Determining anisotropic transmissivity using a simplified Papadopulos method

The straight-line method presented by Papadopulos requires a minimum of three observation wells for determining the transmissivity tensor of a homogeneous and anisotropic aquifer. A simplification of this method was developed for fractured aquifers where the principal directions of the transmissivity tensor are known prior to implementation, such as when fracture patterns on outcropping portions of the aquifer may be used to infer the principal directions. This new method assumes that observation wells are drilled along the two principal directions from the pumped well, thus reducing the required number of observation wells to two. This method was applied for an aquifer test in the fractured Navajo Sandstone of southwestern Utah and yielded minimum and maximum principal transmissivity values of 70 and 1800 m(2)/d, respectively, indicating an anisotropy ratio of approximately 24 to 1.     

用梯度和感应测井联合确定地层电阻率各向异性(英文)

实际地层可能出现 2种电阻率的宏观各向异性 :微观的统计平均效应和裂缝走向等因素的构造效应。三分量感应测井方法可能是确定地层电阻率各向异性的最好方法 ,但是 ,该仪器目前在中国还没有应用。已有的数据一般是梯度和双感应曲线 ,梯度和双感应曲线单独使用都难以揭示各向异性 ,但是 ,将二者联合使用则有可能。在反演模型中考虑了电阻率各向异性的存在 ,给出了梯度和双感应曲线联合求地层电阻率各向异性的方法。通过直井水平层的二维人工模型表明 ,用感应方法可确定地层的水平电阻率和厚度。而梯度方法的视电阻率可以近似看作水平电阻率和纵向电阻率的几何平均值 ,梯度方法的视厚度是各向异性参数和真实厚度的乘积。因而不能用梯度方法单独确定各向异性参数和真实厚度 2个参数中的任何 1个。然而 ,联合梯度和双感应的方法则可能确定 3个参数 :各向异性参数 ,水平电阻率和地层厚度。人工数据的例子表明了这种联合的可行性     

IN SITU SEISMIC MEASUREMENTS OF CRACK ANISOTROPY IN THE CARBONIFEROUS LIMESTONE OF NORTHWEST ENGLAND*

Seismic velocity anisotropy is predicted for cracked rocks containing either a naturally-occurring or an artificially-induced preferred orientation of cracks. Methods developed for the study of velocity anisotropy in the uppermost mantle have been applied to the in situ measurement of P-wave velocity anisotropy in fractured Carboniferous Limestone in Northwest England. At three different sites, first-arrival travel-time data has been obtained using conventional refraction equipment and a weight-drop source. Velocity anisotropy of 15–29% is identified with directions of maximum and minimum velocities that can be broadly related to previously mapped orientations of joints.     

用梯度和感应测井联合确定地层电阻率各向异性

实际地层可能出现2种电阻率的宏观各向异性:微观的统计平均效应和裂缝走向等因素的构造效应.三分量感应测井方法可能是确定地层电阻率各向异性的最好方法,但是,该仪器目前在中国还没有应用.已有的数据一般是梯度和双感应曲线,梯度和双感应曲线单独使用都难以揭示各向异性,但是,将二者联合使用则有可能.在反演模型中考虑了电阻率各向异性的存在,给出了梯度和双感应曲线联合求地层电阻率各向异性的方法.通过直井水平层的二维人工模型表明,用感应方法可确定地层的水平电阻率和厚度.而梯度方法的视电阻率可以近似看作水平电阻率和纵向电阻率的几何平均值,梯度方法的视厚度是各向异性参数和真实厚度的乘积.因而不能用梯度方法单独确定各向异性参数和真实厚度2个参数中的任何1个.然而,联合梯度和双感应的方法则可能确定3个参数:各向异性参数,水平电阻率和地层厚度.人工数据的例子表明了这种联合的可行性.     

A case example of near-surface correction for multicomponent VSPS

A deterministic near-surface correction procedure is developed for multicomponent VSP data, shot using directional sources and recorded using three-component receivers. The method is capable of removing unwanted effects of acquisition such as unequal source strengths or misorientations, but may also remove near-surface multiples and anisotropy. This is of considerable benefit for obtaining accurate and consistent estimates of subsurface anisotropy from different source combinations. Application of the technique is illustrated using a dataset from the Romashkino reservoir in Russia, where three or four different directional sources are used at the same source locations. The technique corrects for the large discrepancies which exist between the estimates obtained using different source combinations. Application of the technique to three wells in the survey region reveals a nearly isotropic subsurface, except for a few isolated zones of moderate to high (2 to 8%) anisotropy which lie close to the expected depth for the reservoir. Although there is no significant correlation with the production figures for each well, the qS1 polarization azimuth within the reservoir does vary at each well location, suggesting that this may be a more sensitive indicator of reservoir Drocess.     

