recharge rate on measured apparent electrical conductivities was modelled for various geophysical devices (including frequency-domain (FEM) and time-domain (TEM) electromagnetic instruments and direct current resistivity). The soil-texture effect was shown to have a greater effect than the solute leaching effect in determining the correlation between recharge and apparent electrical conductivity. Analysis of sensitivity to geological noise showed that variations in soil type below 2 m could disguise any correlation.

Correlations between recharge rate, measured at core sites from chloride tracer techniques, and apparent electrical conductivity, measured with FEM electromagnetic devices, supported the conclusions of the model. For DC resistivity and TEM methods, correlations between recharge and apparent electrical conductivity were not significant, although for resistivity this may be due partly to the small number of measurements made. The FEM device most sensitive to variations in recharge had an operating frequency of 9.8 kHz. At lower frequencies the sensitivity is reduced, as the instruments are sensing too deeply. The poor correlations for TEM, as compared with FEM, are due probably to the relatively deeper penetration of the TEM instrument used in the study, rather than any inherent differences between the techniques.

Because the major reason for the correlation between recharge and apparent electrical conductivity is soil texture, in this area the geophysical devices are mostly mapping soil type.     

Grid refinement for modeling multiphase flow in discretely fractured porous media

A study of the effects of grid discretization on the migration of DNAPL within a discrete-fracture network embedded in a porous rock matrix is presented. It is shown that an insufficiently fine discretization of the fracture elements can lead to an overprediction of the volume of DNAPL that continues to migrate vertically at the intersection of a vertical and horizontal fracture. Uniform discretization of elements at the scale of one centimetre (or less) accurately resolved the density and capillary pressure components of the head gradient in the DNAPL. An alternative, non-uniform method of discretization of elements within the discrete-fracture network is presented whereby only fracture elements immediately adjacent to fracture intersections are refined. To further limit the number of elements employed, the porous matrix elements adjacent to the fracture elements are not similarly refined. Results show this alternative method of discretization reduces the numerical error to an acceptable level, while allowing the simulation of field-scale DNAPL contamination problems. The results from two field-scale simulations of a DNAPL-contaminated carbonate bedrock site in Ontario, Canada are presented. These simulations compare different methods of grid discretization, and highlight the importance of grid refinement when simulating DNAPL migration problems in fractured porous media.     

邻近算法在微地震震源位置和一维速度模型同时反演中的应用

微地震事件的空间分布可以用来监测水力压裂过程中裂缝的发育情况.因此,震源定位是微震监测中重要的环节.震源定位依赖准确的速度模型,而震源位置和速度模型的耦合易导致线性迭代的同时反演方法陷入局部极小值.邻近算法作为一种非线性全局优化算法,能够最大程度地避免陷入局部最优解.本文将邻近算法应用于单井监测的微震定位和一维速度模型...     

Eulerian spatial moments for solute transport in three-dimensional heterogeneous,dual-permeability media

A Eulerian analytical method is developed for nonreactive solute transport in heterogeneous, dual-permeability media where the hydraulic conductivities in fracture and matrix domains are both assumed to be stochastic processes. The analytical solution for the mean concentration is given explicitly in Fourier and Laplace transforms. Instead of using the fast fourier transform method to numerically invert the solution to real space (Hu et al., 2002), we apply the general relationship between spatial moments and concentration (Naff, 1990; Hu et al., 1997) to obtain the analytical solutions for the spatial moments up to the second for a pulse input of the solute. Owing to its accuracy and efficiency, the analytical method can be used to check the semi-analytical and Monte Carlo numerical methods before they are applied to more complicated studies. The analytical method can be also used during screening studies to identify the most significant transport parameters for further analysis. In this study, the analytical results have been compared with those obtained from the semi-analytical method (Hu et al., 2002) and the comparison shows that the semi-analytical method is robust. It is clearly shown from the analytical solution that the three factors, local dispersion, conductivity variation in each domain and velocity convection flow difference in the two domains, play different roles on the solute plume spreading in longitudinal and transverse directions. The calculation results also indicate that when the log-conductivity variance in matrix is 10 times less than its counterpart in fractures, it will hardly influence the solute transport, whether the conductivity field is matrix is treated as a homogeneous or random field.     

Uncertainty propagation of arbitrary probability density functions applied to upscaling of transmissivities

In many fields of study, and certainly in hydrogeology, uncertainty propagation is a recurring subject. Usually, parametrized probability density functions (PDFs) are used to represent data uncertainty, which limits their use to particular distributions. Often, this problem is solved by Monte Carlo simulation, with the disadvantage that one needs a large number of calculations to achieve reliable results. In this paper, a method is proposed based on a piecewise linear approximation of PDFs. The uncertainty propagation with these discretized PDFs is distribution independent. The method is applied to the upscaling of transmissivity data, and carried out in two steps: the vertical upscaling of conductivity values from borehole data to aquifer scale, and the spatial interpolation of the transmissivities. The results of this first step are complete PDFs of the transmissivities at borehole locations reflecting the uncertainties of the conductivities and the layer thicknesses. The second step results in a spatially distributed transmissivity field with a complete PDF at every grid cell. We argue that the proposed method is applicable to a wide range of uncertainty propagation problems.     

Two-dimensional physical-based inversion of confined and unconfined aquifers under unknown boundary conditions

An inverse method is developed to simultaneously estimate multiple hydraulic conductivities, source/sink strengths, and boundary conditions, for two-dimensional confined and unconfined aquifers under non-pumping or pumping conditions. The method incorporates noisy observed data (hydraulic heads, groundwater fluxes, or well rates) at measurement locations. With a set of hybrid formulations, given sufficient measurement data, the method yields well-posed systems of equations that can be solved efficiently via nonlinear optimization. The solution is stable when measurement errors are increased. The method is successfully tested on problems with regular and irregular geometries, different heterogeneity patterns and variances (maximum K_max/K_min tested is 10,000), and error magnitudes. Under non-pumping conditions, when error-free observed data are used, the estimated conductivities and recharge rates are accurate within 8% of the true values. When data contain increasing errors, the estimated parameters become less accurate, as expected. For problems where the underlying parameter variation is unknown, equivalent conductivities and average recharge rates can be estimated. Under pumping (and/or injection) conditions, a hybrid formulation is developed to address these local source/sink effects, while different types of boundary conditions can also exert significant influences on drawdowns. Local grid refinement near wells is not needed to obtain accurate results, thus inversion is successful with coarse inverse grids, leading to high computation efficiency. Furthermore, flux measurements are not needed for the inversion to succeed; data requirement of the method is thus not much different from that of interpreting classic well tests. Finally, inversion accuracy is not sensitive to the degree of nonlinearity of the flow equations. Performance of the inverse method for confined and unconfined aquifer problems is similar in terms of the accuracy of the estimated parameters, the recovered head fields, and the solver speed.     

高温高压下碳酸盐熔体对地幔岩电导率的影响

为了观测含碳酸盐地幔岩部分熔融过程中电导率的变化,厘清碳酸盐熔体在金伯利岩岩浆形成过程中所起的作用,并探讨Slave克拉通中部Lac de Gras地区约80～120km深处的高导成因,我们利用DS 3600t六面顶压机和Solartron 1260阻抗/增益-相位分析仪在1.0～3.0GPa、673～1873K温压条件下分别测量了含碳酸钠(Na_2CO_3)、碳酸钙(CaCO_3)和大洋中脊玄武岩(MORB)的地幔岩样品的电导率.实验结果表明,地幔岩样品的电导率主要受到温度和组分的影响,而压力对其影响较小.在温度低于1023K时,含Na_2CO_3地幔岩样品的电导率明显高于含同比重CaCO_3和MORB的;温度达到1023K时,含Na_2CO_3地幔岩样品开始熔融;但在之后的200K温度区间内,该部分熔融样品的电导率随温度的增加几乎不发生变化.这一现象或许揭示:地幔深部的碳酸质岩浆在快速上升过程中会同化吸收岩石圈地幔中的斜方辉石(Opx),进而形成金伯利岩岩浆,期间岩浆的电导率几乎不发生变化.含CaCO_3和MORB的地幔岩样品分别在1723K和1423K开始熔融,其部分熔融样品的电导率随温度的增加而快速增加.依据前人的研究结果和我们的实验结果,我们认为可以用含碳酸盐的部分熔融样品来解释Slave克拉通中部Lac de Gras地区约80～120km深处的异常高导现象,并推测熔体中碳酸盐的熔体比例小于2wt.%.     

华北地区上地幔及过渡带电性结构研究

采用远参考道和Robust技术,处理了华北地区14个地磁台站资料,得到了相干度超过0.8的地磁测深响应函数.并将其转换为大地电磁测深的响应函数,获取了105~107 s周期范围内的视电阻率和相位.应用ρ+理论对数据进行了一致性检验和反演,结果表明417km,850km深度附近可能存在电性间断面.同时采用基于一维最光滑模型的Occam反演方法得到了300~1000km范围的地幔电性结构,并与前人在其他地区的研究结果进行了对比.发现华北地区地幔过渡带的电导率在大兴安岭—太行山重力梯度带东西两侧表现不同,重力梯度带附近及西侧台站下方过渡带深度的电导率和北美的Tucson地区相当,而华北地区东部的电导率在地幔过渡带范围高出西侧约2~5倍,这很可能和太平洋板块的俯冲有关.     