On occurrence of point singularities in orthorhombic media

Degeneracies of the slowness surfaces of shear (and compressional) waves in low-symmetry anisotropic media (such as orthorhombic), known as point singularities, pose difficulties during modelling and inversion, but can be potentially used in the latter as model parameter constraints. I analyse the quantity and spatial arrangement of point singularities in orthorhombic media, as well as their relation to the overall strength of velocity anisotropy. A classification scheme based on the number and spatial distribution of singularity directions is proposed. In normal orthorhombic models (where the principal shear moduli are smaller than the principal compressional moduli), point singularities can only be arranged in three distinct patterns, and media with the theoretical minimum (0) and maximum (16) number of singularities are not possible. In orthorhombic models resulting from embedding vertical fractures in transversely isotropic background, only two singularity distributions are possible, in contrast to what was previously thought. Although the total number of singularities is independent of the overall anisotropy strength, for general (non-normal) orthorhombic models, different spatial distributions of singularities become more probable with increasing magnitude of anisotropy.     

Analysis and application of the response characteristics of DLL and LWD resistivity in horizontal well

There exist different response characteristics in the resistivity measurements of dual laterolog (DLL) and logging while drilling (LWD) electromagnetic wave propagation logging in highly deviated and horizontal wells due to the difference in their measuring principles. In this study, we first use the integral equation method simulated the response characteristics of LWD resistivity and use the three dimensional finite element method (3D-FEM) simulated the response characteristics of DLL resistivity in horizontal wells, and then analyzed the response differences between the DLL and LWD resistivity. The comparative analysis indicated that the response differences may be caused by different factors such as differences in the angle of instrument inclination, anisotropy, formation interface, and mud intrusion. In the interface, the curves of the LWD resistivity become sharp with increases in the deviation while those of the DLL resistivity gradually become smooth. Both curves are affected by the anisotropy although the effect on DLL resistivity is lower than the LWD resistivity. These differences aid in providing a reasonable explanation in the horizontal well. However, this can also simultaneously lead to false results. At the end of the study, we explain the effects of the differences in the interpretation of the horizontal well based on the results and actual data analysis.     

Multiobjective fuzzy optimization for sustainable groundwater management using particle swarm optimization and analytic element method

Groundwater management involves conflicting objectives as maximization of discharge contradicts the criteria of minimum pumping cost and minimum piping cost. In addition, available data contains uncertainties such as market fluctuations, variations in water levels of wells and variations of ground water policies. A fuzzy model is to be evolved to tackle the uncertainties, and a multiobjective optimization is to be conducted to simultaneously satisfy the contradicting objectives. Towards this end, a multiobjective fuzzy optimization model is evolved. To get at the upper and lower bounds of the individual objectives, particle Swarm optimization (PSO) is adopted. The analytic element method (AEM) is employed to obtain the operating potentio metric head. In this study, a multiobjective fuzzy optimization model considering three conflicting objectives is developed using PSO and AEM methods for obtaining a sustainable groundwater management policy. The developed model is applied to a case study, and it is demonstrated that the compromise solution satisfies all the objectives with adequate levels of satisfaction. Sensitivity analysis is carried out by varying the parameters, and it is shown that the effect of any such variation is quite significant. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of uneven noise source and/or station distribution on estimating the azimuth anisotropy of surface waves

With the development of the dense array, the surface wave velocity and azimuthal anisotropy under the array can be directly obtained by beamforming the noise cross-correlation functions (NCFs). However, the retrieval of the Green's function by cross-correlating the seismic noise requires that the noise source has a uniform distribution. For the case with uneven noise source, the azimuthal dependence on the sources in the expression for the spatial coherence function, which corresponds to the NCF in the time domain, has the same form as the azimuthal dependence of the surface wave velocity in weakly anisotropic media. Therefore, the uneven noise source will affect the surface wave anisotropy extraction. In this study, three passive seismic methods, i.e., beamforming, SPAC (spatial autocorrelation), and NCF, are compared to demonstrate that an uneven source distribution and uneven station distribution have equivalent effects on the outcome from each method. A beamforming method is proposed to directly extract the velocity and azimuthal anisotropy of surface waves. The effect of uneven noise source and/or station distribution on estimating the azimuth anisotropy of surface waves was investigated using data from the ChinArray Phase II. A method for correcting the apparent anisotropy in beamforming results caused by an uneven station distribution is suggested.     