Experimental studies of electrical conductivities and P-wave velocities of gabbro at high pressures and high temperatures

The studies on the physical properties of minerals and rocks in combination with the work in petrology, mineralogy and geochemistry are not only a useful mean to look into the composition and structure of the earth抯 interior, but also can provide extreme…     

Regional changes in groundwater flow patterns and effects on groundwater composition

Wetlands on the Vecht river plain in the Netherlands are threatened by pollution of ground water on the adjacent ridge ‘Het Gooi’. To assess the impact of this pollution, information is needed on the present groundwater flow pattern and hydrochemical processes occurring during flow. In the determination of hydrochemical processes past changes in flow patterns must be taken into consideration.

Over the past 600 years impoldering and groundwater extraction have induced important hydrological changes in the study area. Exercises with a two-dimensional finite difference groundwater model were used to study the effects of these changes on regional groundwater flow patterns. Steady-state simulations along a vertical section were carried out for four different points in time, namely, the 14th century, 1885, 1941 and 1985. Changes in flow patterns are inferred from a comparison of the steady-state simulations. The results indicate that groundwater flow changed from a simple pattern under natural conditions to a complex flow pattern dominated by artificially man-controlled hydraulic heads at present.

The computer simulations are used to estimate the effect of changes in flow patterns on regional groundwater composition. Data on the distribution of chloride and oxygen-18 in ground water provide a verification of the estimated effects and information on the present position of the fresh-brackish groundwater interface in the study area. Isochrones calculated by the model are used to estimate the position of this front where data on water composition are absent. The future displacement of the fresh-brackish groundwater front is inferred from the position of successive isochrones, assuming that the present flow pattern will remain in steady state.

The computer simulations provide a general framework for the determination of hydrochemical processes in future studies addressing the impact of groundwater pollution on wetlands in the river plain.     

A test case for the simulation of three-dimensional variable-density flow and solute transport in discretely-fractured porous media

A test case has been developed for three-dimensional simulations of variable-density flow and solute transport in discretely-fractured porous media. The simulation domain is a low-permeability porous matrix cube containing a single non-planar fracture. The initial solute concentration is zero everywhere. A constant solute concentration is assigned to the top of the domain, which increases near-top fluid density and induces downward density-driven flow. The test case is therefore comparable to downwelling of a dense brine below a saline disposal basin or a waste repository. Numerous fingers and distinct convection cells develop early in the fracture but the fingers later coalesce and convection becomes less apparent. To help test other variable-density flow and transport models, results of the test case are presented both qualitatively (concentration contours and velocity fields) and quantitatively (penetration depth, mass flux, total mass stored, maximum fracture and matrix velocity).     

海城地震孕育的地球物理环境的讨论

根据海城地震余震的空间分布特征，震后地震裂缝分布和形变测量结果，结合震区的地球物理探测资料，对海城地震孕育的地球物理环境做了讨论。     

考虑海底地形的三维频率域可控源电磁响应有限体积法模拟

为了提高海洋可控源电磁的地形响应模拟精度,探讨了三维交错网格剖分有限体积法求解频率域电磁场解的数值方法.在似稳场近似条件下,推导了有限差分法和有限体积法低频电磁场控制方程的离散表达式.通过对离散表达式的分析比较表明,有限体积法较之有限差分具有更高的计算精度,同时也具有与有限差分相当的计算效率.对含地形界面网格单元电导率采用加权平均处理,通过与二维有限元程序的计算结果对比,验证了该方法可以有效提高有限体积法对地形变化的模拟精度.应用有限体积法计算了一个三维带地形储层模型的可控源电磁响应,分析表明地形变化对电场分量影响明显,磁场分量对地形变化不敏感.     

A modified Archie’s law for two conducting phases

Many types of mixing model are used widely within the earth sciences to determine the electrical properties of porous media consisting of solid and fluid phases of known conductivities, volume fractions and distributions (i.e. phase connectivities). Most models are valid for two or more conducting phases. However, of the simple models only Archie’s law includes a variable term, the Archie cementation exponent m, that describes the connectivity of the phases. Unfortunately, Archie’s law is only valid for one conducting phase distributed within a non-conducting phase, which makes it inapplicable in instances where the rock matrix has a significant conductivity such as for clay-rich rocks and in calculations involving partial melting. More complex models exist which account for multiple conducting phases and control over phase conductivity. We have adapted the conventional Archie’s law to produce a simple modified Archie’s law that can be used with two conducting phases of any conductivity and any volume fraction, while retaining the ability to model variable connectivities within those phases that result from variations in their distribution. The modified model has two exponents (m and p) that describe the connectivity of each of the two phases. The exponents are related through an equation that depends also on the volume fractions of the two phases. The modified and the conventional versions of Archie’s law have been tested on a granular analogue porous medium with a conducting matrix and a pore space saturated with a range of saline fluids with different salinities and conductivities. The new model describes the experimentally determined electrical behaviour of the system extremely well, improving greatly on the conventional Archie’s law.