On using simple time-of-travel capture zone delineation methods

As part of its Wellhead Protection Program, the U.S. EPA mandates the delineation of "time-of-travel capture zones" as the basis for the definition of wellhead protection zones surrounding drinking water production wells. Depending on circumstances the capture zones may be determined using methods that range from simply drawing a circle around the well to sophisticated ground water flow and transport modeling. The simpler methods are attractive when faced with the delineation of hundreds or thousands of capture zones for small public drinking water supply wells. On the other hand, a circular capture zone may not be adequate in the presence of an ambient ground water flow regime. A dimensionless time-of-travel parameter T is used to determine when calculated fixed-radius capture zones can be used for drinking water production wells. The parameter incorporates aquifer properties, the magnitude of the ambient ground water flow field, and the travel time criterion for the time-of-travel capture zone. In the absence of interfering flow features, three different simple capture zones can be used depending on the value of T . A modified calculated fixed-radius capture zone proves protective when T < 0.1, while a more elongated capture zone must be used when T > 1. For values of T between 0.1 and 1, a circular capture zone can be used that is eccentric with respect to the well. Finally, calculating T allows for a quick assessment of the validity of circular capture zones without redoing the delineation with a computer model.     

Estimating azimuthal stress‐induced P‐wave anisotropy from S‐wave anisotropy using sonic log or vertical seismic profile data

Most sedimentary rocks are anisotropic, yet it is often difficult to accurately incorporate anisotropy into seismic workflows because analysis of anisotropy requires knowledge of a number of parameters that are difficult to estimate from standard seismic data. In this study, we provide a methodology to infer azimuthal P‐wave anisotropy from S‐wave anisotropy calculated from log or vertical seismic profile data. This methodology involves a number of steps. First, we compute the azimuthal P‐wave anisotropy in the dry medium as a function of the azimuthal S‐wave anisotropy using a rock physics model, which accounts for the stress dependency of seismic wave velocities in dry isotropic elastic media subjected to triaxial compression. Once the P‐wave anisotropy in the dry medium is known, we use the anisotropic Gassmann equations to estimate the anisotropy of the saturated medium. We test this workflow on the log data acquired in the North West Shelf of Australia, where azimuthal anisotropy is likely caused by large differences between minimum and maximum horizontal stresses. The obtained results are compared to azimuthal P‐wave anisotropy obtained via orthorhombic tomography in the same area. In the clean sandstone layers, anisotropy parameters obtained by both methods are fairly consistent. In the shale and shaly sandstone layers, however, there is a significant discrepancy between results since the stress‐induced anisotropy model we use is not applicable to rocks exhibiting intrinsic anisotropy. This methodology could be useful for building the initial anisotropic velocity model for imaging, which is to be refined through migration velocity analysis.     

Analysis of Transient Flow to an Extended Fully Penetrating Well at Constant-Head Pumping

Vertical wells with radial extension at the well bottom can improve the rate of water production. No study has yet investigated the effects of the transient state and anisotropy in directional hydraulic conductivities on the wellbore flux rate for this type of well. This study derives a semianalytical transient drawdown solution for constant-head pumping at a fully penetrating well radially extended at the bottom of a confined, anisotropic aquifer by applying Laplace transform and separation of variables as well as conducting a Fourier analysis. The results of this new solution indicate that transient and steady-state wellbore flux rates can be increased by a factor of two for greater radial extension of the well. Compared with an isotropic aquifer (a ratio of vertical and horizontal hydraulic conductivities equal to one), an anisotropic aquifer with the ratio less than one may produce a higher transient wellbore flux rate and lower steady-state wellbore flux rate. Moreover, the time required to achieve the steady-state wellbore flux rate can be substantially affected by anisotropy of the aquifer.     

直达Ps与接收函数Ps联合分析地壳各向异性

本文尝试直接利用地震图记录中的Ps转换波,而非传统的接收函数方法,检测地壳介质的各向异性.虽然远震记录中的P波对Ps转换波会有干扰,但P波与Ps转换波具有不同的偏振特性,最小能量法可以将Ps转换波的各向异性参数检测出来,对时间窗的选择也很强壮.本文利用IC台网（New China Digital Seismograph Network,中国新数字地震台网）中的KMI,ENH,LSA,BJT,XAN,WMQ六个台站接收的宽频远震记录进行了测试,并且对比了接收函数方法的结果.研究表明,利用最小能量法直接测量与利用旋转相关法测量接收函数中Ps转换波的结果基本一致.两种方法测量所得的快波偏振方向与地壳运动方向,最大水平主压应力方向,震源机制解压缩轴方向,最大主压应变率方向以及已有的各向异性研究结果基本一致.     

随钻方位电磁波测井多参数快速反演

大斜度井/水平井随钻测井技术已被广泛的应用于各种复杂油气藏中,但传统随钻电磁波测井仅提供仪器轴向磁场分量,井斜和各向异性对测井响应影响耦合在一起,难以剥离,无法基于反演同时获取多个参数,进行相应的地层评价,且不能提供方位信息,难以实现地质导向功能.随钻方位电磁波测井在提供仪器轴向磁场分量的基础上,还提供了仪器横向磁场分量,其提取的地质导向信号,对地层界面非常敏感,受井斜、地层电阻率对比度和各向异性影响弱,可以反演得到准确的界面位置.此外,额外的磁场分量信息,有效降低了井斜与各向异性的耦合程度,可基于反演算法实现多参数联合反演,满足电阻率测井精细解释评价需求.     

A Finite Layer Formulation for Groundwater Flow to Horizontal Wells

A finite layer approach for the general problem of three‐dimensional (3D) flow to horizontal wells in multilayered aquifer systems is presented, in which the unconfined flow can be taken into account. The flow is approximated by an integration of the standard finite element method in vertical direction and the analytical techniques in the other spatial directions. Because only the vertical discretization is involved, the horizontal wells can be completely contained in one specific nodal plane without discretization. Moreover, due to the analytical eigenfunctions introduced in the formulation, the weighted residual equations can be decoupled, and the formulas for the global matrices and flow vector corresponding to horizontal wells can be obtained explicitly. Consequently, the bandwidth of the global matrices and computational cost rising from 3D analysis can be significantly reduced. Two comparisons to the existing solutions are made to verify the validity of the formulation, including transient flow to horizontal wells in confined and unconfined aquifers. Furthermore, an additional numerical application to horizontal wells in three‐layered systems is presented to demonstrate the applicability of the present method in modeling flow in more complex aquifer systems.     

一种裂缝流体因子的提出及应用

为了解决各向异性下的流体识别问题,将纵波各向异性裂缝预测以及Russell的流体因子融合到直角坐标系中,提出了一种能够同时检测裂缝发育情况以及流体性质的新的裂缝流体因子(Factor of Fluid-filled Fracture,FFF),并通过一组岩性参数检验了裂缝流体因子在裂缝预测及流体识别中的有效性.在理论研究的基础上,选取松辽盆地某地区的火成岩裂缝及流体识别研究为应用实例.通过与测井流体及裂缝信息的对比验证,裂缝流体因子能够较为准确地预测研究区裂缝和流体的分布情况,且裂缝流体因子在单井上的计算结果与单井含气饱和度吻合度较高.此外,根据实际应用效果,指出裂缝流体因子在应用中的局限性:裂缝流体因子在平面成图时受地层厚度影响较大,且无法预测裂缝方向.     

Study on the simulation of acoustic logging measurements in horizontal and deviated wells

The conventional acoustic logging interpretation method, which is based on vertical wells that penetrate isotropic formations, is not suitable for horizontal and deviated wells penetrating anisotropic formations. This unsuitability is because during horizontal and deviated well drilling, cuttings will splash on the well wall or fall into the borehole bottom and form a thin bed of cuttings. In addition, the high velocity layers at different depths and intrinsic anisotropy may affect acoustic logging measurements. In this study, we examine how these factors affect the acoustic wave slowness measured in horizontal and deviated wells that are surrounded by an anisotropic medium using numerical simulation. We use the staggered-grid finite difference method in time domain (FDTD) combined with hybrid-PML. First, we acquire the acoustic slowness using a simulated array logging system, and then, we analyze how various factors affect acoustic slowness measurements and the differences between the effects of these factors. The factors considered are high-velocity layers, thin beds of cuttings, dipping angle, formation thickness, and anisotropy. The simulation results show that these factors affect acoustic wave slowness measurements differently. We observe that when the wavelength is much smaller than the distance between the borehole wall and high velocity layer, the true slowness of the formation could be acquired. When the wavelengths are of the same order (i.e., in the near-field scenarios), the geometrical acoustics theory is no longer applicable. Furthermore, when a thin bed of cuttings exists at the bottom of the borehole, Fermat's principle is still applicable, and true slowness can be acquired. In anisotropic formations, the measured slowness changes with increments in the dipping angle. Finally, for a measurement system with specific spacing, the slowness of a thin target layer can be acquired when the distance covered by the logging tool is sufficiently long. Based on systematical simulations with different dipping angles and anisotropy in homogenous TI media, slowness estimation charts are established to quantitatively determine the slowness at any dipping angle and for any value of the anisotropic ratio. Synthetic examples with different acoustic logging tools and different elastic parameters demonstrate that the acoustic slowness estimation method can be conveniently applied to horizontal and deviated wells in TI formations with high accuracy.     

Multilayer analytic element modeling of radial collector wells

A new multilayer approach is presented for the modeling of ground water flow to radial collector wells. The approach allows for the inclusion of all aspects of the unique boundary condition along the lateral arms of a collector well, including skin effect and internal friction losses due to flow in the arms. The hydraulic conductivity may differ between horizontal layers within the aquifer, and vertical anisotropy can be taken into account. The approach is based on the multilayer analytic element method, such that regional flow and local three-dimensional detail may be simulated simultaneously and accurately within one regional model. Horizontal flow inside a layer is computed analytically, while vertical flow is approximated with a standard finite-difference scheme. Results obtained with the proposed approach compare well to results obtained with three-dimensional analytic element solutions for flow in unconfined aquifers. The presented approach may be applied to predict the yield of a collector well in a regional setting and to compute the origin and residence time, and thus the quality, of water pumped by the collector well. As an example, the addition of three lateral arms to a collector well that already has three laterals is investigated. The new arms are added at an elevation of 2 m above the existing laterals. The yield increase of the collector well is computed as a function of the lengths of the three new arms.     

横波各向异性在裂缝和应力分析中的应用

针对裂缝性和低孔低渗地层的横波各向异性特征,反演得到横波各向异性参数,研究了裂缝的发育程度、方位和有效性,并对低孔低渗地层的应力场分布状态和方位进行了综合评价;通过对反演得到的快、慢弯曲波形进行频散分析以及计算单极横波各向异性大小,确定了引起横波各向异性的原因,并结合常规测井资料、岩心及FMI成像资料对分析结果进行了验证和对比,最后对研究区8口典型井的横波各向异性进行了综合处理和评价,得到了该区的横波各向异性特征以及和总的应力场走向.结果表明,利用横波的各向异性参数可以有效的评价裂缝的发育程度、走向及有效性,并能准确的确定地应力分布状态和最大水平应力方位.     

Estimating the Horizontal Gradient in Heterogeneous, Unconfined Aquifers: Comparison of Three-Point Schemes

At least two approaches may be used to estimate the horizontal components of the hydraulic gradient based on measured heads from three observation points. First, the gradient may be estimated by passing a plane through the measured heads (h-method). Second, if the elevation of the base of the aquifer is known to be spatially constant, an estimate of the gradient may be obtained using the squares of the measured heads (h²- method). In the present study, these methods are examined in application to a heterogeneous system. Using Monte Carlo analysis, we demonstrate that the magnitude of the gradient estimated via the h-method involved significant bias, which increased when the distance separating the wells increased. In contrast, bias in the estimated magnitude of the gradient based on the h²-method decreased with increasing separation among the wells. Estimation variances for both the magnitude and orientation of the gradient also decreased with separation distance. The variance in the orientation was observed to remain relatively high, however, even at relatively large separations among the wells (e.g., 10 integral scales). These results are Interpreted as implying that the best estimate of the gradient for steady flow in an unconfined aquifer is derived from the h²- method with the wells separated by significant distances. These results also demonstrate the uncertainty inherent in estimating the gradient based on limited field data.